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GMAT Focus problem - Answer seems to be wrong

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GMAT Focus problem - Answer seems to be wrong

by shankyrams » Sun Jun 22, 2008 9:18 am
Please refer attachment.
I thought both statements together solve the problem.

My solution flow is as below -

1) t1 = (d1/r1) ; t2= (d2/r2)
2) From solution option 1 d1= d2+30
3) From solution option 1 r2= r2+30
4) From (2) and (3) t1 = (d2+30)/(r2+30)
5) Is t1 > t2 => {(d2+30)/(r2+30)} > (d2/r2)

Subtracting 1 from both sides we get

{(d2-r2)/(r2+30)} > (d2-r2)/(r2)

Left side denominator greater than right side by 30. Hence t1 is definately not greater that t2. SOLUTION ARRIVED.
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by lvincy » Sun Jun 22, 2008 11:09 am
Answer is E. 1 and 2 not sufficient.
d2+30/r2+30 can be greater then d2/r2 but not always.
For example:
1) assume d2 = 60 r2 = 30,
d2/r2 = 60/30 = 2
d2+30/r2+30 = 90/60 = 1.5
Not greater

2) assume d2 = 30, r2 = 60 .
d2/r2 = 30/60 = 1/2
d2+30 / r2+30 = 60/90 = 2/3
Greater

So E not sufficient
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Re: GMAT Focus problem - Answer seems to be wrong

by Ian Stewart » Sun Jun 22, 2008 2:09 pm
shankyrams wrote: {(d2-r2)/(r2+30)} > (d2-r2)/(r2)

Left side denominator greater than right side by 30. Hence t1 is definately not greater that t2. SOLUTION ARRIVED.
You run into the problem here. The denominator on the left is indeed larger than on the right. This does not guarantee that the left side is smaller than the right, however. If d2-r2 is negative, then the fractions above are negative, and the fraction with the larger denominator will be the larger number, not the smaller number. You appear to have assumed the fractions were positive; when you subtracted 1 from both sides, you may have made them negative.
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