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

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Senior Manager
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Joined: 02 Nov 2018
Posts: 280
Suppose that P = 2 m and Q = 3 n . Which of the following is equal to  [#permalink]

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19 Mar 2019, 07:03
1
00:00

Difficulty:

55% (hard)

Question Stats:

57% (01:57) correct 43% (02:36) wrong based on 35 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$$Q^m$$
NUS School Moderator
Joined: 18 Jul 2018
Posts: 1026
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: Suppose that P = 2 m and Q = 3 n . Which of the following is equal to  [#permalink]

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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.

$$P^{2n}Q^m = 4^{mn}3^{mn} = 12^{mn}$$

Intern
Joined: 18 Jan 2019
Posts: 28
Re: Suppose that P = 2 m and Q = 3 n . Which of the following is equal to  [#permalink]

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23 Mar 2019, 07:14
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
Intern
Joined: 18 May 2017
Posts: 12
Re: Suppose that P = 2 m and Q = 3 n . Which of the following is equal to  [#permalink]

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23 Mar 2019, 08:35
for clarification, that is 12^(mn), not (12^m)*n
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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