If 0 < r < 1 < s < 2, which of the following mus

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AAPL: Moderator; Posts: 2599; Joined: Sun Oct 29, 2017 2:08 pm; Followed by:2 members

If 0 < r < 1 < s < 2, which of the following mus

by AAPL » Sun Jan 28, 2018 2:00 pm

If 0 < r < 1 < s < 2, which of the following must be less than 1?

I. r/s
II. rs
III. s - r

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

The OA is A.

I don't have clear this PS question. Can any expert give an example of why II does not work? I just can't figure it out.I appreciate if any expert explain it for me. Thank you so much.

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Source: Beat The GMAT — Problem Solving | Sun Jan 28, 2018 2:00 pm

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Sun Jan 28, 2018 2:43 pm

AAPL wrote:If 0 < r < 1 < s < 2, which of the following must be less than 1?

I. r/s
II. rs
III. s - r

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

I) r/s
r and s are both POSITIVE, and r is less than s.
So, it MUST be the case that r/s < 1

II) rs
It could be the case that r = 0.9 and s = 1.8, in which case rs = 1.62
So, it NEED NOT be the case that rs < 1

III) s - r
It could be the case that r = 0.1 and s = 1.8, in which case s - r = 1.7
So, it NEED NOT be the case that s - r < 1

Answer: A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Wed Jan 31, 2018 4:26 pm

AAPL wrote:If 0 < r < 1 < s < 2, which of the following must be less than 1?

I. r/s
II. rs
III. s - r

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

We are given that 0 < r < 1 < s < 2 and need to determine which Roman Numeral expressions must be less than 1. Let's test each expression.

I. r/s

Since r is less than s and both r and s are positive, r/s will always be less than 1. Roman numeral I is correct.

II. rs

The product of r and s does not have to be less than 1. For example, if r = 0.8 and s = 1.5 the product of r and s will be (0.8)(1.5) = 1.2, which is greater than 1. Roman numeral II is not correct.

III. s - r

s - r does not have to be less than 1. For example, if s = 1.9 and r = 0.1, s - r = 1.8. Roman number III is not correct.

Answer: A

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