If a is not equal to b, is 1/(a-b) > ab ?

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If a is not equal to b, is 1/(a-b) > ab ? [#permalink]

27 Feb 2013, 13:17

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36% (01:53) correct

63% (00:33) wrong

based on 2 sessions

If a is not equal to b, is 1/(a-b) > ab ?

(1) |a| > |b|
(2) a < b

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Re: If a is not equal to b, is 1/(a-b) > ab ? [#permalink]

27 Feb 2013, 22:22

mun23 wrote:

If a is not equal to b, is 1/(a-b) > ab ?

(1) |a| > |b|
(2) a < b

From F.S 1, let's assume a = -3 and b = -2. Thus, 1/(a-b) = -1 and a*b = 6. Thus, as -1<6, the answer to the question stem is No. Again, pick a = -3 and b = 2, and 1/(a-b) = -0.2, and a*b = -6. In this case we see that -0.2>-6, thus the answer to the question stem is a YES. Insufficient.

From F.S 2, lets again assume a = -3 and b = -2. Just as above we still get a NO. Again choosing the same set for a = -3 and b = 2, we get a YES to the question stem. Insufficient.

Combining both, we know that b-a>0 and mod(a)-mod(b)>0. Thus lets choose a=-7 and b=-2. We get 1/(a-b) = -0.2 and a*b = 14. Thus a NO. Again, choosing b=3 and a=-5, we get a YES . Insufficient.

Basically, the two fact statements given together mean that (a+b)<0. It's because from F.S 1, we get a^2-b^2>0 or (a-b)*(a+b)>0. We have from F.S 2 that a-b<0. Thus, (a+b) has to be negative.

E.

Re: If a is not equal to b, is 1/(a-b) > ab ? [#permalink] 27 Feb 2013, 22:22

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If a is not equal to b, is 1/(a-b) > ab ?

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If a is not equal to b, is 1/(a-b) > ab ?

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