Question: in covering a distance of 30 km , arun takes 22 hours more than anil . if arun doubles his speed , then he would take 1 hour less than anil . what is arun ' s speed ?

<gadget id="calculator">1 + 2</gadget>
<output>3</output>

<gadget id="calculator">3 * 2</gadget>
<output>6</output>

<gadget id="calculator">30 / 6</gadget>
<output>5</output>
<result>5</result>

Choices:
A. 8 kmph
B. 5 kmph
C. 4 kmph
D. 7 kmph
E. 9 kmph

divide(30, multiply(add(1, const_2), const_2))

Explanation: explanation : if arun doubles his speed , he needs 3 hour less . double speed means half time . hence , half of the time required by arun to cover 30 km = 3 hour i . e . , time required by arun to cover 30 km = 6 hour arun ' s speed = 30 / 6 = 5 kmph answer is b


Question: in the new budget the price of wheat rose by 8 % . by how much percent must a person reduce his consumption so that his expenditure on it does not increase ?

<gadget id="calculator">8 / 100</gadget>
<output>2/25 = around 0.08</output>

<gadget id="calculator">(2/25) + 1</gadget>
<output>27/25 = around 1.08</output>

<gadget id="calculator">(2/25) / (27/25)</gadget>
<output>2/27 = around 0.074074</output>

<gadget id="calculator">(2/27) * 100</gadget>
<output>200/27 = around 7.407407</output>
<result>200/27 = around 7.407407</result>

Choices:
A. 7.5 %
B. 7.41 %
C. 10.9 %
D. 12.6 %
E. 15 %

multiply(divide(divide(8, const_100), add(divide(8, const_100), const_1)), const_100)

Explanation: reduce in consumption = r / ( 100 + r ) * 100 % = 8 / 108 * 100 = 7.41 % answer is b


Question: find the length of the wire required to go 12 times round a square field containing 104976 m 2 .

<gadget id="calculator">104_976 ** (1/2)</gadget>
<output>324</output>

<gadget id="calculator">4 * 324</gadget>
<output>1_296</output>

<gadget id="calculator">1_296 * 12</gadget>
<output>15_552</output>
<result>15_552</result>

Choices:
A. 15840
B. 3388
C. 2667
D. 8766
E. 15552

Explanation: "a 2 = 104976 = > a = 324 4 a = 1296 1296 * 12 = 15552 answer : e"


Question: a , b and c started a business with a total investment of rs . 72000 . a invests rs . 6000 more than b and b invests rs . 3000 less than c . if the total profit at the end of a year is rs . 8640 , find a ' s share .

<gadget id="calculator">6_000 + 3_000</gadget>
<output>9_000</output>

<gadget id="calculator">72_000 - 9_000</gadget>
<output>63_000</output>

<gadget id="calculator">63_000 / 3</gadget>
<output>21_000</output>

<gadget id="calculator">21_000 + 6_000</gadget>
<output>27_000</output>

<gadget id="calculator">27_000 / 72_000</gadget>
<output>3/8 = around 0.375</output>

<gadget id="calculator">8_640 * (3/8)</gadget>
<output>3_240</output>
<result>3_240</result>

Choices:
A. rs . 3240
B. rs . 2520
C. rs . 2880
D. rs . 3360
E. none of these

Explanation: explanation : let c ' s investment = rs . x b ' s investment = rs . ( x - 3000 ) a ' s investment = rs . ( x - 3000 + 6000 ) = rs . ( x + 3000 ) now , ( a + b + c ) ' s investment = rs . 72000 = > x + ( x - 3000 ) + ( x + 3000 ) = 72000 = > 3 x = 72000 = > x = 24000 hence , a ' s investment = rs . 27000 b ' s investment = rs . 21000 c ' s investment = rs . 24000 ratio of the capitals of a , b and c = 27000 : 21000 : 24000 = 9 : 7 : 8 a ' s share = rs . [ ( 9 / 24 ) × 8640 ] = rs . 3240 answer : option a


Question: a certain list consists of 21 different numbers . if n is in the list and n is 4 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction e of the sum of the 21 numbers in the list ?

<gadget id="calculator">1 * 1</gadget>
<output>1</output>

<gadget id="calculator">20 / 4</gadget>
<output>5</output>

<gadget id="calculator">5 + 21</gadget>
<output>26</output>

<gadget id="calculator">26 / 4</gadget>
<output>13/2 = around 6.5</output>

<gadget id="calculator">(13/2) * 2</gadget>
<output>13</output>

<gadget id="calculator">13 - 4</gadget>
<output>9</output>

<gadget id="calculator">9 - 3</gadget>
<output>6</output>

<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<result>1/6 = around 0.166667</result>

Choices:
A. 1 / 20
B. 1 / 6
C. 1 / 5
D. 4 / 21
E. 5 / 21

divide(multiply(const_1, const_1), subtract(subtract(multiply(divide(add(divide(20, 4), 21), 4), const_2), 4), const_3))

Explanation: "this is how i used to calculate which i think works pretty well : if you let the average of the 20 other numbers equal a , can you write this equation for sum of the list ( s ) n + 20 a = s the question tells us that n = 4 a plug this back into the first equation and you get that the sum is 24 a 4 a + 20 a = 24 a therefore fraction e of n to the total would be 4 a / 24 a or 1 / 6 answer b"


Question: the s . i . on a certain sum of money for 5 years at 6 % per annum is half the c . i . on rs . 3000 for 2 years at 15 % per annum . the sum placed on s . i . is ?

<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>

<gadget id="calculator">1 + (3/20)</gadget>
<output>23/20 = around 1.15</output>

<gadget id="calculator">(23/20) ** 2</gadget>
<output>529/400 = around 1.3225</output>

<gadget id="calculator">3_000 * (529/400)</gadget>
<output>7_935/2 = around 3_967.5</output>

<gadget id="calculator">(7_935/2) - 3_000</gadget>
<output>1_935/2 = around 967.5</output>

<gadget id="calculator">(1_935/2) / 2</gadget>
<output>1_935/4 = around 483.75</output>

<gadget id="calculator">6 / 100</gadget>
<output>3/50 = around 0.06</output>

<gadget id="calculator">5 * (3/50)</gadget>
<output>3/10 = around 0.3</output>

<gadget id="calculator">(1_935/4) / (3/10)</gadget>
<output>3_225/2 = around 1_612.5</output>
<result>3_225/2 = around 1_612.5</result>

Choices:
A. 1525.2
B. 1256.3
C. 1612.5
D. 1548.5
E. 1254.5

divide(divide(subtract(multiply(3000, power(add(const_1, divide(15, const_100)), 2)), 3000), const_2), multiply(5, divide(6, const_100)))

Explanation: c . i . = [ 3000 * ( 1 + 15 / 100 ) 2 - 3000 ] = ( 3000 * 23 / 20 * 23 / 20 - 3000 ) = rs . 967.5 . sum = ( 483.75 * 100 ) / ( 5 * 6 ) = rs . 1612.5 answer : c


Question: what is rate of interest if principal . amount be 400 , simple interest 80 and time 2 year .

<gadget id="calculator">400 * 2</gadget>
<output>800</output>

<gadget id="calculator">80 / 800</gadget>
<output>1/10 = around 0.1</output>

<gadget id="calculator">(1/10) * 100</gadget>
<output>10</output>
<result>10</result>

Choices:
A. 10
B. 12.5
C. 25
D. 12
E. 14.5

multiply(divide(80, multiply(400, 2)), const_100)

Explanation: "s . i = ( p * r * t ) / 100 80 = 800 r / 100 r = 80 / 8 = 10 % answer a"


Question: if 0.20 : x : : 4 : 2 , then x is equal to

<gadget id="calculator">0.2 * 2</gadget>
<output>0.4</output>

<gadget id="calculator">0.4 / 4</gadget>
<output>0.1</output>
<result>0.1</result>

Choices:
A. 0.2
B. 0.3
C. 0.1
D. 0.5
E. none

Explanation: "sol . ( x × 4 ) = ( 0.20 × 2 ) ⇒ x = 0.4 / 4 = 0.1 . answer c"


Question: along a yard 225 metres long , 26 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between two consecutive trees

<gadget id="calculator">26 - 1</gadget>
<output>25</output>

<gadget id="calculator">225 / 25</gadget>
<output>9</output>
<result>9</result>

Choices:
A. 8
B. 9
C. 10
D. 11
E. 12

Explanation: "explanation : 26 trees have 25 gaps between them , required distance ( 225 / 25 ) = 10 option b"


Question: a retailer marks her goods in such a way that the profit made by selling 50 articles is equal to the selling price of 20 articles . what is the percentage of profit made by the retailer ?

<gadget id="calculator">50 - 20</gadget>
<output>30</output>

<gadget id="calculator">50 / 30</gadget>
<output>5/3 = around 1.666667</output>

<gadget id="calculator">(5/3) - 1</gadget>
<output>2/3 = around 0.666667</output>

<gadget id="calculator">(2/3) * 100</gadget>
<output>200/3 = around 66.666667</output>
<result>200/3 = around 66.666667</result>

Choices:
A. 66.67 %
B. 33.33 %
C. 40 %
D. 25 %
E. 20 %

multiply(subtract(divide(50, subtract(50, 20)), const_1), const_100)

Explanation: let cost price = x profit = y selling price = x + y 50 y = 20 ( x + y ) 30 y = 20 x percentage profit = y / x ∗ 100 = 20 / 30 ∗ 100 = 66.667 answer = a


Question: a basket contains 10 apples , of which 1 is spoiled and the rest are good . if we select 2 apples from the basket simultaneously and at random , what is the probability that the 2 apples selected will include the spoiled apple ?

<gadget id="calculator">10 - 1</gadget>
<output>9</output>

<gadget id="calculator">binomial(9, 1)</gadget>
<output>9</output>

<gadget id="calculator">binomial(10, 2)</gadget>
<output>45</output>

<gadget id="calculator">9 / 45</gadget>
<output>1/5 = around 0.2</output>
<result>1/5 = around 0.2</result>

Choices:
A. 2 / 9
B. 3 / 8
C. 2 / 7
D. 1 / 6
E. 1 / 5

divide(choose(subtract(10, 1), 1), choose(10, 2))

Explanation: "the total number of ways to choose 2 apples is 10 c 2 = 45 the number of ways that include the spoiled apple is 9 c 1 = 9 p ( the spoiled apple is included ) = 9 / 45 = 1 / 5 the answer is e ."


Question: s is a set of 85 consecutive multiples of 5 . if the smallest number in s is 90 , then the greatest number in s is

<gadget id="calculator">85 - 1</gadget>
<output>84</output>

<gadget id="calculator">84 * 5</gadget>
<output>420</output>

<gadget id="calculator">90 + 420</gadget>
<output>510</output>
<result>510</result>

Choices:
A. 158
B. 597
C. 599
D. 402
E. 510

add(90, multiply(subtract(85, const_1), 5))

Explanation: "last term = first term + ( total no . of terms - 1 ) consecutive difference s is a set of 85 consecutive multiples of 5 . if the smallest number in s is 90 , then the greatest number in s is first term = 90 ; total terms = 85 ; difference = 5 90 + ( 84 ) 5 = 510 ans e"


Question: a gardener grows cabbages in her garden that is in the shape of a square . each cabbage takes 1 square feet of area in her garden . this year , she has increased her output by 191 cabbages as compared to last year . the shape of the area used for growing the cabbages has remained a square in both these years . how many cabbages did she produce this year ?

<gadget id="calculator">191 / 2</gadget>
<output>191/2 = around 95.5</output>

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">(1/4) + (1/4)</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">(191/2) + (1/2)</gadget>
<output>96</output>

<gadget id="calculator">96 ** 2</gadget>
<output>9_216</output>
<result>9_216</result>

Choices:
A. 7,251
B. 8406
C. 9216
D. 10,348
E. can not be determined

power(add(divide(191, const_2), add(const_0_25, const_0_25)), const_2)

Explanation: "let the side for growing cabbages this year be x ft . thus the area is x ^ 2 . let the side for growing cabbages last year be y ft . thus , the area was y ^ 2 . the area would have increased by 191 sq ft as each cabbage takes 1 sq ft space . x ^ 2 - y ^ 2 = 191 ( x + y ) ( x - y ) = 191 191 is a prime number and thus it will be ( 96 + 95 ) * ( 96 - 95 ) . thus x = 96 and y = 95 x ^ 2 = 96 ^ 2 = 9216 the answer is c ."


Question: a and b began business with rs . 3000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000 more . at the end of the year , their profits amounted to rs . 630 find the share of a .

<gadget id="calculator">3_000 * 8</gadget>
<output>24_000</output>

<gadget id="calculator">3_000 - 1_000</gadget>
<output>2_000</output>

<gadget id="calculator">12 - 8</gadget>
<output>4</output>

<gadget id="calculator">2_000 * 4</gadget>
<output>8_000</output>

<gadget id="calculator">24_000 + 8_000</gadget>
<output>32_000</output>

<gadget id="calculator">4_000 * 8</gadget>
<output>32_000</output>

<gadget id="calculator">4_000 + 1_000</gadget>
<output>5_000</output>

<gadget id="calculator">5_000 * 4</gadget>
<output>20_000</output>

<gadget id="calculator">32_000 + 20_000</gadget>
<output>52_000</output>

<gadget id="calculator">32_000 + 52_000</gadget>
<output>84_000</output>

<gadget id="calculator">630 / 84_000</gadget>
<output>3/400 = around 0.0075</output>

<gadget id="calculator">(3/400) * 32_000</gadget>
<output>240</output>
<result>240</result>

Choices:
A. 240
B. 288
C. 277
D. 877
E. 361

multiply(divide(630, add(add(multiply(3000, 8), multiply(subtract(3000, 1000), subtract(const_12, 8))), add(multiply(4000, 8), multiply(add(4000, 1000), subtract(const_12, 8))))), add(multiply(3000, 8), multiply(subtract(3000, 1000), subtract(const_12, 8))))

Explanation: "( 3 * 8 + 2 * 4 ) : ( 4 * 8 + 5 * 4 ) 8 : 13 8 / 21 * 630 = 240 answer : a"


Question: on a certain day , tim invested $ 1,000 at 10 percent annual interest , compounded annually , and lana invested 2,000 at 5 percent annual interest , compounded annually . the total amount of interest earned by tim ’ s investment in the first 2 years was how much greater than the total amount of interest earned by lana ’ s investment in the first 2 years ?

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>

<gadget id="calculator">1 + (1/10)</gadget>
<output>11/10 = around 1.1</output>

<gadget id="calculator">(11/10) ** 2</gadget>
<output>121/100 = around 1.21</output>

<gadget id="calculator">1_000 * (121/100)</gadget>
<output>1_210</output>

<gadget id="calculator">1_210 - 1_000</gadget>
<output>210</output>

<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>

<gadget id="calculator">1 + (1/20)</gadget>
<output>21/20 = around 1.05</output>

<gadget id="calculator">(21/20) ** 2</gadget>
<output>441/400 = around 1.1025</output>

<gadget id="calculator">(441/400) * 2_000</gadget>
<output>2_205</output>

<gadget id="calculator">2_205 - 2_000</gadget>
<output>205</output>

<gadget id="calculator">210 - 205</gadget>
<output>5</output>
<result>5</result>

Choices:
A. $ 5
B. $ 15
C. $ 50
D. $ 100
E. $ 105

subtract(subtract(multiply(1,000, power(add(const_1, divide(10, const_100)), 2)), 1,000), subtract(multiply(power(add(const_1, divide(5, const_100)), 2), 2,000), 2,000))

Explanation: "compounded annually means that the interest is applied once per year . one can have 10 % annual interest compounded monthly - in this case 10 % / 12 would be applied each month , or 10 % annual interest compounded daily etc . with respect to the problem at hand , at the end of two years , tim would have 1,000 ( 1.10 ) ^ 2 = 1,000 ( 1.21 ) = 1,210 and lana would have 2,000 ( 1.05 ) ^ 2 = 2,000 ( 1.1025 ) = 2,205 thus , tim earned 210 dollars , while lana earned 205 dollars the difference is $ 5 and the answer is a ."


Question: what is the angle between the minute and the hour hand of the clock which shows 12 : 24 ?

<gadget id="calculator">3 * 2</gadget>
<output>6</output>

<gadget id="calculator">24 * 6</gadget>
<output>144</output>

<gadget id="calculator">144 - 12</gadget>
<output>132</output>
<result>132</result>

Choices:
A. 115
B. 120
C. 124
D. 130
E. 132

subtract(multiply(24, multiply(const_3, const_2)), 12)

Explanation: at 12 : 24 - minute hand will be at 24 * 6 = 144 degrees from position of 12 . - hour hand will move by 2 * 6 = 12 degree during the same time so the difference between the two hands will be 144 - 12 = 132 degrees . answer : e


Question: find the value of ( 70 + 28 / 100 ) × 100

<gadget id="calculator">28 / 100</gadget>
<output>7/25 = around 0.28</output>

<gadget id="calculator">(7/25) + 70</gadget>
<output>1_757/25 = around 70.28</output>

<gadget id="calculator">(1_757/25) * 100</gadget>
<output>7_028</output>
<result>7_028</result>

Choices:
A. 7028
B. 4028
C. 3128
D. 3256
E. 5264

multiply(add(divide(28, 100), 70), const_100)

Explanation: ( 7000 + 28 ) / 100 * 100 = 7028 answer : a


Question: a train with 120 wagons crosses john who is going in the same direction , in 36 seconds . it travels for half an hour from the time it starts ove ( who is also riding on his horse ) coming from the opposite direction in 24 seconds . in how much time after the train has crossed the mike do the john meets to mike ? rtaking the john ( he is riding on the horse ) before it starts overtaking the mike

<gadget id="calculator">36 + 24</gadget>
<output>60</output>

<gadget id="calculator">36 - 24</gadget>
<output>12</output>

<gadget id="calculator">60 / 12</gadget>
<output>5</output>

<gadget id="calculator">5 - 1</gadget>
<output>4</output>

<gadget id="calculator">10 * 3</gadget>
<output>30</output>

<gadget id="calculator">30 * 60</gadget>
<output>1_800</output>

<gadget id="calculator">4 * 1_800</gadget>
<output>7_200</output>

<gadget id="calculator">7_200 / 2</gadget>
<output>3_600</output>

<gadget id="calculator">3_600 - 24</gadget>
<output>3_576</output>
<result>3_576</result>

Choices:
A. 2534
B. 3545
C. 3521
D. 4564
E. 3576

subtract(divide(multiply(subtract(divide(add(36, 24), subtract(36, 24)), const_1), multiply(multiply(const_10, const_3), const_60)), const_2), 24)

Explanation: let the length of the train be l metres and speeds of the train arun and sriram be r , a and s respectively , then - - - - - - - - - - ( i ) and - - - - - - - - - ( ii ) from eq . ( i ) and ( ii ) 3 ( r - a ) = 2 ( r + k ) r = 3 a + 2 k in 30 minutes ( i . e 1800 seconds ) , the train covers 1800 r ( distance ) but the arun also covers 1800 a ( distance ) in the same time . therefore distance between arun and sriram , when the train has just crossed sriram = 1800 ( r - a ) - 24 ( a + k ) time required = = ( 3600 - 24 ) = 3576 s e


Question: the ratio of the length and the width of a rectangle is 4 : 3 and the area of the rectangle is 5808 sq cm . what is the ratio of the width and the area of the rectangle ?

<gadget id="calculator">3 * 5_808</gadget>
<output>17_424</output>

<gadget id="calculator">17_424 ** (1/2)</gadget>
<output>132</output>

<gadget id="calculator">132 / 2</gadget>
<output>66</output>

<gadget id="calculator">66 / 5_808</gadget>
<output>1/88 = around 0.011364</output>
<result>1/88 = around 0.011364</result>

Choices:
A. 1 : 76
B. 1 : 80
C. 1 : 84
D. 1 : 88
E. 1 : 92

divide(divide(sqrt(multiply(3, 5808)), const_2), 5808)

Explanation: "let the length and the width be 4 x and 3 x respectively . area = ( 4 x ) ( 3 x ) = 5808 12 x ^ 2 = 5808 x ^ 2 = 484 x = 22 the ratio of the width and the area is 3 x : 12 x ^ 2 = 1 : 4 x = 1 : 88 the answer is d ."


Question: a shopkeeper sells his goods at cost price but uses a faulty meter that weighs 990 grams . find the profit percent .

<gadget id="calculator">4 + 1</gadget>
<output>5</output>

<gadget id="calculator">5 + 5</gadget>
<output>10</output>

<gadget id="calculator">10 * 100</gadget>
<output>1_000</output>

<gadget id="calculator">1_000 - 990</gadget>
<output>10</output>

<gadget id="calculator">10 / 990</gadget>
<output>1/99 = around 0.010101</output>

<gadget id="calculator">(1/99) * 100</gadget>
<output>100/99 = around 1.010101</output>
<result>100/99 = around 1.010101</result>

Choices:
A. 1.05
B. 1.06
C. 1.01
D. 1.08
E. 1.09

multiply(divide(subtract(multiply(add(add(const_4, const_1), add(const_4, const_1)), const_100), 990), 990), const_100)

Explanation: "explanation : ( 100 + g ) / ( 100 + x ) = true measure / faulty measure x = 0 true measure = 1000 faulty measure = 990 100 + g / 100 + 0 = 1000 / 990 100 + g = 100 / 99 * 100 g = 1.01 answer : c"


Question: a basket contains 9 apples , of which 1 is spoiled and the rest are good . if we select 2 apples from the basket simultaneously and at random , what is the probability that the 2 apples selected will include the spoiled apple ?

<gadget id="calculator">9 - 1</gadget>
<output>8</output>

<gadget id="calculator">binomial(8, 1)</gadget>
<output>8</output>

<gadget id="calculator">binomial(9, 2)</gadget>
<output>36</output>

<gadget id="calculator">8 / 36</gadget>
<output>2/9 = around 0.222222</output>
<result>2/9 = around 0.222222</result>

Choices:
A. 2 / 3
B. 2 / 5
C. 2 / 7
D. 2 / 9
E. 2 / 11

divide(choose(subtract(9, 1), 1), choose(9, 2))

Explanation: the total number of ways to choose 2 apples is 9 c 2 = 36 the number of ways that include the spoiled apple is 8 c 1 = 8 p ( the spoiled apple is included ) = 8 / 36 = 2 / 9 the answer is d .


Question: 26 % of employees are women with fair hair . 40 % of fair - haired employees are women . what percent of employees have fair hair ?

<gadget id="calculator">26 / 40</gadget>
<output>13/20 = around 0.65</output>

<gadget id="calculator">(13/20) * 100</gadget>
<output>65</output>
<result>65</result>

Choices:
A. 25
B. 30
C. 50
D. 55
E. 65

Explanation: "think of 100 people total : from the first fact , 26 of these are women with fair hair . from the second fact , these 20 women make up 40 % of the total fair haired population . we can then make a ratio of 60 : 40 fair haired men to fair haired women . this means that ( 60 / 40 ) * 26 equals the number of fair haired men , which is 39 men with fair hair . add this 39 to the 26 women and get 65 fair haired men and women out of 100 total men and women . 65 % e"


Question: a work as fast as b . if b can complete a work in 24 days independently , the number of days in which a and b can together finish the work in ?

<gadget id="calculator">1 / 24</gadget>
<output>1/24 = around 0.041667</output>

<gadget id="calculator">2 * (1/24)</gadget>
<output>1/12 = around 0.083333</output>

<gadget id="calculator">(1/24) + (1/12)</gadget>
<output>1/8 = around 0.125</output>

<gadget id="calculator">1 / (1/8)</gadget>
<output>8</output>
<result>8</result>

Choices:
A. 2 days
B. 3 days
C. 8 days
D. 5 days
E. 6 days

Explanation: "ratio of rates of working of a and b = 2 : 1 ratio of times taken = 1 : 2 a ' s 1 day work = 1 / 12 b ' s 1 day work = 1 / 24 a + b 1 day work = 1 / 12 + 1 / 24 = 3 / 24 = 1 / 8 a and b can finish the work in 8 days answer is c"


Question: if 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 20 , then n =

<gadget id="calculator">20 * 2</gadget>
<output>40</output>

<gadget id="calculator">40 - 2</gadget>
<output>38</output>

<gadget id="calculator">38 / 2</gadget>
<output>19</output>
<result>19</result>

Choices:
A. 3
B. 6
C. 19
D. 23
E. 24

Explanation: "2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 20 = > 4 x 2 ^ 2 n = 4 ^ 20 = 2 ^ 40 = > 2 ^ 2 x 2 ^ 2 n = 2 ^ 40 = > 2 ^ ( 2 n + 2 ) = 2 ^ 40 = > 2 n + 2 = 40 = > n = 19 so . answer will be c ."


Question: in a division sum , the remainder is 8 and the divisor is 6 times the quotient and is obtained by adding 3 to the thrice of the remainder . the dividend is :

<gadget id="calculator">8 * 3</gadget>
<output>24</output>

<gadget id="calculator">24 + 3</gadget>
<output>27</output>

<gadget id="calculator">27 / 6</gadget>
<output>9/2 = around 4.5</output>

<gadget id="calculator">27 * (9/2)</gadget>
<output>243/2 = around 121.5</output>

<gadget id="calculator">(243/2) + 8</gadget>
<output>259/2 = around 129.5</output>
<result>259/2 = around 129.5</result>

Choices:
A. 110.6
B. 129.5
C. 130.5
D. 86
E. 88

add(multiply(add(multiply(8, const_3), 3), divide(add(multiply(8, const_3), 3), 6)), 8)

Explanation: "diver = ( 8 * 3 ) + 3 = 27 6 * quotient = 27 quotient = 4.5 dividend = ( divisor * quotient ) + remainder dividend = ( 27 * 4.5 ) + 8 = 129.5 b"


Question: a rectangular swimming pool is 20 feet by 20 feet . a deck that has uniform width surrounds the pool . the total area of the pool and deck is 576 square feet . what is the width of the deck ?

<gadget id="calculator">20 - 1</gadget>
<output>19</output>

<gadget id="calculator">19 ** 2</gadget>
<output>361</output>

<gadget id="calculator">20 * 20</gadget>
<output>400</output>

<gadget id="calculator">576 - 400</gadget>
<output>176</output>

<gadget id="calculator">361 + 176</gadget>
<output>537</output>

<gadget id="calculator">537 ** (1/2)</gadget>
<output>sqrt(537) = around 23.17326</output>

<gadget id="calculator">(sqrt(537)) - 19</gadget>
<output>-19 + sqrt(537) = around 4.17326</output>

<gadget id="calculator">(-19 + sqrt(537)) / 2</gadget>
<output>-19/2 + sqrt(537)/2 = around 2.08663</output>
<result>-19/2 + sqrt(537)/2 = around 2.08663</result>

Choices:
A. 2
B. 3
C. 4
D. 5
E. 6

divide(subtract(sqrt(add(power(subtract(20, const_1), const_2), subtract(576, rectangle_area(20, 20)))), subtract(20, const_1)), const_2)

Explanation: "let the width = w total area of the pool and deck = ( 2 w + 20 ) ( 2 w + 20 ) we can test the answer choices along with unit digit method a ) 2 feet . . . . . . . . . . . 24 * 24 has unit digit 6 . . . . . . . . . . hold b ) 2.5 feet . . . . . . . . . 25 * 25 has unit digit 5 . . . . . . . . . . eliminate c ) 3 feet . . . . . . . . . . . . 26 * 26 has unit digit 6 . . . . . . . . . . . elimate ( area is more than stipulated ) d ) 4 feet . . . . . . . . . . . . 28 * 28 has unit digit 4 . . . . . . . . . . . eliminate e ) 5 feet . . . . . . . . . . . . 30 * 30 has unit digit 0 . . . . . . . . . . . eliminate answer : a"


Question: a circle graph shows how the budget of a certain company was spent : 61 percent for salaries , 10 percent for research and development , 6 percent for utilities , 5 percent for equipment , 3 percent for supplies , and the remainder for transportation . if the area of each sector of the graph is proportional to the percent of the budget it represents , how many degrees of the circle are used to represent transportation ?

<gadget id="calculator">61 + 10</gadget>
<output>71</output>

<gadget id="calculator">71 + 6</gadget>
<output>77</output>

<gadget id="calculator">77 + 5</gadget>
<output>82</output>

<gadget id="calculator">82 + 3</gadget>
<output>85</output>

<gadget id="calculator">100 - 85</gadget>
<output>15</output>

<gadget id="calculator">360 * 15</gadget>
<output>5_400</output>

<gadget id="calculator">5_400 / 100</gadget>
<output>54</output>
<result>54</result>

Choices:
A. 18 °
B. 36 °
C. 54 °
D. 72 °
E. 90 °

divide(multiply(const_360, subtract(const_100, add(add(add(add(61, 10), 6), 5), 3))), const_100)

Explanation: the percent of the budget for transportation is 100 - ( 61 + 10 + 6 + 5 + 3 ) = 15 % 100 % of the circle is 360 degrees . then ( 15 % / 100 % ) * 360 = 54 degrees the answer is c .


Question: 10 stickers numbered 1 to 10 are placed in a bowl , mixed up thoroughly and then one sticker is drawn randomly . if it is known that the number on the drawn sticker is more than 3 , what is the probability that it is an even number ?

<gadget id="calculator">4 / 10</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">10 - 3</gadget>
<output>7</output>

<gadget id="calculator">10 / 7</gadget>
<output>10/7 = around 1.428571</output>

<gadget id="calculator">(2/5) * (10/7)</gadget>
<output>4/7 = around 0.571429</output>
<result>4/7 = around 0.571429</result>

Choices:
A. 3 / 7
B. 4 / 7
C. 5 / 7
D. 7 / 11
E. 9 / 11

multiply(divide(const_4, 10), divide(10, subtract(10, 3)))

Explanation: let a be the event ‘ the number on the card drawn is even ’ and b be the event ‘ the number on the card drawn is greater than 3 ’ . we have to find p ( a | b ) . now , the sample space of the experiment is s = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 } then a = { 2 , 4 , 6 , 8 , 10 } , b = { 4 , 5 , 6 , 7 , 8 , 9 , 10 } and a n b = { 4 , 6 , 8 , 10 } also p ( a ) = 5 / 2 , p ( b ) = 7 / 10 and p ( a n b ) = 4 / 10 then p ( a | b ) = p ( a n b ) / p ( b ) = ( 4 / 10 ) / ( 7 / 10 ) = 4 / 7 b )


Question: for a certain exam , a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean . what was the mean score w for the exam ?

<gadget id="calculator">58 * 3</gadget>
<output>174</output>

<gadget id="calculator">98 * 2</gadget>
<output>196</output>

<gadget id="calculator">174 + 196</gadget>
<output>370</output>

<gadget id="calculator">2 + 3</gadget>
<output>5</output>

<gadget id="calculator">370 / 5</gadget>
<output>74</output>
<result>74</result>

Choices:
A. 74
B. 76
C. 78
D. 80
E. 82

divide(add(multiply(58, 3), multiply(98, 2)), add(2, 3))

Explanation: "a score of 58 was 2 standard deviations below the mean - - > 58 = mean - 2 d a score of 98 was 3 standard deviations above the mean - - > 98 = mean + 3 d solving above for mean w = 74 . answer : a ."


Question: tanks a and b are each in the shape of a right circular cylinder . the interior of tank a has a height of 9 meters and a circumference of 8 meters , and the interior of tank b has a height of 8 meters and a circumference of 10 meters . the capacity of tank a is what percent of the capacity of tank b ?

<gadget id="calculator">8 / 10</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">(4/5) ** 2</gadget>
<output>16/25 = around 0.64</output>

<gadget id="calculator">9 / 8</gadget>
<output>9/8 = around 1.125</output>

<gadget id="calculator">(16/25) * (9/8)</gadget>
<output>18/25 = around 0.72</output>

<gadget id="calculator">(18/25) * 100</gadget>
<output>72</output>
<result>72</result>

Choices:
A. 72 %
B. 80 %
C. 100 %
D. 120 %
E. 125 %

multiply(multiply(power(divide(8, 10), const_2), divide(9, 8)), const_100)

Explanation: "for a , r = 8 / 2 pi . its capacity = ( 4 pi ) ^ 2 * 9 = 144 pi for b , r = 10 / pi . its capacity = ( 5 pi ) ^ 2 * 8 = 200 pi a / b = 144 pi / 200 pi = 0.72 a"


Question: 220 metres long yard , 21 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between 2 consecutive trees

<gadget id="calculator">21 - 2</gadget>
<output>19</output>

<gadget id="calculator">19 + 1</gadget>
<output>20</output>

<gadget id="calculator">220 / 20</gadget>
<output>11</output>
<result>11</result>

Choices:
A. 10
B. 12
C. 14
D. 11
E. 17

divide(220, add(subtract(21, 2), const_1))

Explanation: "21 trees have 20 gaps between them , required distance ( 220 / 20 ) = 11 d"


Question: the pinedale bus line travels at an average speed of 60 km / h , and has stops every 5 minutes along its route . yahya wants to go from his house to the pinedale mall , which is 10 stops away . how far away , in kilometers , is pinedale mall away from yahya ' s house ?

<gadget id="calculator">5 * 10</gadget>
<output>50</output>

<gadget id="calculator">50 / 60</gadget>
<output>5/6 = around 0.833333</output>

<gadget id="calculator">60 * (5/6)</gadget>
<output>50</output>
<result>50</result>

Choices:
A. 20 km
B. 30 km
C. 40 km
D. 50 km
E. 60 km

multiply(60, divide(multiply(5, 10), 60))

Explanation: "number of stops in an hour : 60 / 5 = 12 distance between stops : 60 / 12 = 5 km distance between yahya ' s house and pinedale mall : 5 x 10 = 50 km imo , correct answer is ` ` d . ' '"


Question: a student travels from his house to school at 10 km / hr and reaches school 1 hour late . the next day he travels 12 km / hr and reaches school 1 hour early . what is the distance between his house and the school ?

<gadget id="calculator">10 * 12</gadget>
<output>120</output>

<gadget id="calculator">12 - 10</gadget>
<output>2</output>

<gadget id="calculator">1 + 1</gadget>
<output>2</output>

<gadget id="calculator">2 / 2</gadget>
<output>1</output>

<gadget id="calculator">120 * 1</gadget>
<output>120</output>
<result>120</result>

Choices:
A. 100
B. 105
C. 110
D. 115
E. 120

multiply(multiply(10, 12), divide(subtract(12, 10), add(1, 1)))

Explanation: let x be the distance from his house to the school . x / 10 = x / 12 + 2 6 x = 5 x + 120 x = 120 km the answer is e .


Question: two bullet trains of equal lengths take 10 seconds and 30 seconds respectively to cross a telegraph post . if the length of each bullet train be 120 metres , in what time ( in seconds ) will they cross each other travelling in opposite direction ?

<gadget id="calculator">120 + 120</gadget>
<output>240</output>

<gadget id="calculator">120 / 10</gadget>
<output>12</output>

<gadget id="calculator">120 / 30</gadget>
<output>4</output>

<gadget id="calculator">12 + 4</gadget>
<output>16</output>

<gadget id="calculator">240 / 16</gadget>
<output>15</output>
<result>15</result>

Choices:
A. 13 sec .
B. 14 sec .
C. 12 sec .
D. 15 sec .
E. 19 sec .

Explanation: "speed of the first bullet train = 120 / 10 m / sec = 12 m / sec . speed of the second bullet train = 120 / 30 m / sec = 4 m / sec . relative speed = ( 12 + 4 ) = 16 m / sec . required time = ( 120 + 120 ) / 16 sec = 15 sec . d"


Question: kathleen can paint a room in 2 hours , and anthony can paint an identical room in 7 hours . how many hours would it take kathleen and anthony to paint both rooms if they work together at their respective rates ?

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">1 / 7</gadget>
<output>1/7 = around 0.142857</output>

<gadget id="calculator">(1/2) + (1/7)</gadget>
<output>9/14 = around 0.642857</output>

<gadget id="calculator">1 / (9/14)</gadget>
<output>14/9 = around 1.555556</output>

<gadget id="calculator">(14/9) * 2</gadget>
<output>28/9 = around 3.111111</output>
<result>28/9 = around 3.111111</result>

Choices:
A. 28 / 9
B. 4 / 3
C. 15 / 8
D. 9 / 4
E. 15 / 4

multiply(divide(const_1, add(divide(const_1, 2), divide(const_1, 7))), const_2)

Explanation: ( 1 / 2 + 1 / 7 ) t = 2 t = 28 / 9 answer : a


Question: according to a recent student poll , 4 / 6 out of 24 members of the finance club are interested in a career in investment banking . if two students are chosen at random , what is the probability that at least one of them is interested in investment banking ?

<gadget id="calculator">binomial(24, 2)</gadget>
<output>276</output>

<gadget id="calculator">4 / 6</gadget>
<output>2/3 = around 0.666667</output>

<gadget id="calculator">24 * (2/3)</gadget>
<output>16</output>

<gadget id="calculator">24 - 16</gadget>
<output>8</output>

<gadget id="calculator">binomial(8, 2)</gadget>
<output>28</output>

<gadget id="calculator">276 - 28</gadget>
<output>248</output>

<gadget id="calculator">248 / 276</gadget>
<output>62/69 = around 0.898551</output>
<result>62/69 = around 0.898551</result>

Choices:
A. 1 / 14
B. 4 / 49
C. 2 / 7
D. 62 / 69
E. 13 / 14

divide(subtract(choose(24, const_2), choose(subtract(24, multiply(24, divide(4, 6))), const_2)), choose(24, const_2))

Explanation: "16 students are interested , 8 are not interested prob = 1 - 8 c 2 / 24 c 2 = 1 - ( 8 * 7 / ( 24 * 23 ) ) = 1 - 7 / 69 = 62 / 69 answer : d"


Question: in school there are some bicycles and 4 wheeler wagons . one tuesday there are 190 wheels in the campus . how many bicycles are there ?

<gadget id="calculator">4 * 2</gadget>
<output>8</output>

<gadget id="calculator">8 + 2</gadget>
<output>10</output>

<gadget id="calculator">190 / 10</gadget>
<output>19</output>

<gadget id="calculator">19 * 2</gadget>
<output>38</output>
<result>38</result>

Choices:
A. 35
B. 36
C. 37
D. 38
E. 39

multiply(divide(190, add(multiply(4, const_2), const_2)), const_2)

Explanation: let no . of bicycles be x & no . of wagons be y so , 2 x + 4 y = 190 by solving , we get no . of bicycles = 39 ( wheels = > 2 * 39 = 78 ) no . of wagons = 28 ( wheels = > 4 * 28 = 112 ) answer : e


Question: in a certain pond , 90.00001 fish were caught , tagged , and returned to the pond . a few days later , 90 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what ` s the approximate number of fish in the pond ?

<gadget id="calculator">2 / 90</gadget>
<output>1/45 = around 0.022222</output>

<gadget id="calculator">90.00001 / (1/45)</gadget>
<output>4_050.00045</output>
<result>4_050.00045</result>

Choices:
A. 400
B. 625
C. 1250
D. 2500
E. 4091

Explanation: "the percent of tagged fish in the second catch is 2 / 90 * 100 = 2.22 % . we are told that 2.22 % approximates the percent of tagged fish in the pond . since there are 90 tagged fish , then we have 0.022 x = 90 - - > x = 4,091 . answer : e ."


Question: in a garden , there are yellow and green flowers which are straight and curved . if the probability of picking a green flower is 1 / 5 and picking a straight flower is 1 / 2 , then what is the probability of picking a flower which is yellow and straight

<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">(4/5) * (1/2)</gadget>
<output>2/5 = around 0.4</output>
<result>2/5 = around 0.4</result>

Choices:
A. 1 / 7
B. 1 / 8
C. 2 / 5
D. 3 / 4
E. 7 / 8

multiply(subtract(1, divide(1, 5)), divide(1, 2))

Explanation: "good question . so we have a garden where all the flowers have two properties : color ( green or yellow ) and shape ( straight or curved ) . we ' re told that 1 / 5 of the garden is green , so , since all the flowers must be either green or yellow , we know that 4 / 5 are yellow . we ' re also told there is an equal probability of straight or curved , 1 / 2 . we want to find out the probability of something being yellow and straight , pr ( yellow and straight ) . so if we recall , the probability of two unique events occurring simultaneously is the product of the two probabilities , pr ( a and b ) = p ( a ) * p ( b ) . so we multiply the two probabilities , pr ( yellow ) * pr ( straight ) = 4 / 5 * 1 / 2 = 2 / 5 , or c ."


Question: in what time will a railway train 110 m long moving at the rate of 36 kmph pass a telegraph post on its way ?

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>

<gadget id="calculator">36 * (5/18)</gadget>
<output>10</output>

<gadget id="calculator">110 / 10</gadget>
<output>11</output>
<result>11</result>

Choices:
A. 6 sec
B. 7 sec
C. 8 sec
D. 11 sec
E. 2 sec

Explanation: "t = 110 / 36 * 18 / 5 = 11 sec answer : d"


Question: there are two groups of students in the sixth grade . there are 45 students in group a , and 55 students in group b . if , on a particular day , 20 % of the students in group a forget their homework , and 40 % of the students in group b forget their homework , then what percentage of the sixth graders forgot their homework ?

<gadget id="calculator">45 * 20</gadget>
<output>900</output>

<gadget id="calculator">900 / 100</gadget>
<output>9</output>

<gadget id="calculator">55 * 40</gadget>
<output>2_200</output>

<gadget id="calculator">2_200 / 100</gadget>
<output>22</output>

<gadget id="calculator">9 + 22</gadget>
<output>31</output>

<gadget id="calculator">45 + 55</gadget>
<output>100</output>

<gadget id="calculator">31 / 100</gadget>
<output>31/100 = around 0.31</output>

<gadget id="calculator">(31/100) * 100</gadget>
<output>31</output>
<result>31</result>

Choices:
A. 23 %
B. 25 %
C. 29 %
D. 31 %
E. 36 %

multiply(divide(add(divide(multiply(45, 20), const_100), divide(multiply(55, 40), const_100)), add(45, 55)), const_100)

Explanation: "number of students in group a = 45 students who forget homework in group a = 20 % of 45 = 9 students number of students in group b = 55 students who forget homework in group b = 40 % of 55 = 22 students total number of students = 45 + 55 = 100 students who forgot homework = 9 + 22 = 31 students percentage of students who forget homework = 31 / 100 * 100 = 31 % answer : d"


Question: in a factory , an average of 50 tv ' s are produced per day for the fist 25 days of the months . a few workers fell ill for the next 5 days reducing the daily avg for the month to 43 sets / day . the average production per day for day last 5 days is ?

<gadget id="calculator">25 + 5</gadget>
<output>30</output>

<gadget id="calculator">30 * 43</gadget>
<output>1_290</output>

<gadget id="calculator">25 * 50</gadget>
<output>1_250</output>

<gadget id="calculator">1_290 - 1_250</gadget>
<output>40</output>

<gadget id="calculator">40 / 5</gadget>
<output>8</output>
<result>8</result>

Choices:
A. 20
B. 36
C. 8
D. 50
E. 59

divide(subtract(multiply(add(25, 5), 43), multiply(25, 50)), 5)

Explanation: "production during these 5 days = total production in a month - production in first 25 days . = 30 x 43 - 25 x 50 = 40 ∴ average for last 5 days = 40 / 5 = 8 c"


Question: find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 1904 ?

<gadget id="calculator">2 * 5</gadget>
<output>10</output>

<gadget id="calculator">10 + 2</gadget>
<output>12</output>

<gadget id="calculator">12 / 5</gadget>
<output>12/5 = around 2.4</output>

<gadget id="calculator">(12/5) * 5</gadget>
<output>12</output>

<gadget id="calculator">12 / 100</gadget>
<output>3/25 = around 0.12</output>

<gadget id="calculator">(3/25) + 1</gadget>
<output>28/25 = around 1.12</output>

<gadget id="calculator">1_904 / (28/25)</gadget>
<output>1_700</output>
<result>1_700</result>

Choices:
A. 1700
B. 2777
C. 2889
D. 27670
E. 2771

divide(1904, add(divide(multiply(divide(add(multiply(2, 5), 2), 5), 5), const_100), const_1))

Explanation: "1904 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 1700 . answer : a"


Question: the overall age of x and y is 11 year greater than the overall age of y and z . z is how many decades younger that x ?

<gadget id="calculator">11 / 1</gadget>
<output>11</output>
<result>11</result>

Choices:
A. 11
B. 15
C. 12
D. 17
E. 19

Explanation: "a 11 ( x + y ) â € “ ( y + z ) = 11 x â € “ z = 11"


Question: the mean of 50 observations was 36 . it was found later that an observation 47 was wrongly taken as 23 . the corrected new mean is

<gadget id="calculator">36 * 50</gadget>
<output>1_800</output>

<gadget id="calculator">50 - 2</gadget>
<output>48</output>

<gadget id="calculator">48 - 23</gadget>
<output>25</output>

<gadget id="calculator">1_800 + 25</gadget>
<output>1_825</output>

<gadget id="calculator">1_825 / 50</gadget>
<output>73/2 = around 36.5</output>
<result>73/2 = around 36.5</result>

Choices:
A. 35.24
B. 36.16
C. 36.22
D. 36.48
E. none

divide(add(multiply(36, 50), subtract(subtract(50, const_2), 23)), 50)

Explanation: "solution correct sum = ( 36 x 50 + 47 - 23 ) = 1824 . â ˆ ´ correct mean = 1824 / 50 = 36.48 . answer d"


Question: the length of a rectangular floor is more than its breadth by 200 % . if rs . 324 is required to paint the floor at the rate of rs . 3 per sq m , then what would be the length of the floor ?

<gadget id="calculator">324 / 3</gadget>
<output>108</output>

<gadget id="calculator">108 / 3</gadget>
<output>36</output>

<gadget id="calculator">36 ** (1/2)</gadget>
<output>6</output>

<gadget id="calculator">6 * 3</gadget>
<output>18</output>
<result>18</result>

Choices:
A. 27 m
B. 24 m
C. 18 m
D. 21 m
E. none of these

multiply(sqrt(divide(divide(324, 3), const_3)), const_3)

Explanation: "let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 324 / 3 = 108 sq m l b = 108 i . e . , l * l / 3 = 108 l 2 = 324 = > l = 18 . answer : c"


Question: a watch was sold at a loss of 10 % . if it was sold for rs . 182 more , there would have been a gain of 4 % . what is the cost price ?

<gadget id="calculator">182 * 100</gadget>
<output>18_200</output>

<gadget id="calculator">100 + 4</gadget>
<output>104</output>

<gadget id="calculator">100 - 10</gadget>
<output>90</output>

<gadget id="calculator">104 - 90</gadget>
<output>14</output>

<gadget id="calculator">18_200 / 14</gadget>
<output>1_300</output>
<result>1_300</result>

Choices:
A. s : 1000
B. s : 1067
C. s : 1278
D. s : 1300
E. s : 1027

divide(multiply(182, const_100), subtract(add(const_100, 4), subtract(const_100, 10)))

Explanation: "90 % 104 % - - - - - - - - 14 % - - - - 182 100 % - - - - ? = > rs : 1300 answer : d"


Question: a diagonal of a polygon is an segment between two non - adjacent vertices of the polygon . how many diagonals does a regular 10 - sided polygon have ?

<gadget id="calculator">10 - 3</gadget>
<output>7</output>

<gadget id="calculator">7 * 10</gadget>
<output>70</output>

<gadget id="calculator">70 / 2</gadget>
<output>35</output>
<result>35</result>

Choices:
A. 875
B. 35
C. 1425
D. 2025
E. 2500

divide(multiply(subtract(10, const_3), 10), const_2)

Explanation: "there ' s a direct formula for this . number of diagonals in a regular polygon = [ n * ( n - 3 ) ] / 2 , n = number of sides of the regular polygon . here , n = 10 . plugging it in , we get 35 diagonals ! answer ( b ) ."


Question: a and b start walking towards each other at 5 am at speed of 4 kmph and 8 kmph . they were initially 36 km apart . at what time do they meet ?

<gadget id="calculator">4 + 8</gadget>
<output>12</output>

<gadget id="calculator">36 / 12</gadget>
<output>3</output>

<gadget id="calculator">5 + 3</gadget>
<output>8</output>
<result>8</result>

Choices:
A. 8 am
B. 6 am
C. 7 am
D. 10 am
E. 8 pm

Explanation: time of meeting = distance / relative speed = 36 / 8 + 4 = 36 / 12 = 3 hrs after 5 am = 8 am answer is a


Question: a group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 7 with 3 students left over . what is the sum of the two smallest possible values of n ?

<gadget id="calculator">7 * 2</gadget>
<output>14</output>

<gadget id="calculator">14 + 3</gadget>
<output>17</output>

<gadget id="calculator">2 * 3</gadget>
<output>6</output>

<gadget id="calculator">7 * 6</gadget>
<output>42</output>

<gadget id="calculator">42 + 3</gadget>
<output>45</output>

<gadget id="calculator">17 + 45</gadget>
<output>62</output>
<result>62</result>

Choices:
A. 54
B. 58
C. 62
D. 66
E. 70

add(add(multiply(7, const_2), 3), add(multiply(7, multiply(const_2, const_3)), 3))

Explanation: n = 4 k + 1 = 7 j + 3 let ' s start at 1 = 4 ( 0 ) + 1 and keep adding 4 until we find a number in the form 7 j + 3 . 1 , 5 , 9 , 13 , 17 = 7 ( 2 ) + 3 the next such number is 17 + 4 * 7 = 45 . 17 + 45 = 62 the answer is c .


Question: a train 150 m long running at 72 kmph crosses a platform in 28 sec . what is the length of the platform ?

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>

<gadget id="calculator">72 * (5/18)</gadget>
<output>20</output>

<gadget id="calculator">28 * 20</gadget>
<output>560</output>

<gadget id="calculator">560 - 150</gadget>
<output>410</output>
<result>410</result>

Choices:
A. 410 m
B. 354 m
C. 450 m
D. 350 m
E. 250 m

subtract(multiply(28, multiply(72, const_0_2778)), 150)

Explanation: "a 410 a = ( 72 * 5 / 18 ) * 28 - 150 = 410"


Question: the batting average of a particular batsman is 60 runs in 46 innings . if the difference in his highest and lowest score is 170 runs and his average excluding these two innings is 58 runs , find his highest score .

<gadget id="calculator">60 * 46</gadget>
<output>2_760</output>

<gadget id="calculator">46 - 2</gadget>
<output>44</output>

<gadget id="calculator">58 * 44</gadget>
<output>2_552</output>

<gadget id="calculator">2_760 - 2_552</gadget>
<output>208</output>

<gadget id="calculator">170 + 208</gadget>
<output>378</output>

<gadget id="calculator">378 / 2</gadget>
<output>189</output>
<result>189</result>

Choices:
A. 179
B. 367
C. 189
D. 177
E. 191

divide(add(170, subtract(multiply(60, 46), multiply(58, subtract(46, const_2)))), const_2)

Explanation: "explanation : total runs scored by the batsman = 60 * 46 = 2760 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2760 â € “ 2552 = 208 runs . let the highest score be x , hence the lowest score = x â € “ 170 x + ( x - 170 ) = 208 2 x = 378 x = 189 runs answer : c"


Question: the speeds of three asteroids were compared . asteroids x - 13 and y - 14 were observed for identical durations , while asteroid z - 15 was observed for 2 seconds longer . during its period of observation , asteroid y - 14 traveled three times the distance x - 13 traveled , and therefore y - 14 was found to be faster than x - 13 by 1000 kilometers per second . asteroid z - 15 had an identical speed as that of x - 13 , but because z - 15 was observed for a longer period , it traveled five times the distance x - 13 traveled during x - 13 ' s inspection . asteroid x - 13 traveled how many kilometers during its observation ?

<gadget id="calculator">1_000 / 2</gadget>
<output>500</output>

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">500 * (1/2)</gadget>
<output>250</output>
<result>250</result>

Choices:
A. 250
B. 1,600 / 3
C. 1,000
D. 1,500
E. 2,500

multiply(divide(1000, 2), divide(const_1, 2))

Explanation: "x 13 : ( t , d , s ) y 14 : ( t , 3 d , s + 1000 mi / hour ) z 15 : ( t + 2 seconds , s , 5 d ) d = ? distance = speed * time x 13 : d = s * t x 14 : 3 d = ( s + 1000 ) * t = = = > 3 d = ts + 1000 t z 15 : 5 d = s * ( t + 2 t ) = = = > 5 d = st + 2 st = = = > 5 d - 2 st = st 3 d = 5 d - 2 st + 1000 t - 2 d = - 2 st + 1000 t 2 d = 2 st - 1000 t d = st - 500 t x 13 : d = s * t st - 500 t = s * t s - 500 = s - 250 = s i got to this point and could n ' t go any further . this seems like a problem where i can set up individual d = r * t formulas and solve but it appears that ' s not the case . for future reference how would i know not to waste my time setting up this problem in the aforementioned way ? thanks ! ! ! the distance of z 15 is equal to five times the distance of x 13 ( we established that x 13 is the baseline and thus , it ' s measurements are d , s , t ) s ( t + 2 ) = 5 ( s * t ) what clues would i have to know to set up the equation in this fashion ? is it because i am better off setting two identical distances together ? st + 2 s = 5 st t + 2 = 5 t 2 = 4 t t = 1 / 2 we are looking for distance ( d = s * t ) so we need to solve for speed now that we have time . speed y 14 - speed x 13 speed = d / t 3 d / t - d / t = 1000 ( remember , t is the same because both asteroids were observed for the same amount of time ) 2 d = 1000 2 = 500 d = s * t d = 500 * ( 1 / 2 ) d = 250 answer : a"


Question: in town x , 64 percent of the population are employed , and 35 percent of the population are employed males . what percent of the employed people in town x are females ?

<gadget id="calculator">64 - 35</gadget>
<output>29</output>

<gadget id="calculator">29 / 64</gadget>
<output>29/64 = around 0.453125</output>

<gadget id="calculator">(29/64) * 100</gadget>
<output>725/16 = around 45.3125</output>
<result>725/16 = around 45.3125</result>

Choices:
A. 16 %
B. 25 %
C. 32 %
D. 45 %
E. 52 %

multiply(divide(subtract(64, 35), 64), const_100)

Explanation: "we are asked to find the percentage of females in employed people . total employed people 64 % , out of which 35 are employed males , hence 29 % are employed females . ( employed females ) / ( total employed people ) = 29 / 64 = 45 % answer : d ."


Question: find the value of ( 950 + 220 / 900 ) × 900

<gadget id="calculator">220 / 900</gadget>
<output>11/45 = around 0.244444</output>

<gadget id="calculator">(11/45) + 950</gadget>
<output>42_761/45 = around 950.244444</output>

<gadget id="calculator">(42_761/45) * 900</gadget>
<output>855_220</output>
<result>855_220</result>

Choices:
A. 854542
B. 856945
C. 758965
D. 855220
E. 826450

Explanation: "( 855000 + 220 ) / 900 * 900 = 855000 + 220 = 855220 answer : d"


Question: __ 2 a x __ b ____ cc in the multiplication problem above , a , b , and c represent distinct digits . if the sum of a and b is equal to 4.6 , what is the value of c ?

<gadget id="calculator">4.6 - 2</gadget>
<output>2.6</output>

<gadget id="calculator">2.6 * 10</gadget>
<output>26</output>

<gadget id="calculator">4 + 1</gadget>
<output>5</output>

<gadget id="calculator">26 / 5</gadget>
<output>26/5 = around 5.2</output>
<result>26/5 = around 5.2</result>

Choices:
A. 6
B. 5.2
C. 4
D. 3
E. 2

divide(multiply(subtract(4.6, 2), const_10), add(const_4, const_1))

Explanation: if a + b = 4.6 assuming a and b are positive then a * b < 10 ( they could be either 1,2 , 3,4 ) therefore a * b = c 2 * b = c a + b = 4.6 three simple equations - divide the 1 st / 2 nd - - > a = 2 plug it the 3 rd - - > b = 2.6 - - > c = 5.2 ( answer b )


Question: country c imposes a two - tiered tax on imported cars : the first tier imposes a tax of 12 % of the car ' s price up to a certain price level . if the car ' s price is higher than the first tier ' s level , the tax on the portion of the price that exceeds this value is 9 % . if ron imported a $ 18,000 imported car and ended up paying $ 1950 in taxes , what is the first tier ' s price level ?

<gadget id="calculator">2 * 3</gadget>
<output>6</output>

<gadget id="calculator">3 * 6</gadget>
<output>18</output>

<gadget id="calculator">18 * 1_000</gadget>
<output>18_000</output>

<gadget id="calculator">9 / 100</gadget>
<output>9/100 = around 0.09</output>

<gadget id="calculator">18_000 * (9/100)</gadget>
<output>1_620</output>

<gadget id="calculator">1_950 - 1_620</gadget>
<output>330</output>

<gadget id="calculator">12 / 100</gadget>
<output>3/25 = around 0.12</output>

<gadget id="calculator">(3/25) - (9/100)</gadget>
<output>3/100 = around 0.03</output>

<gadget id="calculator">330 / (3/100)</gadget>
<output>11_000</output>
<result>11_000</result>

Choices:
A. $ 11500
B. $ 11000
C. $ 12000
D. $ 12100
E. $ 12500

divide(subtract(1950, multiply(multiply(multiply(const_3, multiply(const_2, const_3)), const_1000), divide(9, const_100))), subtract(divide(12, const_100), divide(9, const_100)))

Explanation: let t be the tier price , p be total price = 18000 per the given conditions : 0.12 t + 0.09 ( p - t ) = 1950 0.12 t + 0.09 * 18000 - 0.09 t = 1950 0.03 t + 1620 = 1950 0.03 t = 1950 - 1620 = 330 t = 330 / 0.03 = 11000 answer b


Question: a scuba diver descends at a rate of 40 feet per minute . a diver dive from a ship to search for a lost ship at the depth of 3000 feet below the sea level . . how long will he take to reach the ship ?

<gadget id="calculator">3_000 / 40</gadget>
<output>75</output>
<result>75</result>

Choices:
A. 70 minutes
B. 72 minutes
C. 75 minutes
D. 76 minutes
E. 77 minutes

Explanation: "time taken to reach = 3000 / 40 = 75 minutes answer : c"


Question: a man , a woman and a boy can together complete a piece of work in 3 days . if a man alone can do it in 6 days and a boy alone in 18 days , how long will a woman take to complete the work ?

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>

<gadget id="calculator">1 / 18</gadget>
<output>1/18 = around 0.055556</output>

<gadget id="calculator">(1/6) + (1/18)</gadget>
<output>2/9 = around 0.222222</output>

<gadget id="calculator">(1/3) - (2/9)</gadget>
<output>1/9 = around 0.111111</output>

<gadget id="calculator">1 / (1/9)</gadget>
<output>9</output>
<result>9</result>

Choices:
A. 9 days
B. 21 days
C. 24 days
D. 27 days
E. 28 days

Explanation: "explanation : ( 1 man + 1 woman + 1 boy ) ’ s 1 day ’ s work = 1 / 3 1 man ’ s 1 day work = 1 / 6 1 boy ’ s 1 day ’ s work = 1 / 18 ( 1 man + 1 boy ) ‘ s 1 day ’ s work = 1 / 6 + 1 / 18 = 2 / 9 therefore , 1 woman ’ s 1 day ’ s work = 1 / 3 – 2 / 9 = 3 - 2 / 9 = 1 / 9 therefore , the woman alone can finish the work in 9 days . answer : option a"


Question: running at the same constant rate , 6 identical machines can produce a total of 270 pens per minute . at this rate , how many pens could 10 such machines produce in 4 minutes ?

<gadget id="calculator">270 / 6</gadget>
<output>45</output>

<gadget id="calculator">45 * 4</gadget>
<output>180</output>

<gadget id="calculator">180 * 10</gadget>
<output>1_800</output>
<result>1_800</result>

Choices:
A. 1500
B. 1545.6
C. 1640.33
D. 1800
E. none of these

multiply(multiply(divide(270, 6), 4), 10)

Explanation: "explanation : let the required number of bottles be x . more machines , more bottles ( direct proportion ) more minutes , more bottles ( direct proportion ) machines 6 : 10 | | : : 270 : x time 1 : 4 | = > 6 * 1 * x = 10 * 4 * 270 = > x = ( 10 * 4 * 270 ) / 6 = > x = 1800 answer : d"


Question: from the sale of sleeping bags , a retailer made a gross profit of 13 % of the wholesale cost . if each sleeping bag was sold for $ 28 , what was the wholesale cost per bag ?

<gadget id="calculator">28 * 100</gadget>
<output>2_800</output>

<gadget id="calculator">100 + 13</gadget>
<output>113</output>

<gadget id="calculator">2_800 / 113</gadget>
<output>2_800/113 = around 24.778761</output>
<result>2_800/113 = around 24.778761</result>

Choices:
A. 3.0
B. 3.36
C. 24.78
D. 25.0
E. 31.36

divide(multiply(28, const_100), add(const_100, 13))

Explanation: "cost price * 1.13 = selling price - - > cost price * 1.13 = $ 28 - - > cost price = $ 24.78 . answer : c ."


Question: a light has a rating of 86 watts , it is replaced with a new light that has 18 % higher wattage . how many watts does the new light have ?

<gadget id="calculator">18 / 100</gadget>
<output>9/50 = around 0.18</output>

<gadget id="calculator">1 + (9/50)</gadget>
<output>59/50 = around 1.18</output>

<gadget id="calculator">86 * (59/50)</gadget>
<output>2_537/25 = around 101.48</output>
<result>2_537/25 = around 101.48</result>

Choices:
A. 105
B. 95
C. 80
D. 60
E. 101

multiply(86, add(const_1, divide(18, const_100)))

Explanation: final number = initial number + 18 % ( original number ) = 86 + 18 % ( 86 ) = 86 + 15 = 101 . answer e


Question: a boat running upstream takes 8 hours 48 minutes to cover a certain distance , while it takes 4 hours to cover the same distance running downstream . what is the ratio between the speed of the boat and speed of the water current respectively ?

<gadget id="calculator">48 / 60</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">(4/5) + 8</gadget>
<output>44/5 = around 8.8</output>

<gadget id="calculator">(44/5) / 4</gadget>
<output>11/5 = around 2.2</output>

<gadget id="calculator">(11/5) + 1</gadget>
<output>16/5 = around 3.2</output>

<gadget id="calculator">(16/5) / 2</gadget>
<output>8/5 = around 1.6</output>

<gadget id="calculator">(11/5) - 1</gadget>
<output>6/5 = around 1.2</output>

<gadget id="calculator">(6/5) / 2</gadget>
<output>3/5 = around 0.6</output>

<gadget id="calculator">(8/5) / (3/5)</gadget>
<output>8/3 = around 2.666667</output>
<result>8/3 = around 2.666667</result>

Choices:
A. 8 / 5
B. 8 / 3
C. 3 / 5
D. 5 / 8
E. 5 / 3

divide(divide(add(divide(add(divide(48, const_60), 8), 4), const_1), const_2), divide(subtract(divide(add(divide(48, const_60), 8), 4), const_1), const_2))

Explanation: let the man ' s rate upstream be x kmph and that downstream be y kmph . then , distance covered upstream in 8 hrs 48 min = distance covered downstream in 4 hrs . 44 * x / 5 = 4 * y y = 11 / 5 * x required ratio = ( y + x ) / 2 : ( y - x ) / 2 = 8 / 5 : 3 / 5 = 8 / 3 ans - b


Question: a worker makes a toy in every 1 h . if he works for 100 h , then how many toys will he make ?

<gadget id="calculator">100 / 1</gadget>
<output>100</output>
<result>100</result>

Choices:
A. 40
B. 54
C. 45
D. 39
E. 100

Explanation: "no . of toys = 100 / 1 = 100 answer : e"


Question: there are 3000 students in a school and among them 20 % of them attends chess class . 40 % of the students who are in the chess class are also enrolled for swimming . no other students are interested in swimming so how many will attend the swimming class if all enrolled attends ?

<gadget id="calculator">20 * 3_000</gadget>
<output>60_000</output>

<gadget id="calculator">60_000 / 100</gadget>
<output>600</output>

<gadget id="calculator">600 * 40</gadget>
<output>24_000</output>

<gadget id="calculator">24_000 / 100</gadget>
<output>240</output>
<result>240</result>

Choices:
A. 240
B. 10
C. 100
D. 50
E. 20

divide(multiply(divide(multiply(20, 3000), const_100), 40), const_100)

Explanation: "20 % of 3000 gives 600 . so 600 attends chess and 40 % of 600 gives 240 so 240 enrolled for swimming answer : a"


Question: the present population of a town is 280 . population increase rate is 10 % p . a . find the population of town after 1 years ?

<gadget id="calculator">280 * 10</gadget>
<output>2_800</output>

<gadget id="calculator">2_800 / 100</gadget>
<output>28</output>

<gadget id="calculator">280 + 28</gadget>
<output>308</output>
<result>308</result>

Choices:
A. 100
B. 120
C. 200
D. 220
E. 308

add(280, divide(multiply(280, 10), const_100))

Explanation: "p = 280 r = 10 % required population of town = p * ( 1 + r / 100 ) ^ t = 280 * ( 1 + 10 / 100 ) = 280 * ( 11 / 10 ) = 308 answer is e"


Question: mary sold boxes of butter cookies . ann sold 5 times as much as she did . 18 boxes of cookies were sold that day , how many boxes did mary sell ?

<gadget id="calculator">5 + 1</gadget>
<output>6</output>

<gadget id="calculator">18 / 6</gadget>
<output>3</output>
<result>3</result>

Choices:
A. 3
B. 5
C. 6
D. 10
E. 18

Explanation: # of boxes of cookies mary sold = x ann sold 5 times more = 5 x x + 5 x = 18 6 x = 18 x = 18 / 6 = 3 answer : a


Question: a batsman in his 9 th inning makes a score of 75 and their by increasing his average by 7 . what is his average after the 9 th inning ?

<gadget id="calculator">7 * 9</gadget>
<output>63</output>

<gadget id="calculator">75 - 63</gadget>
<output>12</output>

<gadget id="calculator">12 + 7</gadget>
<output>19</output>
<result>19</result>

Choices:
A. 12
B. 19
C. 26
D. 33
E. 40

Explanation: 8 x + 75 = 9 ( x + 7 ) x = 12 + 7 = 19 answer : b


Question: a man can row at 5 kmph in still water . if the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back , how far is the place ?

<gadget id="calculator">5 - 1</gadget>
<output>4</output>

<gadget id="calculator">4 * 3</gadget>
<output>12</output>

<gadget id="calculator">12 / 5</gadget>
<output>12/5 = around 2.4</output>
<result>12/5 = around 2.4</result>

Choices:
A. 3.2 km
B. 3 km
C. 2.4 km
D. 3.6 km
E. none of these

divide(multiply(subtract(5, 1), const_3), 5)

Explanation: "explanation : speed in still water = 5 kmph speed of the current = 1 kmph speed downstream = ( 5 + 1 ) = 6 kmph speed upstream = ( 5 - 1 ) = 4 kmph let the requited distance be x km total time taken = 1 hour = > x / 6 + x / 4 = 1 = > 2 x + 3 x = 12 = > 5 x = 12 = > x = 2.4 km . answer : option c"


Question: working alone at its constant rate , machine a produces x boxes in 10 minutes and working alone at its constant rate , machine b produces 2 x boxes in 5 minutes . how many minutes does it take machines a and b , working simultaneously at their respective constant rates , to produce 4 x boxes ?

<gadget id="calculator">4 * 10</gadget>
<output>40</output>

<gadget id="calculator">10 / 10</gadget>
<output>1</output>

<gadget id="calculator">2 * 10</gadget>
<output>20</output>

<gadget id="calculator">20 / 5</gadget>
<output>4</output>

<gadget id="calculator">1 + 4</gadget>
<output>5</output>

<gadget id="calculator">40 / 5</gadget>
<output>8</output>
<result>8</result>

Choices:
A. 3 minutes
B. 4 minutes
C. 5 minutes
D. 6 minutes
E. 8 minutes

divide(multiply(4, 10), add(speed(10, 10), speed(multiply(2, 10), 5)))

Explanation: rate = work / time given rate of machine a = x / 10 min machine b produces 2 x boxes in 5 min hence , machine b produces 4 x boxes in 10 min . rate of machine b = 4 x / 10 we need tofind the combined time that machines a and b , working simultaneouslytakeat their respective constant rates let ' s first find the combined rate of machine a and b rate of machine a = x / 10 min + rate of machine b = 4 x / 10 = 5 x / 10 now combine time = combine work needs to be done / combine rate = 4 x / 5 x * 10 = 8 min ans : e


Question: in a certain brick wall , each row of bricks above the bottom row contains one less brick than the row just below it . if there are 4 rows in all and a total of 134 bricks in the wall , how many bricks does the bottom row contain ?

<gadget id="calculator">134 - 1</gadget>
<output>133</output>

<gadget id="calculator">133 - 2</gadget>
<output>131</output>

<gadget id="calculator">131 - 3</gadget>
<output>128</output>

<gadget id="calculator">128 - 4</gadget>
<output>124</output>

<gadget id="calculator">124 / 4</gadget>
<output>31</output>
<result>31</result>

Choices:
A. 30
B. 31
C. 32
D. 33
E. 34

divide(subtract(subtract(subtract(subtract(134, const_1), const_2), const_3), const_4), 4)

Explanation: "the bottom row has x bricks x + x - 1 + x - 2 + x - 3 = 134 4 x - 6 = 134 4 x = 128 x = 32 answer : c"


Question: if paint costs $ 3.10 per quart , and a quart covers 20 square feet , how much will it cost to paint the outside of a cube 10 feet on each edge ?

<gadget id="calculator">3.1 / 20</gadget>
<output>0.155</output>

<gadget id="calculator">6 * (10 ** 2)</gadget>
<output>600</output>

<gadget id="calculator">0.155 * 600</gadget>
<output>93</output>
<result>93</result>

Choices:
A. $ 1.60
B. $ 16.00
C. $ 93.00
D. $ 108.00
E. $ 196.00

Explanation: "total surface area = 6 a ^ 2 = 6 * 10 * 10 = 600 each quart covers 20 sqr ft thus total number of quarts = 600 / 20 = 30 cost will be 30 * 3.1 = $ 93 ans : c"


Question: a man engaged a servant on the condition that he would pay him rs . 1000 and a uniform after one year service . he served only for 9 months and received uniform and rs . 550 , find the price of the uniform ?

<gadget id="calculator">9 * 1_000</gadget>
<output>9_000</output>

<gadget id="calculator">3 * 4</gadget>
<output>12</output>

<gadget id="calculator">12 * 550</gadget>
<output>6_600</output>

<gadget id="calculator">9_000 - 6_600</gadget>
<output>2_400</output>

<gadget id="calculator">12 * 1</gadget>
<output>12</output>

<gadget id="calculator">2_400 / 12</gadget>
<output>200</output>

<gadget id="calculator">200 * 4</gadget>
<output>800</output>
<result>800</result>

Choices:
A. s . 80
B. s . 85
C. s . 90
D. s . 800
E. s . 120

multiply(divide(subtract(multiply(9, 1000), multiply(multiply(const_3, const_4), 550)), multiply(multiply(const_3, const_4), const_1)), const_4)

Explanation: "9 / 12 = 3 / 4 * 1000 = 750 550 - - - - - - - - - - - - - 200 1 / 4 - - - - - - - - 200 1 - - - - - - - - - ? = > rs . 800 answer : d"


Question: a glass was filled with 24 ounces of water , and 0.06 ounce of the water evaporated each day during a 12 - day period . what percent of the original amount of water evaporated during this period ?

<gadget id="calculator">0.06 * 12</gadget>
<output>0.72</output>

<gadget id="calculator">0.72 / 24</gadget>
<output>0.03</output>

<gadget id="calculator">0.03 * 100</gadget>
<output>3</output>
<result>3</result>

Choices:
A. 0.003 %
B. 0.03 %
C. 3 %
D. 2 %
E. 30 %

multiply(divide(multiply(0.06, 12), 24), const_100)

Explanation: "in 12 days 12 * 0.06 = 0.72 ounces of water evaporated , which is 0.72 / 24 â ˆ — 100 = 3 of the original amount of water . answer : c ."


Question: i chose a number and divide it by 4 . then i subtracted 18 from the result and got 7 . what was the number i chose ?

<gadget id="calculator">18 + 7</gadget>
<output>25</output>

<gadget id="calculator">25 * 4</gadget>
<output>100</output>
<result>100</result>

Choices:
A. 600
B. 100
C. 800
D. 900
E. none

Explanation: solution : let x be the number i chose , then x / 4 â ˆ ’ 18 = 7 x / 4 = 25 x = 100 answer b


Question: there are 76 persons . 54 can read hindu , 43 can read times , 37 can read deccan and 15 can read all . if 24 can read hindu and deccan and 27 can read deccan and times then what is the number of persons who read only times and hindu .

<gadget id="calculator">24 - 15</gadget>
<output>9</output>

<gadget id="calculator">27 - 15</gadget>
<output>12</output>

<gadget id="calculator">9 + 12</gadget>
<output>21</output>
<result>21</result>

Choices:
A. 21
B. 22
C. 23
D. 24
E. 25

Explanation: let ' a ' can be read hindu , let ' b ' can be read times , let ' c ' can be read deccan , from the given data : n ( aubuc ) = 76 , n ( a ) = 54 , n ( b ) = 43 , n ( c ) = 37 , n ( anbnc ) = 15 , n ( anc ) = 24 , n ( bnc ) = 27 , n ( anb ) = ? n ( aubuc ) = n ( a ) + n ( b ) + n ( c ) - n ( anb ) - n ( bnc ) - n ( anc ) + n ( anbnc ) = = > 76 = 54 + 43 + 37 - n ( anb ) - 24 - 27 + 15 = = > n ( anb ) = 54 + 43 + 37 + 15 - 24 - 27 - 76 = = > n ( anb ) = 149 - 127 = = > n ( anb ) = 22 answer : b


Question: the original price of a suit is $ 100 . the price increased 20 % , and after this increase , the store published a 20 % off coupon for a one - day sale . given that the consumers who used the coupon on sale day were getting 20 % off the increased price , how much did these consumers pay for the suit ?

<gadget id="calculator">100 * 20</gadget>
<output>2_000</output>

<gadget id="calculator">2_000 / 100</gadget>
<output>20</output>

<gadget id="calculator">100 + 20</gadget>
<output>120</output>

<gadget id="calculator">120 * 20</gadget>
<output>2_400</output>

<gadget id="calculator">2_400 / 100</gadget>
<output>24</output>

<gadget id="calculator">120 - 24</gadget>
<output>96</output>
<result>96</result>

Choices:
A. $ 88
B. $ 96
C. $ 100
D. $ 106
E. $ 110

subtract(add(100, divide(multiply(100, 20), const_100)), divide(multiply(add(100, divide(multiply(100, 20), const_100)), 20), const_100))

Explanation: "0.8 * ( 1.2 * 100 ) = $ 96 the answer is b ."


Question: the average runs scored by a batsman in 20 matches is 40 . in the next 30 matches the batsman scored an average of 20 runs . find his average in all the 50 matches ?

<gadget id="calculator">40 * 20</gadget>
<output>800</output>

<gadget id="calculator">20 * 30</gadget>
<output>600</output>

<gadget id="calculator">800 + 600</gadget>
<output>1_400</output>

<gadget id="calculator">20 + 30</gadget>
<output>50</output>

<gadget id="calculator">1_400 / 50</gadget>
<output>28</output>
<result>28</result>

Choices:
A. 31
B. 46
C. 28
D. 13
E. 12

divide(add(multiply(40, 20), multiply(20, 30)), add(20, 30))

Explanation: "total score of the batsman in 20 matches = 800 . total score of the batsman in the next 30 matches = 600 . total score of the batsman in the 50 matches = 1400 . average score of the batsman = 1400 / 50 = 28 . answer : c"


Question: in an election between two candidates , one got 55 % of the total valid votes , 20 % of the votes were invalid . if the total number of votes was 5000 , the number of valid votes that the other candidate got , was :

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">55 / 100</gadget>
<output>11/20 = around 0.55</output>

<gadget id="calculator">1 - (11/20)</gadget>
<output>9/20 = around 0.45</output>

<gadget id="calculator">(4/5) * (9/20)</gadget>
<output>9/25 = around 0.36</output>

<gadget id="calculator">(9/25) * 5_000</gadget>
<output>1_800</output>
<result>1_800</result>

Choices:
A. 1800
B. 2700
C. 2900
D. 2200
E. 2300

multiply(multiply(subtract(const_1, divide(20, const_100)), subtract(const_1, divide(55, const_100))), 5000)

Explanation: "a number of valid votes = 80 % of 5000 = 4000 . valid votes polled by other candidate = 45 % of 4000 = ( 45 / 100 x 4000 ) = 1800 ."


Question: for a group of n people , k of whom are of the same sex , the ( n - k ) / n expression yields an index for a certain phenomenon in group dynamics for members of that sex . for a group that consists of 20 people , 8 of whom are females , by how much does the index for the females exceed the index for the males in the group ?

<gadget id="calculator">20 - 8</gadget>
<output>12</output>

<gadget id="calculator">12 / 20</gadget>
<output>3/5 = around 0.6</output>

<gadget id="calculator">8 / 20</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">(3/5) - (2/5)</gadget>
<output>1/5 = around 0.2</output>
<result>1/5 = around 0.2</result>

Choices:
A. 0.05
B. 0.0625
C. 0.2
D. 0.25
E. 0.6

subtract(divide(subtract(20, 8), 20), divide(8, 20))

Explanation: index for females = ( 20 - 8 ) / 20 = 3 / 5 = 0.6 index for males = ( 20 - 12 / 20 = 2 / 5 = 0.4 index for females exceeds males by 0.6 - 0.4 = 0.2 answer : c


Question: chocolate bars are sold in packages of 4 or 9 only . if mark bought 97 chocolate bars exactly , what could be the number of large packs mark bought ?

<gadget id="calculator">4 * 4</gadget>
<output>16</output>

<gadget id="calculator">97 - 16</gadget>
<output>81</output>

<gadget id="calculator">81 / 9</gadget>
<output>9</output>
<result>9</result>

Choices:
A. 3
B. 4
C. 8
D. 9
E. 13

Explanation: let number of packs of four = f let number of packs of nine = n 4 f + 9 n = 97 now , we need to test for values of n . since sum 97 is odd and 4 f will always be even , n ca n ' t be even . now , we can test for values e = 2 , 4 and 6 4 * 4 + 9 * 9 = 16 + 81 = 97 answer d


Question: the percentage profit earned by selling an article for rs . 1920 is equal to the percentage loss incurred by selling the same article for rs . 1280 . at what price should the article be sold to make 20 % profit ?

<gadget id="calculator">100 + 20</gadget>
<output>120</output>

<gadget id="calculator">120 / 100</gadget>
<output>6/5 = around 1.2</output>

<gadget id="calculator">1_920 + 1_280</gadget>
<output>3_200</output>

<gadget id="calculator">3_200 / 2</gadget>
<output>1_600</output>

<gadget id="calculator">(6/5) * 1_600</gadget>
<output>1_920</output>
<result>1_920</result>

Choices:
A. 2000
B. 2778
C. 2299
D. 1920
E. 2771

multiply(divide(add(const_100, 20), const_100), divide(add(1920, 1280), const_2))

Explanation: "let c . p . be rs . x . then , ( 1920 - x ) / x * 100 = ( x - 1280 ) / x * 100 1920 - x = x - 1280 2 x = 3200 = > x = 1600 required s . p . = 120 % of rs . 1600 = 120 / 100 * 1600 = rs . 1920 . answer : d"


Question: find the least number must be subtracted from 531742 so that remaining no . is divisible by 3 ?

<gadget id="calculator">531_742 / 3</gadget>
<output>531_742/3 = around 177_247.333333</output>

<gadget id="calculator">floor(531_742/3)</gadget>
<output>177_247</output>

<gadget id="calculator">177_247 * 3</gadget>
<output>531_741</output>

<gadget id="calculator">531_742 - 531_741</gadget>
<output>1</output>
<result>1</result>

Choices:
A. 4
B. 5
C. 1
D. 2
E. 3

subtract(531742, multiply(floor(divide(531742, 3)), 3))

Explanation: "on dividing 531742 by 3 we get the remainder 1 , so 1 should be subtracted c"


Question: 10 men can cut 10 trees in 2 hours . if 2 men leave the job , how many trees will be cut in 3 hours ?

<gadget id="calculator">10 - 2</gadget>
<output>8</output>

<gadget id="calculator">10 / 2</gadget>
<output>5</output>

<gadget id="calculator">5 / 10</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">8 * (1/2)</gadget>
<output>4</output>

<gadget id="calculator">4 * 3</gadget>
<output>12</output>
<result>12</result>

Choices:
A. 12
B. 15
C. 16
D. 18
E. 20

multiply(multiply(subtract(10, 2), divide(divide(10, 2), 10)), 3)

Explanation: 10 men - working 2 hrs - cut 10 trees 1 men - working 1 hr - cuts = 10 / 10 * 2 thus 8 men - working 3 hrs - cut = 10 * 8 * 3 / 10 * 2 = 12 trees answer is a


Question: if x and y are integers such that x ^ 2 = 2 y and xy = 32 , then x – y = ?

<gadget id="calculator">32 * 2</gadget>
<output>64</output>

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">64 ** (1/3)</gadget>
<output>4</output>

<gadget id="calculator">32 / 4</gadget>
<output>8</output>

<gadget id="calculator">4 - 8</gadget>
<output>-4</output>
<result>-4</result>

Choices:
A. - 30
B. - 20
C. - 5
D. - 4
E. 20

subtract(power(multiply(32, 2), const_0_33), divide(32, power(multiply(32, 2), const_0_33)))

Explanation: "here x and y are integers . x ^ 2 = 2 y , xy = 32 . substitute ( x ^ 2 ) / 2 = y in xy = > x ^ 3 = 32 * 2 = > x ^ 3 = 64 . here x 3 is positive , x is also positive . x = 4 then y = 8 . x - y = - 4 so option d is correct"


Question: a shopkeeper loses 15 % , if an article is sold for $ 102 . what should be the selling price of the article to gain 20 % ?

<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>

<gadget id="calculator">1 - (3/20)</gadget>
<output>17/20 = around 0.85</output>

<gadget id="calculator">102 / (17/20)</gadget>
<output>120</output>

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">120 * (1/5)</gadget>
<output>24</output>

<gadget id="calculator">120 + 24</gadget>
<output>144</output>
<result>144</result>

Choices:
A. $ 165
B. $ 174
C. $ 144
D. $ 164
E. $ 183

add(divide(102, subtract(const_1, divide(15, const_100))), multiply(divide(102, subtract(const_1, divide(15, const_100))), divide(20, const_100)))

Explanation: "c $ 144 given that sp = $ 102 and loss = 15 % cp = [ 100 ( sp ) ] / ( 100 - l % ) = ( 100 * 102 ) / 85 = 20 * 6 = $ 120 . to get 20 % profit , new sp = [ ( 100 + p % ) cp ] / 100 = ( 120 * 120 ) / 100 = $ 144"


Question: after decreasing 24 % in the price of an article costs rs . 912 . find the actual cost of an article ?

<gadget id="calculator">24 / 100</gadget>
<output>6/25 = around 0.24</output>

<gadget id="calculator">1 - (6/25)</gadget>
<output>19/25 = around 0.76</output>

<gadget id="calculator">912 / (19/25)</gadget>
<output>1_200</output>
<result>1_200</result>

Choices:
A. 226
B. 255
C. 1200
D. 2771
E. 332

divide(912, subtract(const_1, divide(24, const_100)))

Explanation: "cp * ( 76 / 100 ) = 912 cp = 12 * 100 = > cp = 1200 answer : c"


Question: a man sells an article at 10 % gain . had be sold at for rs . 60 / - more he could have gained 20 % what is cost price of article

<gadget id="calculator">20 - 10</gadget>
<output>10</output>

<gadget id="calculator">60 / 10</gadget>
<output>6</output>

<gadget id="calculator">6 * 100</gadget>
<output>600</output>
<result>600</result>

Choices:
A. rs . 500
B. rs . 600
C. rs . 650
D. rs . 760
E. rs . 800

multiply(divide(60, subtract(20, 10)), const_100)

Explanation: first selling price = 110 % - - - - - > x rupees = sold at for rs . 60 / - = 120 % - - - - - > x + 60 rupees ~ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 10 % - - - - - - - - > 60 100 % - - - - - - - > rs . 600 / - option ' b '


Question: if x ¤ y = ( x + y ) ^ 2 - ( x - y ) ^ 2 . then √ 7 ¤ √ 7 =

<gadget id="calculator">7 ** (1/2)</gadget>
<output>sqrt(7) = around 2.645751</output>

<gadget id="calculator">(sqrt(7)) + (sqrt(7))</gadget>
<output>2*sqrt(7) = around 5.291503</output>

<gadget id="calculator">(2*sqrt(7)) ** 2</gadget>
<output>28</output>
<result>28</result>

Choices:
A. 0
B. 5
C. 10
D. 15
E. 28

Explanation: "x = √ 7 and y also = √ 7 applying the function ( √ 7 + √ 7 ) ^ 2 - ( √ 7 - √ 7 ) ^ 2 = ( 2 √ 7 ) ^ 2 - 0 = 4 x 7 = 28 . note : alternative approach is the entire function is represented as x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) which can be simplified as ( x + y + x - y ) ( x + y - ( x - y ) ) = ( 2 x ) ( 2 y ) = 4 xy . substituting x = √ 7 and y = √ 7 you get the answer 28 . answer e"


Question: 6 people can do work in 80 days how much people they required to complete the work in 16 days ?

<gadget id="calculator">6 * 80</gadget>
<output>480</output>

<gadget id="calculator">480 / 16</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 10
B. 20
C. 30
D. 40
E. 50

Explanation: man and days concept . . . 6 m * 80 d = m * 16 d solve it , total no of people required is 30 ; answer : c


Question: the average of 10 consecutive integers is 15 . then , 9 is deducted from the first consecutive number , 8 is deducted from the second , 7 is deducted form the third , and so on until the last number which remains unchanged . what is the new average ?

<gadget id="calculator">10 * 15</gadget>
<output>150</output>

<gadget id="calculator">4 + 1</gadget>
<output>5</output>

<gadget id="calculator">5 * 9</gadget>
<output>45</output>

<gadget id="calculator">150 - 45</gadget>
<output>105</output>

<gadget id="calculator">105 / 10</gadget>
<output>21/2 = around 10.5</output>
<result>21/2 = around 10.5</result>

Choices:
A. 10
B. 10.5
C. 11
D. 11.5
E. 12

divide(subtract(multiply(10, 15), multiply(add(const_4, const_1), 9)), 10)

Explanation: "the total subtracted is ( 9 + 8 + . . . + 1 ) = ( 9 * 10 ) / 2 = 45 on average , each number will be reduced by 45 / 10 = 4.5 therefore , the overall average will be reduced by 4.5 the answer is b ."


Question: on a map the distance between two mountains is 312 inches . the actual distance between the mountains is 140 km . ram is camped at a location that on the map is 34 inch from the base of the mountain . how many km is he from the base of the mountain ?

<gadget id="calculator">34 * 140</gadget>
<output>4_760</output>

<gadget id="calculator">4_760 / 312</gadget>
<output>595/39 = around 15.25641</output>
<result>595/39 = around 15.25641</result>

Choices:
A. 14.83
B. 14.81
C. 14.8
D. 15.25
E. 14.12

Explanation: "explanation : since 312 inch = 140 km so 1 inch = 140 / 312 km so 34 inch = ( 140 ã — 34 ) / 312 = 15.25 km answer : d"


Question: a man invested rs . 14,400 in rs . 100 shares of a company at 20 % premium . if the company declares 8 % dividend at the end of the year , then how much does he get ?

<gadget id="calculator">10 * 1_000</gadget>
<output>10_000</output>

<gadget id="calculator">4 * 1_000</gadget>
<output>4_000</output>

<gadget id="calculator">10_000 + 4_000</gadget>
<output>14_000</output>

<gadget id="calculator">4 * 100</gadget>
<output>400</output>

<gadget id="calculator">14_000 + 400</gadget>
<output>14_400</output>

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">100 * (1/5)</gadget>
<output>20</output>

<gadget id="calculator">100 + 20</gadget>
<output>120</output>

<gadget id="calculator">14_400 / 120</gadget>
<output>120</output>

<gadget id="calculator">100 * 120</gadget>
<output>12_000</output>

<gadget id="calculator">8 / 100</gadget>
<output>2/25 = around 0.08</output>

<gadget id="calculator">12_000 * (2/25)</gadget>
<output>960</output>
<result>960</result>

Choices:
A. rs . 500
B. rs . 600
C. rs . 960
D. rs . 720
E. none

multiply(multiply(100, divide(add(add(multiply(const_10, const_1000), multiply(const_4, const_1000)), multiply(const_4, 100)), add(100, multiply(100, divide(20, 100))))), divide(8, 100))

Explanation: "solution number of shares = ( 14400 / 120 ) = 120 . face value = rs . ( 100 x 120 ) = rs . 12000 . annual income = rs . ( 8 / 100 x 12000 ) = rs . 960 . answer c"


Question: a man took loan from a bank at the rate of 12 % p . a . s . i . after 20 years he had to pay rs . 1500 interest only for the period . the principal amount borrowed by him was ?

<gadget id="calculator">1_500 * 100</gadget>
<output>150_000</output>

<gadget id="calculator">150_000 / 20</gadget>
<output>7_500</output>

<gadget id="calculator">7_500 / 12</gadget>
<output>625</output>
<result>625</result>

Choices:
A. 625
B. 700
C. 950
D. 825
E. 630

divide(divide(multiply(1500, const_100), 20), 12)

Explanation: principal = ( 100 * 1500 ) / ( 12 * 20 ) = rs . 625 answer : a


Question: david and lewis leave chennai for tirupati simultaneously at 7 a . m in the morning driving in two cars at speeds of 60 mph and 80 mph respectively . as soon as lewis reaches tirupati he returns back to chennai along the same route and meets david on the way back . if the distance between the two cities is 160 miles , how far from chennai did david and lewis meet ?

<gadget id="calculator">2 * 60</gadget>
<output>120</output>
<result>120</result>

Choices:
A. 100 mlies
B. 120 miles
C. 90 miles
D. 95 miles
E. 110 miles

Explanation: time taken by lewis to reach tirupati = 160 / 80 = 2 hours in 2 hours , david travels 60 * 2 = 120 miles so distance at which they meet should be greater than 120 miles . only b satisfies . answer is b .


Question: the product of x and y is a constant . if the value of x is increased by 60 % , by what percentage must the value of y be decreased ?

<gadget id="calculator">100 + 60</gadget>
<output>160</output>

<gadget id="calculator">100 / 160</gadget>
<output>5/8 = around 0.625</output>

<gadget id="calculator">1 - (5/8)</gadget>
<output>3/8 = around 0.375</output>

<gadget id="calculator">(3/8) * 100</gadget>
<output>75/2 = around 37.5</output>
<result>75/2 = around 37.5</result>

Choices:
A. 30 %
B. 32 %
C. 35 %
D. 37.5 %
E. 40 %

multiply(subtract(const_1, divide(const_100, add(const_100, 60))), const_100)

Explanation: "x * y = constt . let x = y = 100 in beginning i . e . x * y = 100 * 100 = 10000 x ( 100 ) - - - becomes - - - > 1.6 x ( 120 ) i . e . 160 * new ' y ' = 10000 i . e . new ' y ' = 10000 / 160 = 62.5 i . e . y decreases from 100 to 62.5 i . e . decrease of 37.5 % answer : option d"


Question: linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 400 , what were her original savings ?

<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">1 - (3/4)</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">400 / (1/4)</gadget>
<output>1_600</output>
<result>1_600</result>

Choices:
A. $ 1500
B. $ 1600
C. $ 1700
D. $ 1800
E. $ 1900

divide(400, subtract(const_1, divide(3, 4)))

Explanation: if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 400 . so 1 / 4 of her savings is $ 400 . so her original savings are 4 times $ 400 = $ 1600 correct answer b


Question: city a to city b , andrew drove for 1 hour at 50 mph and for 3 hours at 60 mph . what was the average speed for the whole trip ?

<gadget id="calculator">50 * 1</gadget>
<output>50</output>

<gadget id="calculator">60 * 3</gadget>
<output>180</output>

<gadget id="calculator">50 + 180</gadget>
<output>230</output>

<gadget id="calculator">3 + 1</gadget>
<output>4</output>

<gadget id="calculator">230 / 4</gadget>
<output>115/2 = around 57.5</output>
<result>115/2 = around 57.5</result>

Choices:
A. 56
B. 57.5
C. 58.9
D. 61.4
E. 62

divide(add(multiply(50, 1), multiply(60, 3)), add(3, 1))

Explanation: the total distance is 1 × 50 + 3 × 60 = 2301 × 50 + 3 × 60 = 230 . and the total time is 4 hours . hence , average speed = ( total distancetotal time ) = 2304 = 57.5 b


Question: laxmi and prasanna set on a journey . laxmi moves northwards at a speed of 15 kmph and prasanna moves southward at a speed of 45 kmph . how far will be prasanna from laxmi after 60 minutes ?

<gadget id="calculator">15 + 45</gadget>
<output>60</output>
<result>60</result>

Choices:
A. 11
B. 50
C. 28
D. 27
E. 60

Explanation: "explanation : we know 60 min = 1 hr total northward laxmi ' s distance = 15 kmph x 1 hr = 15 km total southward prasanna ' s distance = 45 kmph x 1 hr = 45 km total distance between prasanna and laxmi is = 15 + 45 = 60 km . answer : e"


Question: car x began traveling at an average speed of 35 miles per hour . after 84 minutes , car y began traveling at an average speed of 42 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ?

<gadget id="calculator">84 / 60</gadget>
<output>7/5 = around 1.4</output>

<gadget id="calculator">(7/5) * 35</gadget>
<output>49</output>

<gadget id="calculator">42 - 35</gadget>
<output>7</output>

<gadget id="calculator">49 / 7</gadget>
<output>7</output>

<gadget id="calculator">35 * 7</gadget>
<output>245</output>
<result>245</result>

Choices:
A. 140
B. 175
C. 210
D. 245
E. 270

multiply(35, divide(multiply(divide(84, const_60), 35), subtract(42, 35)))

Explanation: in 84 minutes , car x travels 49 miles . car y gains 7 miles each hour , so it takes 7 hours to catch car x . in 7 hours , car x travels 245 miles . the answer is d .


Question: the cost of producing x tools by a company is given by c ( x ) = 600 x + 5500 ( in $ ) a ) what is the cost of 100 tools ?

<gadget id="calculator">100 * 600</gadget>
<output>60_000</output>

<gadget id="calculator">60_000 + 5_500</gadget>
<output>65_500</output>
<result>65_500</result>

Choices:
A. 65500 $
B. 125800 $
C. 125900 $
D. 6500 $
E. 122500 $

Explanation: solution c ( 100 ) = 600 * 100 + 5500 = 125500 $ answer a


Question: how many odd numbers between 10 and 1,000 are the squares of integers ?

<gadget id="calculator">10 + 4</gadget>
<output>14</output>
<result>14</result>

Choices:
A. 12
B. 13
C. 14
D. 15
E. 16

Explanation: the square of an odd number is an odd number : 10 < odd < 1,000 10 < odd ^ 2 < 1,000 3 . something < odd < 31 . something ( by taking the square root ) . so , that odd number could be any odd number from 5 to 31 , inclusive : 5 , 7 , 9 , 11 , 13 , 15 , 17 , 19 , 21 , 23 , 25 , 27 , 29 , and 31 . 14 numbers . answer : c .


Question: a man can row 11 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and back . what is the total distance traveled by the man ?

<gadget id="calculator">11 + 1.2</gadget>
<output>12.2</output>

<gadget id="calculator">11 - 1.2</gadget>
<output>9.8</output>

<gadget id="calculator">12.2 * 9.8</gadget>
<output>119.56</output>

<gadget id="calculator">12.2 + 9.8</gadget>
<output>22</output>

<gadget id="calculator">119.56 / 22</gadget>
<output>5.434545</output>

<gadget id="calculator">5.434545 * 2</gadget>
<output>10.86909</output>
<result>10.86909</result>

Choices:
A. 6.24 km
B. 6 km
C. 5.76 km
D. 5.66 km
E. 10.87 km

multiply(divide(multiply(add(11, 1.2), subtract(11, 1.2)), add(add(11, 1.2), subtract(11, 1.2))), const_2)

Explanation: "m = 11 s = 1.2 ds = 12.2 us = 9.8 x / 12.2 + x / 9.8 = 1 x = 5.43 d = 5.43 * 2 = 10.87 answer : e"


Question: if the l . c . m of two numbers is 720 and their product is 38880 , find the h . c . f of the numbers .

<gadget id="calculator">38_880 / 720</gadget>
<output>54</output>
<result>54</result>

Choices:
A. 50
B. 30
C. 125
D. 54
E. none of these

Explanation: "h . c . f = ( product of the numbers ) / ( their l . c . m ) = 38880 / 720 = 54 . answer : d"


Question: a , b and c have rs . 400 between them , a and c together have rs . 200 and b and c rs . 350 . how much does c have ?

<gadget id="calculator">200 + 350</gadget>
<output>550</output>

<gadget id="calculator">550 - 400</gadget>
<output>150</output>
<result>150</result>

Choices:
A. 150
B. 140
C. 130
D. 120
E. 110

Explanation: "a + b + c = 400 a + c = 200 b + c = 350 - - - - - - - - - - - - - - a + b + 2 c = 550 a + b + c = 400 - - - - - - - - - - - - - - - - c = 150 answer : a"


Question: an agent , gets a commission of 2.5 % on the sales of cloth . if on a certain day , he gets rs . 12.50 as commission , the cloth sold through him on that day is worth

<gadget id="calculator">2.5 / 100</gadget>
<output>0.025</output>

<gadget id="calculator">12.5 / 0.025</gadget>
<output>500</output>
<result>500</result>

Choices:
A. 333
B. 500
C. 887
D. 299
E. 132

Explanation: explanation : let the total sale be rs . x . then , 2.5 % . of x = 12.50 < = > ( 25 / 100 * 1 / 100 * x ) = 125 / 10 < = > x = 500 . answer : b ) 500


Question: an empty wooden vessel weighs 20 % of its total weight when filled with paint . if the weight of a partially filled vessel is one half that of a completely filled vessel , what fraction of the vessel is filled .

<gadget id="calculator">20 / 2</gadget>
<output>10</output>

<gadget id="calculator">10 - 1</gadget>
<output>9</output>

<gadget id="calculator">20 - 1</gadget>
<output>19</output>

<gadget id="calculator">9 / 19</gadget>
<output>9/19 = around 0.473684</output>
<result>9/19 = around 0.473684</result>

Choices:
A. 3 / 5
B. 5 / 9
C. 1 / 24
D. 9 / 19
E. 2 / 5

divide(subtract(divide(20, const_2), const_1), subtract(20, const_1))

Explanation: an empty wooden vessel weighs 20 % of its total weight when filled with paint : vessel = 0.2 ( vessel + paint ) ; 20 v = v + p ( so the weight of completely filled vessel is 10 v ) p = 19 v ( so the weight of the paint when the vessels is completely filled is 19 v ) . the weight of a partially filled vessel is one half that of a completely filled vessel : v + p ' = 1 / 2 * 20 v ; p ' = 9 v ( so the weight of the paint when the vessels is partially filled is 9 v ) . what fraction of the vessel is filled ? so , we need to find the ratio of the weight of the paint when the vessel iscompletely filledto the weight of the paint when the vessel ispartially filled : p ' / p = 9 v / 19 v = 9 / 19 . answer : d .


Question: a cycle is bought for rs . 900 and sold for rs . 990 , find the gain percent ?

<gadget id="calculator">990 - 900</gadget>
<output>90</output>

<gadget id="calculator">90 / 900</gadget>
<output>1/10 = around 0.1</output>

<gadget id="calculator">(1/10) * 100</gadget>
<output>10</output>
<result>10</result>

Choices:
A. 39 %
B. 20 %
C. 23 %
D. 74 %
E. 10 %

multiply(divide(subtract(990, 900), 900), const_100)

Explanation: "900 - - - - 90 100 - - - - ? = > 10 % answer : e"


Question: ( 0.0066 ) ( 3.6 ) / ( 0.04 ) ( 0.1 ) ( 0.006 ) =

<gadget id="calculator">0.0066 * 3.6</gadget>
<output>0.02376</output>

<gadget id="calculator">0.04 * 0.1</gadget>
<output>0.004</output>

<gadget id="calculator">0.004 * 0.006</gadget>
<output>0.000024</output>

<gadget id="calculator">0.02376 / 0.000024</gadget>
<output>990</output>
<result>990</result>

Choices:
A. 990
B. 99.0
C. 9.9
D. 0.99
E. 0.099

Explanation: "( 0.0066 ) ( 3.6 ) / ( 0.04 ) ( 0.1 ) ( 0.006 ) = 0.0060 * 360 / 4 * ( 0.1 ) ( 0.006 ) = 0.066 * 90 / 1 * 0.006 = 66 * 90 / 6 = 11 * 90 = 990 answer : a"


Question: in the manufacture of a certain product , 9 percent of the units produced are defective and 5 percent of the defective units are shipped for sale . what percent of the units produced are defective units that are shipped for sale ?

<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>

<gadget id="calculator">9 * (1/20)</gadget>
<output>9/20 = around 0.45</output>
<result>9/20 = around 0.45</result>

Choices:
A. 0.15 %
B. 0.45 %
C. 0.8 %
D. 1.25 %
E. 2.0 %

Explanation: "0.09 * 0.05 = 0.0045 = 0.45 % the answer is b ."


Question: if the sales tax reduced from 3 1 / 2 % to 3 1 / 3 % , then what difference does it make to a person who purchases an article with market price of rs . 9600 ?

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">(1/2) + 3</gadget>
<output>7/2 = around 3.5</output>

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">(1/3) + 3</gadget>
<output>10/3 = around 3.333333</output>

<gadget id="calculator">(7/2) - (10/3)</gadget>
<output>1/6 = around 0.166667</output>

<gadget id="calculator">(1/6) * 9_600</gadget>
<output>1_600</output>

<gadget id="calculator">1_600 / 100</gadget>
<output>16</output>
<result>16</result>

Choices:
A. 11
B. 13
C. 14
D. 18
E. 16

divide(multiply(subtract(add(divide(1, 2), 3), add(divide(1, 3), 3)), 9600), const_100)

Explanation: required difference = [ 3 ½ % of rs . 9600 ] – [ 3 1 / 3 % of rs . 9600 ] = [ ( 7 / 20 - ( 10 / 3 ) ] % of rs . 9600 = 1 / 6 % of rs . 9600 = rs . [ ( 1 / 6 ) 8 ( 1 / 100 ) * 9600 ] = rs . 16 . answer is e .


Question: a 6 % stock yields 8 % . the market value of the stock is :

<gadget id="calculator">100 / 8</gadget>
<output>25/2 = around 12.5</output>

<gadget id="calculator">(25/2) * 6</gadget>
<output>75</output>
<result>75</result>

Choices:
A. 33
B. 75
C. 44
D. 27
E. 91

Explanation: for an income of rs . 8 , investment = rs . 100 . for an income of rs . 6 , investment = rs . 100 x 6 = rs . 75 . 8 market value of rs . 100 stock = rs . 75 . answer : b


Question: john bought a shirt on sale for 25 % off the original price and another 25 % off the discounted price . if the final price was $ 16 , what was the price before the first discount ?

<gadget id="calculator">100 * 100</gadget>
<output>10_000</output>

<gadget id="calculator">10_000 * 16</gadget>
<output>160_000</output>

<gadget id="calculator">100 - 25</gadget>
<output>75</output>

<gadget id="calculator">75 * 100</gadget>
<output>7_500</output>

<gadget id="calculator">75 * 25</gadget>
<output>1_875</output>

<gadget id="calculator">7_500 - 1_875</gadget>
<output>5_625</output>

<gadget id="calculator">160_000 / 5_625</gadget>
<output>256/9 = around 28.444444</output>
<result>256/9 = around 28.444444</result>

Choices:
A. $ 18.44
B. $ 28.44
C. $ 48.44
D. $ 58.44
E. $ 38.44

divide(multiply(multiply(const_100, const_100), 16), subtract(multiply(subtract(const_100, 25), const_100), multiply(subtract(const_100, 25), 25)))

Explanation: "let x be the price before the first discount . the price after the first discount is x - 25 % x ( price after first discount ) a second discount of 25 % of the discounted price after which the final price is 16 ( x - 25 % x ) - 25 % ( x - 25 % x ) = 16 solve for x x = $ 28.44 correct answer b"


Question: in an election between the two candidates , the candidates who gets 60 % of votes polled is winned by 280 votes majority . what is the total number of votes polled ?

<gadget id="calculator">100 * 280</gadget>
<output>28_000</output>

<gadget id="calculator">100 - 60</gadget>
<output>40</output>

<gadget id="calculator">60 - 40</gadget>
<output>20</output>

<gadget id="calculator">28_000 / 20</gadget>
<output>1_400</output>
<result>1_400</result>

Choices:
A. 1400
B. 1600
C. 1800
D. 2000
E. 2100

divide(multiply(const_100, 280), subtract(60, subtract(const_100, 60)))

Explanation: "note : majority ( 20 % ) = difference in votes polled to win ( 60 % ) & defeated candidates ( 40 % ) 20 % = 60 % - 40 % 20 % - - - - - > 280 ( 20 × 14 = 280 ) 100 % - - - - - > 1400 ( 100 × 14 = 1400 ) a )"


Question: the height of a cylinder is 60 cm and the diameter of its base is 5 cm . the total surface area of the cylinder is

<gadget id="calculator">5 / 2</gadget>
<output>5/2 = around 2.5</output>

<gadget id="calculator">2 * pi * (5/2) * ((5/2) + 60)</gadget>
<output>625*pi/2 = around 981.747704</output>
<result>625*pi/2 = around 981.747704</result>

Choices:
A. 918.14
B. 981.41
C. 982.14
D. 928.41
E. none of them

Explanation: given h = 60 cm and r = 5 / 2 cm total surface area = 2 π rh + 2 & pir ( power 2 ) = 2 π r ( h + r ) = [ 2 × 22 / 7 × 5 / 2 × ( 60 + 5 / 2 ) ] cm ( power 2 ) = [ 44 / 7 × 5 / 2 × ( ( 120 + 5 ) / 2 ) ] cm ( power 2 ) = 22 / 7 × 5 × 125 / 2 cm ( power 2 ) = ( 55 × 125 ) / 7 cm ( power 2 ) = 6875 / 7 cm ( power 2 ) = 982.14 cm ( power 2 ) answer is c .


Question: a tank is filled by 3 pipes a , b , c in 7 hours . pipe c is twice as fast as b and b is twice as fast as a . how much will pipe a alone take to fill the tank ?

<gadget id="calculator">2 * 2</gadget>
<output>4</output>

<gadget id="calculator">4 + 2</gadget>
<output>6</output>

<gadget id="calculator">6 + 1</gadget>
<output>7</output>

<gadget id="calculator">7 * 7</gadget>
<output>49</output>
<result>49</result>

Choices:
A. 25 hr
B. 35 hr
C. 40 hr
D. 49 hr
E. 50 hr

multiply(add(add(multiply(const_2, const_2), const_2), const_1), 7)

Explanation: "suppose pipe a alone take x hours to fill the tank then pipe b and c will take x / 2 and x / 4 hours respectively to fill the tank . 1 / x + 2 / x + 4 / x = 1 / 7 7 / x = 1 / 7 x = 49 hours answer is d"