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13 Sep 2017, 21:44
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
68% (01:34) correct
32%
(01:29)
wrong
based on 239
sessions
History
Date
Time
Result
Not Attempted Yet
Is \(ab < 0\)?
(1) \(ab^2 < b^2\)
(2) \(b^2 < b\)
(1) \(ab^2 < b^2\)
(2) \(b^2 < b\)
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
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Statement 1: \(ab^2-b^2<0\) or \(b^2(a-1)<0\). as \(b^2\) is always positive, this implies that \(a-1<0\)
or \(a<1\)--------------(1). but we don't know whether \(a\) is positive or negative and we don't have any information about \(b\). Hence Insufficient
Statement 2: \(b^2<b\). this implies that \(b\) is positive and it is less than \(1\). so \(0<b<1\)
But we have no information about \(a\). Hence Insufficient
Combining 1 & 2 we don't know the sign of \(a\). if \(0<a<1\), then \(ab>0\) and if \(a<0\), then \(ab<0\). Hence insufficient
Option E
14 Sep 2017, 19:06
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Statement 1 - ab^2<b^2. On simplifying ab^2-b^2<0, further simplifying b^2(a-1)<0, which makes a<1 & b^ can never be negative as it is a square of a number. Now since a<1 means for a=-1, ab will be <0 but if a can be 0 also in which case ab=0 and hence not sufficient.
Statement 2 - b^2<b. Simplifying, b^2-b<0, further simplifying b(b-1)<0. This states that b<1 and as b<0 also falls in the range but this only states about the polarity of b and since the main equation has dependence on value of a also which is not covered here, hence this statement is also insufficient.
Statement 1+2 - states the polarity of b as negative but the dual possibility of a (i.e a can be 0 as well as negative) from Statement 1.hence in either case either ab=0 or ab>0 since (-ve)*(-ve)=+ve, so ab is not <0. hence C.
What is the original OA.
Sent from my SM-N920G using GMAT Club Forum mobile app
Statement 2 - b^2<b. Simplifying, b^2-b<0, further simplifying b(b-1)<0. This states that b<1 and as b<0 also falls in the range but this only states about the polarity of b and since the main equation has dependence on value of a also which is not covered here, hence this statement is also insufficient.
Statement 1+2 - states the polarity of b as negative but the dual possibility of a (i.e a can be 0 as well as negative) from Statement 1.hence in either case either ab=0 or ab>0 since (-ve)*(-ve)=+ve, so ab is not <0. hence C.
What is the original OA.
Sent from my SM-N920G using GMAT Club Forum mobile app
