Inequalities - ManhattanGMATPrep

This topic has expert replies
Master | Next Rank: 500 Posts
Posts: 110
Joined: 05 Apr 2012
Thanked: 3 times
Followed by:1 members

Inequalities - ManhattanGMATPrep

by shanice » Wed Aug 15, 2012 11:46 pm
If 1>1-ab>0, which of the following must be true?

I. a/b>0

II. a/b<1


A)I only
B)II only
C)III only
D)I and II only
E)I and III only

My workings:-


From the book:-


Answer is E.

I don't understand why my workings does not match with the one in the book. Someone, please help.

In between, can someone teach me how to use the spoiler to hide the answer.

Thank you very much.

User avatar
Community Manager
Posts: 1060
Joined: 13 May 2011
Location: Utrecht, The Netherlands
Thanked: 318 times
Followed by:52 members

by neelgandham » Thu Aug 16, 2012 12:18 am
My workings:-

One must be aware that, If all the terms in an inequality are multiplied by a negative number, the inequality reverses.(Read here - ... lving.html). For example, 5>4. but when you multiply both sides with -1, you get -5 < -4. (Did you see how the inequality reversed from > to <)

You are absolutely correct in what you did.Starting from where you left, let me multiply all the terms in the inequation with -1.
0*1 < -1*-ab < -1*-1
So, from the equation we know that ab<1 (Option III is a MUST BE TRUE condition) and ab>0.

If the value of ab>0, a and b can be both positive(positive*positive = positive) or both negative(negative*negative = positive).
If a,b are both positive(say 1 and 2), a/b > 0 (1/2>0)
If a,b are both negative(say -2 and -2), a/b > 0 (-2/-1 = 2/1 >0)
So, the value of a/b is always greater than 0, i.e a/b > 0(so is the value of b/a). So, Option I is a MUST BE TRUE condition, if 0<ab<1.

We also know that the value of a/b can be greater than 1(=2 if a = -2 and b = -1) or less then 1(=1/2 if a = 1 and b = 2). So, condition II is not always true.

Answer E

p.s: Here is a link - that will help you with the usage of spoilers.
Anil Gandham
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now's online course at