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If la-bl > a-b, then which of the following must be true A) a > b B)

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GMATinsight
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If la-bl > a-b, then which of the following must be true A) a > b B) [#permalink] New post   04 Apr 2020, 23:44
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If a*b≠0 and la-bl > a-b, then which of the following must be true

A) a > b
B) a < b
C) lal > b
D) lal < b
E) lal < lbl

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B
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chetan2u
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Re: If la-bl > a-b, then which of the following must be true A) a > b B) [#permalink] New post   05 Apr 2020, 00:16
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GMATinsight wrote:
If a*b≠0 and la-bl > a-b, then which of the following must be true

A) a > b
B) a < b
C) lal > b
D) lal < b
E) lal < lbl



There are only two possibilities here..
1) la-bl = a-b, when a-b>0 or a-b=0
2) la-bl > a-b, when a-b<0

We are given la-bl > a-b, so a-b<0....a<b

B
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Re: If la-bl > a-b, then which of the following must be true A) a > b B) [#permalink] New post   05 Apr 2020, 04:22
if we draw a graph of |x| and x then |x|>x only when x<0 hence |a-b|> a-b is only valid only when a-b<0
=a<b
hence answer is b
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Re: If la-bl > a-b, then which of the following must be true A) a > b B) [#permalink] New post   05 Apr 2020, 05:29
GMATinsight wrote:
If a*b≠0 and la-bl > a-b, then which of the following must be true

A) a > b
B) a < b
C) lal > b
D) lal < b
E) lal < lbl

Source: https://www.GMATinsight.com


given condition la-bl > a-b possible when
b>a ; when both are +ve eg b=5 and a = 1
b>a ; when a is -ve & b is +ve ; eg a=-1 and b = +5
clearly option B a<b is must true condition
option B
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Re: If la-bl > a-b, then which of the following must be true A) a > b B) [#permalink] New post   28 May 2020, 22:13
Can anyone please tell me why option E) lal < lbl is wrong ?
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Re: If la-bl > a-b, then which of the following must be true A) a > b B) [#permalink] New post   28 May 2020, 23:17
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funkyakki wrote:
Can anyone please tell me why option E) lal < lbl is wrong ?


funkyakki

The condition la-bl > a-b is also true for

a = -5 and b = 2 i.e lal > lbl hence option E is incorrect

I hope that help! :)
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Re: If la-bl > a-b, then which of the following must be true A) a > b B) [#permalink] New post   29 May 2020, 00:03
Given: a*b≠0 and la-bl > a-b

For (a-b): three possibilities possible

Scenario 1: (a-b) = +ve, then LHS = RHS Not possible
Scenario 2: (a-b) = 0, then LHS = RHS Not possible
Scenario 3: (a-b) = -ve, so that la-bl = +ve of (a-b) and thus LHS > RHS.

So a-b < 0 or a<b

B
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Re: If la-bl > a-b, then which of the following must be true A) a > b B) [#permalink] New post   29 May 2020, 11:15
For la-bl > a-b to be true, a - b < 0.
b>a.
Option B
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If la-bl > a-b, then which of the following must be true A) a > b B) [#permalink] New post   29 May 2020, 11:26
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[quote="GMATinsight"]If a*b≠0 and la-bl > a-b, then which of the following must be true

A) a > b
B) a < b
C) lal > b
D) lal < b
E) lal < lbl

|a-b| implies the distance between a and b, and is always positive

Now, |a-b| >a-b if a-b is negative
=> a-b<0
=> a<b
Answer :B
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Re: If la-bl > a-b, then which of the following must be true A) a > b B) [#permalink] New post   02 Aug 2021, 04:29
Could anyone explain why D is incorrect?
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Re: If la-bl > a-b, then which of the following must be true A) a > b B) [#permalink] New post   04 Aug 2021, 07:03
funkyakki, martijntugenberg

For many questions it is best to eliminate all incorrect answers but in this case I think it is faster to find the correct answer, than to disprove the 4 wrong options. Therefore let's transform the given information to find the correct answer

Given: a*b≠0 and la-bl > a-b

Logic: When is la-bl bigger than a-b? --> This is the case only when a-b is negative, because where a-b positive both la-bl and a-b are equal, but we want la-bl to be bigger. (la-bl would be bigger because la-bl would become positive (everything negative in I I becomes positive) while a-b would remain negative and thus clearly be smaller)

Therefore we know that a-b<0. When is a-b<0? When a is smaller than b --> a<b

Therefore we can choose B as the correct answer and don't have to be concerned with any other options.
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Re: If la-bl > a-b, then which of the following must be true A) a > b B) [#permalink] New post   20 May 2023, 07:52
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Re: If la-bl > a-b, then which of the following must be true A) a > b B) [#permalink]
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