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

Question

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 : www.GMATinsight.com

chetan2u · Answer

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

Zuki1803 · Answer

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

Archit3110 · Answer

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

funkyakki · Answer

Can anyone please tell me why option E) lal < lbl is wrong ?

GMATinsight · Answer

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!

NitishJain · Answer

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

naveenban · Answer

For la-bl > a-b to be true, a - b < 0.
b>a. 
 Option B

ManishaPrepMinds · Answer

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: www.GMATinsight.com

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Official Answer

B

martijntugenberg · Answer

Could anyone explain why D is incorrect?

GMATE1 · Answer

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

Dhruv381 · Answer

The way I solved this was going back to the basics since a*b≠0 and we know that |a-b|>(a-b) I did 2 cases 1)(a-b)>(a-b) = a>a which is not possible 2) (a-b)<-(a-b) = 2a<2b = a

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

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