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

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GRE Prep Club Legend
Joined: 07 Jun 2014
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GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Which of the following values times 12 is not a multiple of [#permalink]  12 Aug 2018, 16:10
Expert's post
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Question Stats:

42% (01:12) correct 57% (01:12) wrong based on 7 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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Sandy
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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 105

Kudos [?]: 1783 [0], given: 397

Re: Which of the following values times 12 is not a multiple of [#permalink]  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] 17 Aug 2018, 16:16
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