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If 1 > 1 - ab > 0, which of the following must be true

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by VJesus12 » Sat Feb 24, 2018 3:13 am

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00:00

Answers

A

B

C

D

E

Stats

Difficulty—

If 1 > 1 - ab > 0, which of the following must be true?

I. a/b > 0
I. a/b < 1
III. ab < 1

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

The OA is the option E.

Experts, can you help me here? Any example? How should I solve this PS question? Thanks in advanced.
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by Brent@GMATPrepNow » Sat Feb 24, 2018 7:23 am
VJesus12 wrote:If 1 > 1 - ab > 0, which of the following must be true?

I. a/b > 0
II. a/b < 1
III. ab < 1

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
GIVEN: 1 > 1 - ab > 0
Multiply all 3 sides by -1 to get: -1 < -1 + ab < 0 [since I multiplied by a NEGATIVE number, I had to REVERSE the inequality symbols]
Add 1 to all 3 sides to get: 0 < ab < 1

First, if 0 < ab, then a and b are the SAME SIGN, which means a/b > 0
So, statement I is TRUE
ELIMINATE B and C

Second, our new inequality clearly tells us that ab < 1
So, statement III is TRUE
ELIMINATE A and D

So, we need not even check whether statement II is true.

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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