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What is the value of ab if the sum of the squares of positive integers a and b is 80?
(A) 4
(B) 16
(C) 30
(D) 32
(E) 64
(A) 4
(B) 16
(C) 30
(D) 32
(E) 64
19 Oct 2020, 06:47
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Given that \(a^2 + b^2 = 80\) and that a and b are integers
The only pair (a,b) that satisfies the above is (4,8)
Therefore ab = 4*8 = 32
Option D
Arun Kumar
The only pair (a,b) that satisfies the above is (4,8)
Therefore ab = 4*8 = 32
Option D
Arun Kumar
19 Oct 2020, 10:07
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GMATBusters
The question obviously has at least two answers, one positive and one negative. 4 and 8 are the only two positive integers that work, but it's also possible, for example, that a = -4 and b = 8, because (-4)^2 + 8^2 = 80 as well. So ab can equal 32 or -32.
Unless the question says a and b are positive integers, it needs to ask what the value of ab "could be", not what the value "is", since there is more than one solution.
