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Inequality, can we divide by zero?

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by arora007 » Fri Aug 13, 2010 3:51 am
For what range of values of 'x' will the inequality 15 x - (2/x) > 1?
A. x > 0.4
B. x < (1/3)
C. (-1/3)< x < 0.4, x >(15/2)
D. (-1/3)< x < 0.4, x >(25)
E. x < (-1/3) and x > (2/5)

OA - A

My question also is... in inequalities, can we eliminate by divide by zero is undefined, concept ?

say over here B , C and E can they be outright eliminated ??

This question is from papgust's 300 questions.
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by GMATGuruNY » Fri Aug 13, 2010 4:41 am
arora007 wrote:For what range of values of 'x' will the inequality 15 x - (2/x) > 1?
A. x > 0.4
B. x < (1/3)
C. (-1/3)< x < 0.4, x >(15/2)
D. (-1/3)< x < 0.4, x >(25)
E. x < (-1/3) and x > (2/5)

OA - A

My question also is... in inequalities, can we eliminate by divide by zero is undefined, concept ?

say over here B , C and E can they be outright eliminated ??

This question is from papgust's 300 questions.
The question doesn't explicitly exclude 0. Since x=0 is undefined in the original inequality, we can eliminate B, C and D because these answers include x=0 in their respective ranges.

Since the only difference between A and E is that E includes x<-1/3, all we have to do now is try a negative value in the original inequality.

Plug in x = -1.
15*(-1) - 2/(-1)>1
-15 + 2 > 1
-13 > 1.
Doesn't work. Eliminate E.

The correct answer is A.

If a GMAT question doesn't explicitly exclude 0, we must include x=0 as an option.
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by arora007 » Fri Aug 13, 2010 4:57 am
Thanks a lot guru... this small thing that x=0 can be used to check in a range , is going to shorten many a calculation!
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