how many positive integers q between 200 and 300 ( both inclusive ) are not divisible by 2, 3 or 5? Pick
A) 3  B) 16  C) 75  D) 24  E) 26
<gadget id="calculator">300 - 200</gadget>
<output>100</output>

<gadget id="calculator">100 + 1</gadget>
<output>101</output>

<gadget id="calculator">300 / 2</gadget>
<output>150</output>

<gadget id="calculator">200 / 2</gadget>
<output>100</output>

<gadget id="calculator">150 - 100</gadget>
<output>50</output>

<gadget id="calculator">50 + 1</gadget>
<output>51</output>

<gadget id="calculator">101 - 51</gadget>
<output>50</output>

<gadget id="calculator">300 / 3</gadget>
<output>100</output>

<gadget id="calculator">200 / 3</gadget>
<output>200/3 = around 66.666667</output>

<gadget id="calculator">100 - (200/3)</gadget>
<output>100/3 = around 33.333333</output>

<gadget id="calculator">(100/3) + 1</gadget>
<output>103/3 = around 34.333333</output>

<gadget id="calculator">10 + 5</gadget>
<output>15</output>

<gadget id="calculator">15 + 2</gadget>
<output>17</output>

<gadget id="calculator">(103/3) - 17</gadget>
<output>52/3 = around 17.333333</output>

<gadget id="calculator">(52/3) + 1</gadget>
<output>55/3 = around 18.333333</output>

<gadget id="calculator">floor(55/3)</gadget>
<output>18</output>

<gadget id="calculator">50 - 18</gadget>
<output>32</output>

<gadget id="calculator">300 / 5</gadget>
<output>60</output>

<gadget id="calculator">200 / 5</gadget>
<output>40</output>

<gadget id="calculator">60 - 40</gadget>
<output>20</output>

<gadget id="calculator">20 + 1</gadget>
<output>21</output>

<gadget id="calculator">21 - 15</gadget>
<output>6</output>

<gadget id="calculator">32 - 6</gadget>
<output>26</output>

<result>E</result>
how many positive integers q between 200 and 300 ( both inclusive ) are not divisible by 2, 3 or 5?
subtract(subtract(subtract(add(subtract(300, 200), const_1), add(subtract(divide(300, 2), divide(200, 2)), const_1)), floor(add(subtract(add(subtract(divide(300, 3), divide(200, 3)), const_1), add(add(const_10, 5), 2)), const_1))), subtract(add(subtract(divide(300, 5), divide(200, 5)), const_1), add(const_10, 5)))
1 ) i figured there are 101 integers ( 300 - 200 + 1 = 101 ) . since the set begins with an even and ends with an even , there are 51 evens . 2 ) question says integers are not divisible by 2 , leaving all of the odds ( 101 - 51 = 50 integers ) . 3 ) question says integers are not divisible by 5 , removing all the integers ending in 5 ( already took out those ending in 0 ) . take out 10 integers ( 2 ? 5 , ? = 0 to 9 ) , leaving us with 40 integers . 4 ) now the painstaking part . we have to remove the remaining numbers that are multiples of 3 . those are 201 , 207 , 213 , 219 , 231 , 237 , 243 , 249 , 261 , 267 , 273 , 279 , 291 , and 297 . . . a total of 14 numbers . 26 numbers left ! 6 ) answer choice e .