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# If a<b and c<b, is abc<a?

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Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3334
Location: India
GPA: 3.12
If a<b and c<b, is abc<a?  [#permalink]

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15 Apr 2018, 10:19
2
00:00

Difficulty:

45% (medium)

Question Stats:

63% (02:25) correct 38% (02:15) wrong based on 40 sessions

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If a<b and c<b, is abc<a?

1. ab < 0
2. ac > 0

Source: Experts Global

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Senior PS Moderator
Status: It always seems impossible until it's done.
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Posts: 673
Re: If a<b and c<b, is abc<a?  [#permalink]

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15 Apr 2018, 10:39
pushpitkc wrote:
If a<b and c<b, is abc<a?

1. ab < 0
2. ac > 0

Source: Experts Global

IMO C. I will approach this question with cases approach!

Q: Is abc < a ?

based on sign of a we can simplify the question further... which will help us in the cases.

Case 1) a > 0 : then the Q : bc < 1 ? ( cancelling a )

Case 2) a < 0 : then the Q : bc > -1 ? ( cancelling negative a )

1. ab < 0

Case 1) not possible here as b > a : so if a > 0 ... b also > 0 and ab < 0 not possible.

Case 2) a < 0. If ab < 0 then b > 0. Our Q for case 2 is : Is bc > -1 ? we do not know if c > 0 or not.

Hence 1. is Insufficient!

2. ac > 0

Case 1) a > 0 . If ac > 0 then c > 0. Since we know b > c... hence b > 0. Q : is bc < 1 ? could be either yes or no depending on magnitude of b & c.

Case 2) a < 0. If ac > 0 then c < 0. Since we know b > c ... b could be positive or negative. Our Q: is bc > -1? could be yes or no depending on if b is positive or negative.

Hence 2. is insufficient.

(1) + (2) together...

Case 1) a > 0 is not possible as ab < 0. and b > a.

Case 2) a must be less than zero. Our question is : Is bc > -1?

ac > 0 hence c > 0 & b > c hence b >0

hence bc > 0.

Hence the answer to the question in this case is "YES" always. This means both 1. and 2. together are sufficient to answer.

Hence Option (C) is our answer.

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Re: If a<b and c<b, is abc<a?  [#permalink]

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29 Apr 2018, 05:16
I)ab<0
B>a given so b +be a-ve
But don't know abt C so insufficient

II) ac>0
Both a and c can be +be or -ve.also no info about b
So insufficient

Combining both
a>0 from 1) so c>0 from 2)
So got sign of a b and c

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Re: If a<b and c<b, is abc<a? &nbs [#permalink] 29 Apr 2018, 05:16
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