# Positive Integers

If a and b are positive integers and a2 - b2 = 7, what is the value of a? (A) 3 (B) 4 (C) 5 (D) 6 (E) 7

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### Answer:

Choice B Level of difficulty E M H There is only one pair of positive integers whose difference of squares is equal to seven. Since we know a is larger than b (because the difference is positive), it doesn't take more than a few tries to determine that a = 4 and b = 3. Since a = 4, the answer is choice B.

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