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Integers a and b are such that a - b > 0. Is |a| > |b| ?

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Integers a and b are such that a - b > 0. Is |a| > |b| ? [#permalink]

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New post 10 Aug 2014, 07:51
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Integers a and b are such that a - b > 0. Is |a| > |b| ?

(1) ab > 0
(2) a + b = 12

Source : 4Gmat
[Reveal] Spoiler: OA

Last edited by Bunuel on 12 Aug 2014, 07:47, edited 1 time in total.
Renamed the topic and edited the question.

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Re: Integers a and b are such that a - b > 0. Is |a| > |b| ? [#permalink]

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New post 10 Aug 2014, 08:23
alphonsa wrote:
Integers a and b are such that a-b> 0

Is |a| > |b| ?

1) ab> 0
2) a+b = 12



Source : 4Gmat


Start with the question. Do some algebra, move the b to the other side of the inequality and you can quickly figure out that a > b.

Next, we look at statement 1:
ab > 0
This means that a and b are positive or both are negative.
The question is asking about absolute values. Therefore we have to consider that in the negative values, the smaller the number, the greater its absolute value. Therefore, since we don't know whether a and be are positive or negative, we have to say statement 1 is insufficient.

Examples:
a= 2
b = 1
TRUE

a=-2
b=-3
FALSE

INSUFFICIENT

Eliminate A, D.

Next, we do statement 2:

The question tells us that b < a.
a+b = 12.

If b < a, then a can't be a negative number, otherwise statement 2 would not hold true. Therefore a is positive, and |b| must also be less than a.

SUFFICIENT

Correct answer is B.

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Re: Integers a and b are such that a - b > 0. Is |a| > |b| ? [#permalink]

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New post 01 Jun 2017, 01:02
Integers a and b are such that a - b > 0. Is |a| > |b| ?

(1) ab > 0
(2) a + b = 12

Integers a and b are such that a - b > 0
means a > b

(1) ab > 0 Not sufficient

while selecting values keep in mind a > b

take a= 5 and b =3 ( Is |a| > |b| = yes )

take a= -5 and b = -10 ( Is |a| > |b| = no )

(2) a + b = 12
while selecting values keep in mind a > b
here a can be positive and b positive
or
a can be positive and b negative .

therefore
( Is |a| > |b| = yes )

B ans .

Regards,
Press Kudos if you like the post .
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Re: Integers a and b are such that a - b > 0. Is |a| > |b| ? [#permalink]

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New post 17 Aug 2017, 19:26
B is correct, the key here is a + b = 12.
since a > b => a >6 > b and |a| = a
now, the question is a > |b|?

we have, a = 12 - b, if b < 0, then a = 12 + |b| => a > |b| => solved
if b > 0, then a > b > 0 => a > |b|

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Re: Integers a and b are such that a - b > 0. Is |a| > |b| ?   [#permalink] 17 Aug 2017, 19:26
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