Question: A perfect square is a number that becomes an integer when square rooting it. A, B, and C are three positive integers. The ratio of the three numbers is 1 : 2 : 3, respectively. Which one of the following expressions must be a perfect square?

(A) A + B + C
(B) A^2 + B^2 + C^2
(C) A^3 + B^3 + C^3
(D) 3A^2 + B^2 + C^2
(E) 3A^2 + 4B^2 + 4C^2

Correct Answer: D
Solution and Explanation:
Approach Solution 1:

This question has only one approach solution
We can let A = x, B = 2x and C = 3x for some integer x. Let’s analyse each answer choice. We have:

A) A + B + C = x + 2x + 3x = 6x is not necessarily a perfect square.
B) A^2 + B^2 + C^2 = x^2 + 4x^2 + 9x^2 = 13x^2 is not necessarily a perfect square.
C) A^3 + B^3 + C^3 = x^3 + 8x^3 + 27x^3 = 36x^3 is not necessarily a perfect square.
D) 3A^2 + B^2 + C^2 = 3x^2 + 4x^2 + 9x^2 = 16x^2 is a perfect square since 16x^2 = (4x)^2.

“A perfect square is a number that becomes an integer when square”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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