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

Question

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

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

Source : 4Gmat

LighthousePrep · Answer

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.

TheKingInTheNorth · Answer

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,
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chesstitans · Answer

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|

Archit3110 · Answer

#1
ab can be both -ve or +ve
not sufficient
#2
given a-b>0 so a>b
so a+b=12 
means
|a| > |b|
sufficient
IMO B

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

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GMAT Data Sufficiency (DS) Questions

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

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