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Joe Komagawa
Average Member

Japan
11 Posts

Posted - 12/01/2013 :  00:20:28  Show Profile  Reply with Quote
GMAT-the official guide, #157
"A certain right triangle has sides of length X, Y, and of course Z.where X<Y<Z. IF the area of the triangle region is 1, which of the following shows all values of Y?
a) Y>sq.rt 2 b)sq.rt3/2<Y<sq.rt.2 c) sq.rt.2/3<Y<sq.rt.3/2 d)sq.rt.3/4<Y<sq.rt.2/3 e) Y<sq.rt.3/4 ."

1)Ok, I get the area and xy=2, and thus y=2/x, The next step, X<Y implies 1/X>1/Y, I don't see why the inequality is switched. I thought it only switched when mult. by a negative something. Secondly, I want to know what is the thinking guiding 1/x >1/y. I didn't think like this when I was trying to solve this problem.

2) text: Alternatively, if X<sq.rt2 and y<sq.rt.2 then xy<2. If X>sq.rt2 and y>sq.rt.2 then xy>2. But xy =2, so one of x or y must be less than sq.rt.2 and the other must be greater than sq.rt.2, since x<y , it follows that x<sq.rt.2,Y and y> sq.rt.2".

I am really lost in the understanding of 2)

sq. rt.2 means square root. of 2
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Joe Komagawa
Average Member

Japan
11 Posts

Posted - 12/01/2013 :  00:24:15  Show Profile  Reply with Quote
#157 answer is A y>sq.rt.2
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