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
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GMATbeater12
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neelgandham
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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
(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
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XY * YX = XZXGMATbeater12 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
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.
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kul512
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Easiest way to solve is through answers-
A can not be answer as X and Y are different digits.
we have 12 and 13 to check as it will automaticaly check 21 and 31.
so 12X21=252, So if we choose 21 as XY then XY and YX multiplied generates a number XZX.
so 21 is the answer.D[/spoiler]
A can not be answer as X and Y are different digits.
we have 12 and 13 to check as it will automaticaly check 21 and 31.
so 12X21=252, So if we choose 21 as XY then XY and YX multiplied generates a number XZX.
so 21 is the answer.D[/spoiler]
Sometimes there is very fine line between right and wrong: perspective.
