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Can someone please explain why the answer is not Option A.

I know why statement 2 is insufficient as the case changes for positive and negative numbers.

(1) |a – b| = b – a. So, |a – b| = -(a - b), which means that \(a \leq b\). So, a could be equal to b (answer NO) as well as a could be less than b (answer YES). Not sufficient.

Re: Is a < b? (1) |a – b| = b – a (2) a/b < 1 [#permalink]

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05 Jun 2017, 10:37

Bunuel wrote:

sonikavadhera wrote:

Can someone please explain why the answer is not Option A.

I know why statement 2 is insufficient as the case changes for positive and negative numbers.

(1) |a – b| = b – a. So, |a – b| = -(a - b), which means that \(a \leq b\). So, a could be equal to b (answer NO) as well as a could be less than b (answer YES). Not sufficient.

Re: Is a < b? (1) |a – b| = b – a (2) a/b < 1 [#permalink]

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05 Jun 2017, 18:51

Hi, Why B is not sufficient.. given a/b<1 => a<b.. which is what we are trying to prove right.. or am I missing something more fundamental in inequalities?

Re: Is a < b? (1) |a – b| = b – a (2) a/b < 1 [#permalink]

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05 Jun 2017, 21:53

1

This post received KUDOS

sasidharrs wrote:

Hi, Why B is not sufficient.. given a/b<1 => a<b.. which is what we are trying to prove right.. or am I missing something more fundamental in inequalities?

We cannot multiply b on both sides as we do not know the sign on 'b'. Never multiply/divide on both sides unless you are sure of the sign. When positive its the way you put it, if negative the inequality sign changes.
_________________

Re: Is a < b? (1) |a – b| = b – a (2) a/b < 1 [#permalink]

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05 Jun 2017, 22:09

sasidharrs wrote:

Hi, Why B is not sufficient.. given a/b<1 => a<b.. which is what we are trying to prove right.. or am I missing something more fundamental in inequalities?

Hi

In case of inequalities, you cannot multiply or divide both sides by a variable until and unless you know the sign of that variable (positive or negative)

So if you are given: a/b < 1 you will have to take both the cases:

Case 1. b is positive. In this case, we will multiply both sides by b, and since b is positive, the sign of inequality will Not change. So a/b * b < 1*b or a < b

Case 2. b is negative. In this case, we will multiply both sides by b, and since b is negative, the sign of inequality Will change. So a/b * b > 1*b or a > b

Re: Is a < b? (1) |a – b| = b – a (2) a/b < 1 [#permalink]

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01 Nov 2017, 01:19

(1) |a – b| = b – a => |a – b| = -a + b = - (a-b) => a-b ≤ 0 => insufficient (2) a/b = 1 => (a-b)/ b < 0. We have 2 cases: b<0 and a<b or b>0 and a>b => insufficient

(1) + (2) => a-b <0 => a <b => sufficient. Hence, the answer is C ----

Kindly press +1 kudos if the explanation is clear! Thank you