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 one:	A) 143	B) 200	C) 157	D) 122	E) 132
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 &amp; 7 (or multiple of 42) from 1 to 200.   So, total multiples of 6 or 7 less than 201 = 33 + 28 - 4= 
<gadget id="calculator">33 + 28 - 4</gadget>
<output>57</output>
57. Number of numbers with non-zero units digit= 200 - 57= 
<gadget id="calculator">200 - 57</gadget>
<output>143</output>
143.   Correct 143nswer : 143
<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?