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# Is |a|*b < a? (1) a > b (2) ab < 0

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Math Expert
Joined: 02 Aug 2009
Posts: 7212
Is |a|*b < a? (1) a > b (2) ab < 0  [#permalink]

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11 Apr 2018, 22:17
00:00

Difficulty:

65% (hard)

Question Stats:

70% (02:13) correct 30% (01:55) wrong based on 102 sessions

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Is |a|*b < a?

(1) a > b
(2) ab < 0

New Question....

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Joined: 24 Jun 2013
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Re: Is |a|*b < a? (1) a > b (2) ab < 0  [#permalink]

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12 Apr 2018, 02:28
IMO C,

I picked up numbers

chose for a,b (2,1), (-1,-2), (1,0.5), (-0.5,-1) for all chosen number the ineq was true for when a,b had oppo sign and a>b
stmt 1) a>b but sign is not known
stmt 2) ab<0, this says ab have oppo sign but magnitude not given

combine we have the ans so C

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Joined: 28 Apr 2014
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GMAT 1: 640 Q50 V25
Re: Is |a|*b < a? (1) a > b (2) ab < 0  [#permalink]

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12 Apr 2018, 06:43
IMO C

St1 sign not know and also the magnitude
St 2 ab<0
Case1: Let a be +ve
Therefore b is -ve
-<+ true
Case 2: let a be -ve
Therefore b is +ve
+<- Not true
Hence insufficient

Combining statements,
since a>b and ab <0
a is+ve and b is -ve , already solved as Case 1
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Re: Is |a|*b < a? (1) a > b (2) ab < 0  [#permalink]

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12 Apr 2018, 07:08
St1) (a,b) can be (2,1) or (2,-1) hence the answer to the question stem can be yes or no.
Not sufficient.
St2) (a,b) can be (-1,1) or (1,-1), hence the answer to question stem can be no or yes.
Not sufficient.

Combining St1 & St2, we get that a is positive and b is negative.
Hence mod(a) * b < a.
Sufficient.
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Re: Is |a|*b < a? (1) a > b (2) ab < 0  [#permalink]

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25 Apr 2018, 21:56
1)a>b
Cases. Result on equation
3>2 no
-2>-3. No
2>-3. Yes
Not sufficient

2)ab<0
A +ve b-ve result in equation-yes
A -ve b+ve result in equation-No

Not sufficient as both yes and no appears

Combining both statements
One common case
A+ve B-ve
Result in equation-yes

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Re: Is |a|*b < a? (1) a > b (2) ab < 0 &nbs [#permalink] 25 Apr 2018, 21:56
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