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Inequality

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Inequality

by knight247 » Tue Aug 23, 2011 12:34 am
If ab>1 then which of the following MUST be less than one?
(A)-a
(B)-b
(C)(a+1)(b+1)
(D)(a-1)(b-1)
(E)(ab)^-1

The answer is E. From the question, just divide both sides by ab and since ab is +ve there is no need to flip the sign...Only one scenario to be considered.
1>1/(ab)
1>(ab)^-1

However, I was hoping to get some help in eliminating the other answer choices because I want to improve on my math skills. And sometimes the correct answer may not be so obvious. Detailed explanations would be appreciated. Thanks
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by Anurag@Gurome » Tue Aug 23, 2011 1:07 am
knight247 wrote:However, I was hoping to get some help in eliminating the other answer choices because I want to improve on my math skills. And sometimes the correct answer may not be so obvious. Detailed explanations would be appreciated. Thanks
Different problems has different methods to solve them efficiently. Option elimination may be the efficient method for some problems, but this is definitely not one of them. We can proceed to eliminate the options as follows, but believe me it is the last thing one may need to solve this problem.

In this case, from ab > 1 we can conclude that a and b are of same sign and their product is greater than 1.

Now let us analyze the options one by one,
  • A. If a = -2 and b = -2, ab > 1 but -a = 2 > 1
    B. Same example as above, -b = 2 > 1
    C. Same example as above, (a + 1)(b + 1) = (-1)*(-1) = 1
    D. Same example as above, (a - 1)(b - 1) = (-3)*(-3) = 9
So first four options are cancelled. Option E remains.
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by saketk » Tue Aug 23, 2011 10:16 pm
knight247 wrote:If ab>1 then which of the following MUST be less than one?
(A)-a
(B)-b
(C)(a+1)(b+1)
(D)(a-1)(b-1)
(E)(ab)^-1

The answer is E. From the question, just divide both sides by ab and since ab is +ve there is no need to flip the sign...Only one scenario to be considered.
1>1/(ab)
1>(ab)^-1

However, I was hoping to get some help in eliminating the other answer choices because I want to improve on my math skills. And sometimes the correct answer may not be so obvious. Detailed explanations would be appreciated. Thanks
Hi,
As Anurag rightly said -- this question is not suited for elimination method because we can do it directly by using the logic and can save time.

As you said, A & B have the same sign.. And it is given that the product of AB is greater than 1.

So, logically thinking -- inverse of any number which is greater than 1 will always yield us a value lesser than 1. Option E i.e.
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by GmatKiss » Wed Aug 24, 2011 4:04 am
+1 for E
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by gmatdriller » Wed Aug 24, 2011 8:51 am
infact, problems with variables in the answer choices are best solved
by picking and substituting suitable numbers.
This way, you eliminate the chance of errors associated with algebra
or equations.
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