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

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Director
Joined: 18 Feb 2019
Posts: 603
Location: India
GMAT 1: 460 Q42 V13
GPA: 3.6
Is |a| + |b| > |a + b|? (1) |ab| > ab (2) a/b < 0  [#permalink]

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01 Mar 2019, 10:17
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1
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Difficulty:

25% (medium)

Question Stats:

72% (01:07) correct 28% (01:21) wrong based on 82 sessions

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Is |a| + |b| > |a + b|?

(1) |ab| > ab

(2) a/b < 0
Manager
Joined: 16 Oct 2011
Posts: 109
GMAT 1: 570 Q39 V41
GMAT 2: 640 Q38 V31
GMAT 3: 650 Q42 V38
GMAT 4: 650 Q44 V36
GMAT 5: 570 Q31 V38
GPA: 3.75
Re: Is |a| + |b| > |a + b|? (1) |ab| > ab (2) a/b < 0  [#permalink]

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01 Mar 2019, 10:46
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kiran120680 wrote:
Is |a|+|b| > |a+b|?

I. |ab|>ab
II. a/b<0

(1) |ab| > ab

For absolute value/modulus, I always try to test negative integers, negative fractions, positive fraction, and positive whole numbers. If these categories give you a consistent YES or NO answer, we can mark sufficient

let a =-1 b =-1 --> |ab| >ab --> No. As you can see a and b have to be different signs in order for |ab| > ab

ok let a =-1 b =1 then |a|+ |b| =|-1| + |1| =2 and |a+b|| = |-1+2| = 1 so we get a yes answer

let a =-1/2 b =1 then |a|+|b| = 1/2 +1 = 3/2 >|-1/2 +1| =1/2, so we get a yes answer

Since we have tested all cases for (1) and we get a consistent "yes", statement 1 is sufficient

(2) a/b <0 This means that a and b must be different signs, so we can only test values where a is negative and b is positive (or vice versa)

We can actually test the same values as (1) then. Letting a =-1, b =1, and a=-1/2 and b=1 as in (1), we will get only yes answers, thus (2) is sufficient.

VP
Joined: 31 Oct 2013
Posts: 1489
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: Is |a| + |b| > |a + b|? (1) |ab| > ab (2) a/b < 0  [#permalink]

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03 Mar 2019, 01:17
kiran120680 wrote:
Is |a| + |b| > |a + b|?

(1) |ab| > ab

(2) a/b < 0

This is only true if either a or b is negative.

Statement 1:

|ab| > ab.

we have ab on the both side of the inequality. but |ab| is greater than ab. It indicates that a or b is negative.

Sufficient.

Statement 2 : a/b<0. Sufficient. It's only possible if one of a or b is negative.
Re: Is |a| + |b| > |a + b|? (1) |ab| > ab (2) a/b < 0   [#permalink] 03 Mar 2019, 01:17
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