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Let the numbers PE Q and N.

=> (Q + N)/2 = PQ
=> Q + N = 2PQ
=> N = 2PQ - Q

Answer: A

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SajjadAhmad
The arithmetic mean (average) of two numbers is \(P * Q\). If the first number is Q, what is the other number?

(A) \(2PQ - Q\)

(B) \(PQ - 2Q\)

(C) \(2PQ - P\)

(D) \(P\)

(E) \(PQ - Q\)

To introduce an easy way of approach to fellow test-takers of GMAT, I will use the method of POE by substitution and will supplement it by an algebraic solution as well.

POE by substititon

Let Q be equal to 2, P be 4 and other unknown number be x.

From the Question stem, Average, (x+Q)/2 = PQ
=>(x+2)/2 = (2*4)
=>x = 14

Going to the answer choices

(A) 2PQ - Q = 2(2*4) - 2 = 14 CORRECT

(B) PQ - 2Q = (2*4) - 2*2 = 4 WRONG

(C) 2PQ - P = 2(2*4) - 4 = 12 WRONG

(D) P = 4 WRONG

(E) PQ - Q = (2*4) - 2 = 4 WRONG

Hence, OA should be A

This method of substitution looks so long on the first read, but on practice, it saves a lot of time.

Algebraic Solution

(x+Q)/2 = PQ
=>x = 2PQ - Q

Hence, OA should be A

SajjadAhmad Bunuel daagh GMATinsight GMATBusters egmat gmatwhiz @wizako Correct me if my approach can be tweaked to save time.
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