BTGModeratorVI wrote: ↑

Fri Apr 03, 2020 9:31 am

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

Answer: E
Source: Manhattan prep

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

BTGModeratorVI wrote: ↑

Fri Apr 03, 2020 9:31 am

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

Answer: E
Source: Manhattan prep

Simplifying the given inequality, we have:

0 > -ab > -1

0 < ab < 1

We see that statement III is true. Furthermore, since ab is positive, the values of a and b have the same sign and therefore, a/b is also positive. So statement I is also true. However, a/b is not necessarily less than 1. For example, if a = 0.5 and b = 0.5, we see that a/b = 1. So statement II is not true.

Answer: E