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Digits

by mbamph2012 » Wed Oct 26, 2011 11:19 am
Can someone please explain this to me.

If xy represents a positive two-digit number, where x and y are single digit integers, which of the following CANNOT be true?
x + y = 9
xy = 9
x - y = 9
y - x = 9
x/y = 9
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by GmatMathPro » Wed Oct 26, 2011 11:58 am
x+y=9.....54
xy=9......91
x-y=9.....90
y-x=9.....impossible
x/y=9.....91

y-x=9 is impossible because the only two digits with a difference of 9 is 9 and 0, so it would have to be that y=9 and x=0, but that would make the number xy, 09 or just 9. But 9 is a one-digit number, not a two-digit number.
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by mbamph2012 » Wed Oct 26, 2011 1:27 pm
Ok thanks, I was thinking that in the question it was saying xy=9
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by GmatMathPro » Wed Oct 26, 2011 1:33 pm
Yeah it probably could have been written more clearly.
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by neya » Wed Oct 26, 2011 6:41 pm
Since xy is a positive two-digit number, then xy=9 is it true? Confused.
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by GmatMathPro » Wed Oct 26, 2011 7:05 pm
Yeah, the confusing thing is that they use xy to mean two different things in this problem. When they say xy=9 in the answer choices they mean x*y=9. In other words, the ten's digit times the unit's digit equals nine. This is certainly possible if x is 9 and y is 1.

On the other hand, in the question they use xy to represent a two digit integer, where if x=9 and y=1 xy=91, and xy does NOT mean to multiply x and y.

Usually xy would be understood to mean "x times y" but since they define it in a different way in the question, they should really use a more explicit notation for multiplication.

Of course, the writers of a real GMAT question would be careful to avoid this kind of ambiguity.
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by Cheese12 » Wed Oct 26, 2011 8:41 pm
even i read xy as "x times y" :|
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