Is ab

Question

Is  ab<1 ?

(1)  a^2b<a  
(2)  ab^2<b

Archit3110 · Answer

target is ab<1
possible when either of them is -ve or 0 or fraction value of both
#2
a^2b<a
a*(ab-1)<0
possible when a is -ve or b is -ve & a is +ve or a is +ve (0<a<1) but b is 0 or both a,b are -ve such that value of ab>1
insufficient
#2
same as #1
insufficient
from 1 &2 we do not get anything in common
insufficient
option E

ColumbiaBaby · Answer

GMATNinja   chetan2u   Archit3110  shouldn't this be c?

#1 gives a<0 or ab<1 and #2 gives b<0 or ab<1

ab<1 is common between the two.

Please let me know where I'm going wrong. thanks

chetan2u · Answer

Is ab<1 ? (1) a^2b0, that is ab>1. Thus, a<0, b<0 and ab>1 a>0 and ab-1<0, that is ab<1. Thus, a>0, b<0 and ab<1. (2) ab^20, that is ab>1. Thus, a<0, b<0 and ab>1 b>0 and ab-1<0, that is ab<1. Thus, a<0, b>0 and ab<1. Nothing new when combined. E ColumbiaBaby , you are slightly wrong in analysing the statements. Take an example. Let a=b=-2, then (-2)^3<-2 or -8<-2 ….Yes Let a=b=-1, then (-1)^3<-1 or -1<-1 ….No

ColumbiaBaby · Answer

Ah got it! I solved it like a normal quadratic and not like an inequality.

Thank you!

aditiagg · Answer

This is what I'm doing and still not sure why the answer is not C

chetan2u · Answer

Statement I gives you two informations If a<0, then ab-1>0 or ab>1, but if a>0, then ab-1<0 or ab<1. Similarly for statement II. Combined too, we get ab>1 or ab<1. Only thing you can say is that ab eq 1

bumpbot · Answer

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

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