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If a and b are nonzero numbers, Is a-b>0?

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If a and b are nonzero numbers, Is a-b>0?  [#permalink]

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New post Updated on: 30 Jul 2017, 11:24
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If a and b are nonzero numbers, Is a-b>0?

(1) |a|-b>0
(2) a-|b|>0

Originally posted by DHAR on 30 Jul 2017, 10:08.
Last edited by Bunuel on 30 Jul 2017, 11:24, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If a and b are nonzero numbers, Is a-b>0?  [#permalink]

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New post 30 Jul 2017, 10:26
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DH99 wrote:
If a and b are nonzero numbers, Is a-b>0?

Statement 1: |a|-b>0
Statement 2: a-|b|>0

Bunuel: Can you please help solve this question.I don't have OA.


Re-arrange the equation in the question stem by adding b to both sides and we notice that the question is really asking:
Is a > b?

Also note that both a and b cannot be 0:

S1:
Re-arrange the equation by adding b to both sides and we get:
|a| > b
Note that the abs value hides the sign of a. We can test a few numbers that both meets the criteria |a| > b :
If a = -3 and b = 2 a < b
If a = 3 and b = 2 then a > b
Therefore, it is not sufficient.

S2:
Re-arrage the equation by adding |b| to both sides and we get:
a > |b|
Note that |b| hides the sign of b, but since a > |b| that means a must be positive since absolute value of a number is always positive and b cannot be 0
if b is negative: a > b since a is positive and a positive is always > a negative
if b is positive, a > b since we are given that a > |b|

Therefore, the answer is B
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Re: If a and b are nonzero numbers, Is a-b>0?  [#permalink]

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New post 30 Jul 2017, 11:23
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Re: If a and b are nonzero numbers, Is a-b>0?  [#permalink]

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New post 20 Feb 2019, 08:02
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Re: If a and b are nonzero numbers, Is a-b>0?   [#permalink] 20 Feb 2019, 08:02
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