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a and b are positive integers. a + b = 12. Quantity A: The maximum value of ab. Quantity B: 36.

GRE · 2024 · quant slot 1
Question:
a and b are positive integers. a + b = 12. Quantity A: The maximum value of ab. Quantity B: 36.

Options

(A) Quantity A is greater
(B) Quantity B is greater
(C) The two quantities are equal
(D) The relationship cannot be determined from the information given
Answer: (C) The two quantities are equal

Explanation:
For a fixed sum, product ab is maximized when a and b are equal or as close as possible. a = b = 6 gives ab = 36. Any other pair gives a smaller product. So maximum ab = 36, equal to Quantity B.

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