Is a

Question

Is a < b?

(1) |a – b| = b – a
(2) a/b < 1

mahdwen · Answer

Detailed Answer

Is a < b?
I. |a – b| = b – a
II. a/b < 1

I. |a-b| = b-a means b-a ≥ 0, or b ≥ a.
So a<b or a=b are both satisfactory answers => Insufficient

II. a/b<1, implying that b different than 0. We have two cases: if b > 0 then a < b, and if b < 0, then a > b => Insufficient

Both Statement together are sufficient to get to the conclusion a < b, answer C

Bunuel · Answer

Thst's correct. Check more questions to practice: DS Abolute Values Questions to practice: https://gmatclub.com/forum/search.php?se ... &tag_id=37 PS Abolute Values Questions to practice: https://gmatclub.com/forum/search.php?se ... &tag_id=58 Hard set on Abolute Values: https://gmatclub.com/forum/inequality-an ... 86939.html

sonikavadhera · Answer

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.

Bunuel · Answer

(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.

Hope it's clear.

sonikavadhera · Answer

Oh I forgot the equal possibility. Thanks.

sasidharrs · Answer

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?

origen87 · Answer

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.

amanvermagmat · Answer

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 Hope this helps

anhht13 · Answer

(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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Is a < b? (1) |a – b| = b – a (2) a/b < 1

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions