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# Is a > b ? (1) |a|/|b| > 1 (2) |a - b| < |a|

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Is a > b ? (1) |a|/|b| > 1 (2) |a - b| < |a|  [#permalink]

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Updated on: 23 Dec 2017, 05:40
00:00

Difficulty:

45% (medium)

Question Stats:

71% (02:30) correct 29% (01:37) wrong based on 46 sessions

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Is a > b ?

(1) |a|/|b| > 1

(2) |a - b| < |a|

Source: http://www.GMATinsight.com

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Originally posted by GMATinsight on 23 Dec 2017, 04:57.
Last edited by Bunuel on 23 Dec 2017, 05:40, edited 1 time in total.
Renamed the topic, edited the question
Math Expert
Joined: 02 Aug 2009
Posts: 7034
Re: Is a > b ? (1) |a|/|b| > 1 (2) |a - b| < |a|  [#permalink]

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23 Dec 2017, 06:07
GMATinsight wrote:
Is a > b ?

(1) |a|/|b| > 1

(2) |a - b| < |a|

Source: http://www.GMATinsight.com

(1) $$\frac{|a|}{|b|} > 1$$.......
It tells us that the numeric value of a is MORE than that of b..
so if a is -ive .... ans is NO as a<b
if a is +ive..... ans is YES as a>b
insuff

(2) |a - b| < |a|
square both sides
$$a^2-2ab+b^2<a^2....................b(b-2a)<0$$
so both b and b-2a are of OPPOSITE sign
if b>0, b-2a<0 or b<2a, so a>0
if b<0, b-2a>0 or b>2a, so a<0
so nothing much except BOTH are of same sign
insuff

combined
both are positive a>b... yes
both are -ive, a<b... no
insuff

E
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Re: Is a > b ? (1) |a|/|b| > 1 (2) |a - b| < |a|  [#permalink]

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23 Dec 2017, 07:09
GMATinsight wrote:
Is a > b ?

(1) |a|/|b| > 1

(2) |a - b| < |a|

Source: http://www.GMATinsight.com

1. It is insufficient, since |a|>|B| doesn't mean that a>b
2. Use a=-2 b=-3 we get 1<2 -- true --a>b
and a=2 b=3 we get 1<2 --true --a<b

Both 1 and 2. use a=-3 b=-2 we get 1<3 --true --a<b
and a=3 b=2 we get 1<3 --true --a>b

thus insufficient
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Re: Is a > b ? (1) |a|/|b| > 1 (2) |a - b| < |a|  [#permalink]

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29 May 2018, 00:13
GMATinsight wrote:
Is a > b ?

(1) |a|/|b| > 1

(2) |a - b| < |a|

Source: http://www.GMATinsight.com

1. |a|/|b| > 1 or |a| > |b| which can be true in two ways

i) a > b (okay)
ii) a > -b (not okay)

thus insufficient.

2. |a - b| < |a| which can also be true in two ways

i) a - b < a or 0 < b or b>0
ii) -( a - b) < a or b < 2a or a > b/2 which means if b (for ex) is 6, A can be 4 or 7. Thus Insufficient

Re: Is a > b ? (1) |a|/|b| > 1 (2) |a - b| < |a| &nbs [#permalink] 29 May 2018, 00:13
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# Is a > b ? (1) |a|/|b| > 1 (2) |a - b| < |a|

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