all numbers from 1 to 200 ( in decimal system ) are written in base 6 and base 7 systems. how many of the numbers will have a non - zero units digit in both base 6 and base 7 notations?
Choose the correct answer
A) 143
B) 200
C) 157
D) 122
E) 132
<gadget id="calculator">200 / 6</gadget>
<output>100/3 = around 33.333333</output>

<gadget id="calculator">200 / 7</gadget>
<output>200/7 = around 28.571429</output>

<gadget id="calculator">(100/3) + (200/7)</gadget>
<output>1_300/21 = around 61.904762</output>

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

<gadget id="calculator">200 / 42</gadget>
<output>100/21 = around 4.761905</output>

<gadget id="calculator">(1_300/21) - (100/21)</gadget>
<output>400/7 = around 57.142857</output>

<gadget id="calculator">200 - (400/7)</gadget>
<output>1_000/7 = around 142.857143</output>

<result>A</result>
all numbers from 1 to 200 ( in decimal system ) are written in base 6 and base 7 systems. how many of the numbers will have a non - zero units digit in both base 6 and base 7 notations?
subtract(200, subtract(add(divide(200, 6), divide(200, 7)), divide(200, multiply(6, 7))))
detailed solution if a number written in base 6 ends with a zero , it should be a multiple of 6 . in other words , the question wants us to find all numbers from 1 to 200 that are not multiples of 6 or 7 . there are 33 multiples of 6 less than 201 . there are 28 multiples of 7 less than 201 . there are 4 multiples of 6 & 7 ( or multiple of 42 ) from 1 to 200 . so , total multiples of 6 or 7 less than 201 = 33 + 28 - 4 = 57 . number of numbers with non - zero units digit = 200 - 57 = 143 . correct answer : a