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OG For Quantitative Review : PS : Q 174

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by shrutikasat2703 » Tue Feb 25, 2014 12:41 pm
I am not able to comprehend the explanation given for Question 174 in the OG for Quantitative Review 2nd Edition.
It is in the Problem Solving category.

The product of the two digit number is a three digit number □◇□
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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

Cheers,
Brent
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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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