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 Author: questioner [ Mon May 13, 2013 10:38 am ] Post subject: GMAT Number Theory The product of the squares of two positive integers is 400. How many pairs of positive integers satisfy this condition?A. 0B. 1C. 2D. 3E.4(D) 400 = 2 × 2 × 2 × 2 × 5 × 5Combine the prime factors in pairs.400 = (2 × 2) × (2 × 2) × (5 × 5)Now brake the factorization into two parts, each one will be a square.The possible combinations are:400 = (2 × 2) × [(2 × 2) × (5 × 5)]400 = [(2 × 2) × (2 × 2)] × (5 × 5)But don't forget that 400 = 1 × 400, where 1 = 1². So we also have:400 = (1 × 1) × [(2 × 2) × (2 × 2) × (5 × 5)]Thus all the possible combinations of the factors that make the product of two squares are the following:1² × 20² = 4002² × 10² = 4004² × 5² = 400There are three possible pairs that fit the criterion. The correct answer is D.---------The answer should be E. 4 , because your explanation has missed the possibility of 20² × 20² . It is not mentioned that the numbers should be distinct.

 Author: Gennadiy [ Mon May 13, 2013 10:38 am ] Post subject: Re: GMAT Number Theory Quote:The answer should be E. 4 , because your explanation has missed the possibility of 20² × 20² . It is not mentioned that the numbers should be distinct.20² × 20² = 400 × 400 = 160,000 , NOT 400.

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