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Which of the following values times 12 is not a multiple of

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Retired Moderator
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GRE 1: Q167 V156
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Which of the following values times 12 is not a multiple of [#permalink] New post 12 Aug 2018, 16:10
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Question Stats:

51% (01:01) correct 48% (01:13) wrong based on 29 sessions
Which of the following values times 12 is not a multiple of 64?

Indicate all such values.

A. \(6^6\)
B. \(12^2\)
C. \(18^3\)
D. \(30^3\)
E. \(222\)
[Reveal] Spoiler: OA

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Retired Moderator
User avatar
Joined: 07 Jun 2014
Posts: 4805
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 163

Kudos [?]: 2753 [0], given: 394

Re: Which of the following values times 12 is not a multiple of [#permalink] New post 17 Aug 2018, 16:16
Expert's post
Explanation

Because \(64 = 2^6\), multiples of 64 would have at least six 2’s among their prime factors.

Since 12 (which is 2 × 2 × 3) has two 2’s already, a number that could be multiplied by 12 to generate a multiple of 64 would need to have, at minimum, the other four 2’s needed to generate a multiple of 64.

Since you want the choices that don’t multiply with 12 to generate a multiple of 64, select only the choices that have fewer than four 2’s within their prime factors.

\(6^6=(2 \times 3)^6\) ........... six 2's ............ INCORRECT

\(12^2=(2^2 \times 3)^2\) ........... four 2's ............ INCORRECT

\(18^3=(2 \times 3^2)^3\) ........... three 2's ............ CORRECT

\(30^3=(2 \times 3 \times)^3\) ........... three 2's ............ CORRECT

\(222=(2 \times 3 \times 37)^2\) ........... one 2's ............ CORRECT
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Re: Which of the following values times 12 is not a multiple of [#permalink] New post 14 Jun 2020, 03:13
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sandy wrote:
Which of the following values times 12 is not a multiple of 64?

Indicate all such values.

A. \(6^6\)
B. \(12^2\)
C. \(18^3\)
D. \(30^3\)
E. \(222\)


The most accurate approach here is to use the calculator and test the answer choices:

A) (6^6*12)/64 -> 46 656/64=729 (Numerator is perfectly divisible by denominator. But this is not what we are looking for)
B) (12^2*12)/64 -> 1728/64=27 ((Numerator is perfectly divisible by denominator. But this is not what we are looking for)
C) (18^3*12)/64 -> 69 984/64=1093,5 (Numerator is not a multiple of 64,in other words numerator is not divisible by 64, that's what we are looking for)
D) (30^3*12)/64 -> 324 000/64=5062.5 (Numerator is not a multiple of 64,in other words numerator is not divisible by 64, that's what we are looking for)
E) (222*12)/64 -> 2664/64=41.625 (Numerator is not a multiple of 64,in other words numerator is not divisible by 64, that's what we are looking for)

Thus we have three correct answers: C/D/E
Re: Which of the following values times 12 is not a multiple of   [#permalink] 14 Jun 2020, 03:13
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Which of the following values times 12 is not a multiple of

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