Question

How many numbers between 1 and 200 are exactly divisible by exactly two of 3, 9 and 27?

• A. 14
• B. 15
• C. 16
• D. 17

Answer 1

The correct option is B 15

All numbers divisible by 27 would also be divisible by 3 and 9. Numbers divisible by 9 but not by 27 would be divisible by 3 and 9 only and need to be counted to give us our answer. The numbers which satisfy the given condition are 9, 18, 36, 45, 63, 72. 90, 99, 117, 126. 144. 153. 171, 180 and 198. There are 15 such numbers. Alternately, you could also think of this as: Between 1 to 200 there are 22 multiples of 9. But not all these 22 have to be counted as multiples of 27 need to be excluded from the count. There are 7 multiples of 27 between 1 and 200. Thus, the answer would be given by 22 - 7 =15. Option (b) is correct.