Bunuel wrote:
If x and y are positive integers and 2013 + x^2 = y^2, what is the minimum possible value of xy?
A. 8342
B. 671
C. 668
D. 658
E. 645
The minimum possible value of \(xy\) occurs \(x \) and \(y\) have as close values as possible
\(x^2 - y^2 = -2013\)
Prime factorization of \(2013 = 3 * 11 * 61\)
\(x^2 - y^2 = -3 * 11 * 61\)
\((x+y)(x-y) = -33 * 61\)
\(x - y = -33\)
\(x + y= 61\)
Solve for x and y
\(x = 14\)
\(y = 47\)
\(x * y = 14 * 47 = 658\)
Option D
Statistics : Posted by gmatophobia • on 19 Sep 2023, 09:06 • Replies 2 • Views 212
