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I am thinking about this question which I believe is a possible GRE question.

"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?

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  • $\begingroup$ 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... $\endgroup$ May 3 '16 at 18:32
  • $\begingroup$ 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. $\endgroup$ May 3 '16 at 18:36
  • $\begingroup$ I don't much like it. Have you any reason for not writing the numbers as $190000, 1900000, 19000$? $\endgroup$
    – almagest
    May 3 '16 at 18:47
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    $\begingroup$ @almagest Maybe because as $19 \times 10^4$, $19 \times 10^5$ and $19 \times 10^3$ the question becomes much, much easier. $\endgroup$
    – Mr. Brooks
    May 3 '16 at 20:28
  • $\begingroup$ Are calculators allowed on the GRE test? $\endgroup$
    – Mr. Brooks
    May 3 '16 at 20:28
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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 $10=2×5$

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

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