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Page 85, question 174, GMAC Quant Rev, Green book

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Page 85, question 174, GMAC Quant Rev, Green book

by Wakka Wakka » Wed Aug 06, 2008 3:22 pm
I give the referenacein the title because this question comes with symbols. I will try to recreate it here using the square="X", the triangle equal to "Y" and the diamond equal to "v".

XY times YX =

The product of the two-digit numbers above is the three-digit number XvX, where X, Y, v, are three different nonzero numbers. If X times Y is less than 10, what is the two-digit number XY?

Answers: 11, 12, 13, 21, 31

I did the problem and got stuck between 12 and 21. I figure that each one could be the answer however, the book tries to explain that the answer is 21...but doesn't tell me why it can't be 12.

Thanks for the help!
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by parallel_chase » Wed Aug 06, 2008 4:17 pm
XY
YX
__
XvX

The question say X * Y is less 10,
Then X * Y= X, and Y is 1 because there is no carry forward. Hence the number is 21.

if XY=12, YX=21 then X in the product has to be 1 which is not possible.

Let me know if you still have any doubts.
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by Wakka Wakka » Thu Aug 07, 2008 8:30 am
I guess my problem is understanding the whole "carry over" statement. Can you please explain to me what that means. I am assuming that it means that when we multiply Y and X in the first column nothing is carried over to the column to the left. But then x cold be 1 or 2 and Y would be the other. I appreciate the help, thank you.
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by pepeprepa » Thu Aug 07, 2008 8:47 am
I think I see what is your problem.

Formula: XY times YX = XvX
They ask us what is the txo-digit number XY?

If X=1 and Y=2 then, 12 * 21 = 252, here there is a problem because the result must have the form XvX but in 252 X=2 and we said at the beginning X=1... so the number XY cannot be 12
If X=2 and Y=1 then, 21 * 12 = 252, and with 252 we have the form XvX with X=2, so it's perfect.


If the question were, "what is the two digit number YX?" it would have been 12 and not 21
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