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![[#44] 2 Min. Challenge: Positive Integer](/forum/styles/gmatclub_light/imageset/icon_post_target_unread.svg "[#44] 2 Min. Challenge: Positive Integer"){kind=icon}
11 May 2004, 18:39
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Level : Intermediate
Time yourself and solve under 2 minutes.
What is the smallest positive integer A for which there is an integer C and a right triangle with side lengths A and 17 and hypotenuse of length C ?
a. 1
b. 8
c. 16
d. 39
e. 144
Time yourself and solve under 2 minutes.
What is the smallest positive integer A for which there is an integer C and a right triangle with side lengths A and 17 and hypotenuse of length C ?
a. 1
b. 8
c. 16
d. 39
e. 144
Archived Topic
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12 May 2004, 00:45
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Praetorian
A^2 + 17^2 = C^2 => C^2 - A^2 = 17^2 => (C-A)*(C+A) = 17*17. 17 is prime number => C-A = 1, C + A = 17*17. => C = (17^2+1)/2 = 145, A = (17^2-1)/2 = 144.
E.
12 May 2004, 05:45
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Praetorian
By the way, 144 is not only the smallest positive integer A that satisfies this, but also THE ONLY positive integer which satisfies the equation.
