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by GMATGuruNY » Tue Feb 25, 2014 1:13 pm
XY * YX

The product of the two-digit numbers above is the three-digit number XZX, where X,Y and Z, are three different nonzero digits. If X * Y < 10, what is the two-digit number XY?

(A) 11
(B) 12
(C) 13
(D) 21
(E) 31
XY * YZ = XZX.
We can PLUG IN THE ANSWERS, which represent the value of XY.
Since X and Y must be different digits, eliminate A.

B: If XY=12, then XY*YX = 12*21 = 252.
D: If XY=21, then XY*YX = 21*12 = 252.
In each case, XZX = 252, implying that X=2 and that XY = 21.

The correct answer is D.
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by Brent@GMATPrepNow » Tue Feb 25, 2014 1:22 pm
XY * YX

The product of the two-digit numbers above is the three-digit number XZX, where X,Y and Z, are three different nonzero digits. If X * Y < 10, what is the two-digit number XY?

(A) 11
(B) 12
(C) 13
(D) 21
(E) 31
At the outset, if we focus on the units digits, we can eliminate 2 answer choices.
We have: (XY)(YX) = XZX

When we focus on the units digits we see that (Y)(X) = X, so Y must be 1
So, the correct answer is A, D, or E

Next, we can eliminate A because we're told that the digits are DIFFERENT.

This leaves us with D or E.

Test ONE of them. If it works, we're done. If it doesn't work, the other one must work, so we're also done.

Answer: D

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by Dblooos » Sat Apr 26, 2014 4:26 pm
Mitch/Brent,

Can you please explain how did you select between choice B & D? Thank you.
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by Brent@GMATPrepNow » Sat Apr 26, 2014 5:26 pm
Dblooos wrote:Mitch/Brent,

Can you please explain how did you select between choice B & D? Thank you.
Answer choice B: If the 2-digit number is 12 (x = 1 and y = 2), then the resulting product = (12)(21) = 252. This product must = XZX, but we have a problem. If XZX = 252, then x = 2, but X is supposed to equal 1.

So, we can eliminate B

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