If a > 2, is b < 1?

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If a > 2, is b < 1?

by BTGModeratorVI » Fri Jul 03, 2020 7:16 am

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If a > 2, is b < 1?

(1) ab<2
(2) ab>0

Answer: A
Source: Economist GMAT

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Re: If a > 2, is b < 1?

by Brent@GMATPrepNow » Sat Jul 04, 2020 5:56 am

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BTGModeratorVI wrote:
Fri Jul 03, 2020 7:16 am
If a > 2, is b < 1?

(1) ab<2
(2) ab>0

Answer: A
Source: Economist GMAT
Target question: Is b < 1?

Given: a > 2

Statement 1: ab < 2
Since we're told that a > 2, we know that a is POSITIVE, which means we can safely divide both sides of the inequality by a.
When we do this we get: b < 2/a
Since a > 2, we know that the fraction's denominator is greater its numerator, which means 2/a must be less than 1
So, 2/a < 1
Since b < 2/a, we get: b < 2/a < 1
In other words, b < 1
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: ab > 0
Let's TEST some numbers.
There are several values of a and b that satisfy statement 2. Here are two:
Case a: a = 3 and b = 2, in which case b > 1
Case b: a = 3 and b = 0.1, in which case b < 1
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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