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(1) and (2) are insufficient alone. How do they fare together?

(1) a < 0 AND (2) ab >= 0 is equivalent to a<0 AND b <=0.

a Â· |b| < a â€“ b?

|b| = -b; then: -ab < a-b. Reordering the expression: -a/(a-1)>b. The term to the left is (-), and as b is (-) itself, we cannot ascertain that the expression always holds (it could be that -1/(a-1) = -3/4 and b = -1/2 or -1, yielding the inequality false or true, respectively).

for |a| > |b| with plugging in we get four possibilities

a = -8 , b = 3 a = -8 , b = -3 a = 8 , b = -3 a = 8 , b=3

A) If a < 0

a = -8 , b =3

-8 |3| < -8-3 -24<-11

a = -8 , b = -3

-8 |-3| < -8-(-3) -24 < -5

A is sufficient

2) if ab>=0

a=-3, b=-3

-8 |-3| < -8-(-3) -24 < -5

a=3, b=3

8|3|<8-3 24<5

Insufficient

Hence, the answer should be A. Isn't it?

If a and b are integers, and |a| > |b|, is a · |b| < a – b?

(1) \(a<0\). If \(a=-3\) and \(b=0\), then \(a*|b|=0>a-b=-3\) and the answer is NO but if \(a=-3\) and \(b=-1\), then \(a*|b|=-3<a-b=-2\) and the answer is YES. Two different answers. Not sufficient.

(2) \(ab\geq{0}\)

Above example works here as well: \(a=-3\) and \(b=0\) --> \(a*|b|=0>a-b=-3\) --> answer NO; \(a=-3\) and \(b=-1\) --> \(a*|b|=-3<a-b=-2\) --> answer YES. Two different answers. Not sufficient.

(1)+(2) Again the same example satisfies the stem and both statements and gives two different answers to the question whether \(a*|b|<a-b\). Hence not sufficient.

Re: If a and b are integers, and |a| > |b|, is a |b| < a [#permalink]

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10 Aug 2015, 01:05

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