Is ab

Question

Is  ab < 0 ?

(1)  ab^2 < b^2

(2)  b^2 < b

niks18 · Answer

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

kaulshanx · Answer

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

kaulshanx · Answer

Also from statement 2 b can never be negative as the equation is of a parabola which only touches the x axis at the origin. So either ab=0 or ab<0 so the statements are insufficient. So answer is E.
Just made a correction to my answer. Sorry for the change in answer.

Sent from my SM-N920G using  GMAT Club Forum mobile app

goalMBA1990 · Answer

E. 
From statement 1, a can be either less than zero or between 0 and 1. Not sufficient.
From statement 2, b is between 0 and 1. Not sufficient because no information about a. 
Combine 1+2 is not sufficient to answer.

Sent from my XT1663 using  GMAT Club Forum mobile app

Dkingdom · Answer

Lets try to solve for C. 
1) & 2)
a*b^2 - b^2 <0
Hence a<1

b^2-b<0
Hence b(b-1)<0 (only true when b<1)

So now we have a<1 and b<1
Both conditions together are not sufficient. 
Hence if answer is not C, then it has to be E.

Ans. : E

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Is ab < 0? (1) ab^2 < b^2 (2) b^2 < b

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions