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Suppose that P = 2 m and Q = 3 n . Which of the following is equal to

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Suppose that P = 2 m and Q = 3 n . Which of the following is equal to  [#permalink]

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New post 19 Mar 2019, 07:03
1
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

58% (01:43) correct 42% (02:13) wrong based on 26 sessions

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Suppose that \(P = 2^m\) and \(Q = 3^n\) . Which of the following is equal to\(12^mn\) for every pair of integers (m,n)?

(A)P^2Q

(B) \(P^n\)\(Q^m\)

(C) \(p^n\)Q^2m

(D) P^2m\(Q^n\)

(E) P^2n\(Q^m\)

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Re: Suppose that P = 2 m and Q = 3 n . Which of the following is equal to  [#permalink]

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New post 19 Mar 2019, 10:30
1
\(P = 2^m\)
\(Q = 3^n\)

Here Powers of P and Q are different.
Hence to get \(12^[mn}\), we need to make the powers the same.
Only option E does that.

\(P^{2n}Q^m = 4^{mn}3^{mn} = 12^{mn}\)

E is the answer.
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Re: Suppose that P = 2 m and Q = 3 n . Which of the following is equal to  [#permalink]

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New post 23 Mar 2019, 07:14
Noshad wrote:
Suppose that \(P = 2^m\) and \(Q = 3^n\) . Which of the following is equal to\(12^mn\) for every pair of integers (m,n)?

(A)P^2Q

(B) \(P^n\)\(Q^m\)

(C) \(p^n\)Q^2m

(D) P^2m\(Q^n\)

(E) P^2n\(Q^m\)


the way the question is written is quite misleading, i think you need to stick to one method of writing the powers because to me D and E looked like P^(2mQ^n) and P^(2nQ^m) respectively
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Re: Suppose that P = 2 m and Q = 3 n . Which of the following is equal to  [#permalink]

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New post 23 Mar 2019, 08:35
for clarification, that is 12^(mn), not (12^m)*n
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Re: Suppose that P = 2 m and Q = 3 n . Which of the following is equal to   [#permalink] 23 Mar 2019, 08:35
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Suppose that P = 2 m and Q = 3 n . Which of the following is equal to

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