GMATbeater12 wrote:XY times YX equals XZX, where X, Y, and Z are three different nonzero digits. If X times Y is less than ten, what is the two-digit number XY?
(A) 11
(B) 12
(C) 13
(D) 21
(E) 31
XY * YX = XZX
X * Y < 10
(A) If XY = 11, then YX = 11, but since X, Y are different nonzero digits, so this is not the correct choice.
(B) If XY = 12, then YX = 21. So, XY * YX = 12 * 21 = 252 (= XZX), which cannot be true as X = 1 and XZZX = 252 implies X = 2, which is a contradiction. Again this is not the correct choice.
(C) If XY = 13, then YX = 31, So, XY * YX = 13 * 31 = 403, cannot be true as the units and hundreds digit should be the same in XZX.
(D)If XY = 21, then YX = 12. So, XY * YX = 21 * 12 = 252 (= XZX), which holds true.
The correct answer is
D.
