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Source: — Data Sufficiency |
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OA B

by smackmartine » Sat Oct 03, 2009 11:21 am
1. V^2-U^2=11
Y=6=2UV
From above eq V=3/U and so (9/U^2 -U^2) = 11
=> U^4 + 11 U^2 - 9 = 0 ,it has more than one solution and thus V has more than one value so NOT SUFFICIENT.

2. U^2 = 16 =>

Given V^2-U^2=11 => V^2=25 => V= +/- 5

SO Z= V^2 + U^2 = (+/- 5)^2 + (+/- 4)^2 = 25 + 16 = 41

So we have only one solution. Hence,SUFFICIENT.

So,option B is the Answer I think.
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by ern5231 » Sat Oct 03, 2009 9:12 pm
OA is B
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by aidin86 » Fri Feb 21, 2014 10:45 am
1) x+z = 2u^2
x- z = - 2v^2
(x+z)(x-z)= x^2 - z^2 = -4(uv)^2
[(x^2 - z^2)/ y^2 ] = (2uv)^2 / -4(uv)^2 -------- z^2 = x^2 + y^2
z = +- ( 11^2 + 60^2 ) but as z = u^2 + v^2 so z is positive
so 1 is sufficient

2) x+z = 2u^2
2 is sufficient
so D is correct answer
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by Patrick_GMATFix » Fri Feb 21, 2014 11:41 am
ern5231 wrote:X=V^2-U^2, Y=2UV, Z=V^2+U^2, X=11. What is the value of Z?
(1) Y=6
(2) U^2=16
The 2nd statement is straightforward. We know that x=v^2-u^2=11; since u^2=16, v^2=27. We have u^2 and v^2, so we can find Z=u^2+v^2. SUFF.

The first statement is trickier, but I also find Sufficiency. Below is my work:
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by Patrick_GMATFix » Fri Feb 21, 2014 12:06 pm
There is a problem with this question though. The two statements contradict the prompt data.

(2) tells us that u = 4 or -4
(1) tells us that uv = 3, which would make v =3/4 or -3/4

So the statements together tell us that (u,v) = (4,3/4) or (-4, -3/4). OK fine. Problem is that the prompt says that x = v^2 - u^2 = 11 but that is not possible from the statement data.

As a result, I don't think this could be an official GMAT question
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