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

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Retired Moderator
Joined: 07 Jun 2014
Posts: 4804
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Kudos [?]: 2776 [0], given: 394

Which of the following values times 12 is not a multiple of [#permalink]  12 Aug 2018, 16:10
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Question Stats:

54% (01:13) correct 45% (01:13) wrong based on 31 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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Retired Moderator
Joined: 07 Jun 2014
Posts: 4804
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 163

Kudos [?]: 2776 [0], given: 394

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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Sandy
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Re: Which of the following values times 12 is not a multiple of [#permalink]  14 Jun 2020, 03:13
1
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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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