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
(A) 11
(B) 12
(C) 13
(D) 21
(E) 31
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 - Because X,Y are different non-zero digits and which is not the case with this option, this option is incorrect.
(B) 12 - The Unit's digit of XY*YX should be X. Because the Unit's digit of 12*21 is 2, which is not equal to x(=1),this option is incorrect.
(C) 13 - The Unit's digit of XY*YX should be X. Because the Unit's digit of 13*31 is 3, which is not equal to x(=1),this option is incorrect.
(D) 21 - 21*12(XY*YX)= 252 =(XZX) - Bingo! Correct!
(E) 31 - Forget it
IMO D
