# Determining a multiple of a power of 2.

"Which of the following numbers is exactly divisible by 32?

A) $1.9 \times 10^5$

B) $1.9 \times 10^6$

C) $1.9 \times 10^4$ "

In this case I believe that if x is a non-zero integer then $x \times 10 ^n$ is exactly divisible by $2^n$.

My question is this: Is this a good question for GRE students?

• Depending on your definition of "exactly" (for example, is $64$ exactly divisible by $32$?), you should change your belief from "$x$ is a non-zero integer" to "$x$ is an odd integer". I previously answered the question at the top, but it seems to be aside the main point here or something... May 3 '16 at 18:32
• Yes I know that the answer is B, @barak manos. But I just wanted you explain whether the question is good or not for entrance examinations. I up voted your answer. May 3 '16 at 18:36
• I don't much like it. Have you any reason for not writing the numbers as $190000, 1900000, 19000$? May 3 '16 at 18:47
• @almagest Maybe because as $19 \times 10^4$, $19 \times 10^5$ and $19 \times 10^3$ the question becomes much, much easier. May 3 '16 at 20:28
• Are calculators allowed on the GRE test? May 3 '16 at 20:28

HINT:

Write it as

$19×10^4 , 19×10^5 , 19×10^3$

Since 19 is not divisible by 32, the power of 10 must be.

Use $32=2^5$ and $10=2×5$

• say something about GRE for me to accept your answer, @N.S.JOHN. But I will up vote it. May 4 '16 at 9:45
• @patrickchidzalo Sorry I don't know about GRE May 4 '16 at 9:47
• I mean entrance exams May 4 '16 at 9:48
• I tryped GRE but auto correct made it HER:( May 4 '16 at 9:49