BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Given the inequalities above, which of the following CANNOT be the value of r?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
User avatar
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

Re: Given the inequalities above, which of the following CANNOT be the value of r?

by Brent@GMATPrepNow » Wed Mar 18, 2020 5:53 am
BTGModeratorVI wrote: ↑
Sat Mar 14, 2020 6:28 am
 3r ≤ 4s + 5
|s| ≤ 5

Given the inequalities above, which of the following CANNOT be the value of r?

A. –20
B. –5
C. 0
D. 5
E. 20

Answer: E
Source: Official Guide
Let's see what happens when we minimize and maximize the value of s

GIVEN: |s| ≤ 5
So s = 5 is the GREATEST possible value of s
And s = -5 is the LEAST possible value of s

If s = 5, we get: 3r ≤ (4)(5) + 5
Simplify to get: 3r ≤ 25
Divide both sides by 3 to get: r ≤ 8.3333..

At this point, we don't have to explore what happens when we minimize the value of s, w hey buddye can readily see that r CANNOT equal 20

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Legendary Member
Posts: 2532
Joined: Sun Oct 29, 2017 2:04 pm
Followed by:6 members

Re: Given the inequalities above, which of the following CANNOT be the value of r?

by swerve » Wed Mar 18, 2020 6:56 am
BTGModeratorVI wrote: ↑
Sat Mar 14, 2020 6:28 am
 3r ≤ 4s + 5
|s| ≤ 5

Given the inequalities above, which of the following CANNOT be the value of r?

A. –20
B. –5
C. 0
D. 5
E. 20

Answer: E
Source: Official Guide
\(3r-4s \le 5\)------ 1
\(5 \ge s \ge -5\)-------2

Now lets put answer options in equation 1 keeping equation 2 in mind

\(r=-20\). Even if \(s\) takes the smaller value -5 or +5, it will always be less than 5
\(r= -5\). If \(s\) is +5 then the value of equation 1 will be less than 5
\(r=0\). If \(s=+5\) than the value of equation 1 will be less than 5
\(r=5\). If \(s= +5\) than the value of equation 1 will be less than 5
\(r=20\). It doesn't matter whether the value of s is maximum or minimum, the value of equation 1 will always be greater than 5

E is the correct answer.
Top
User avatar
GMAT Instructor
Posts: 8131
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

Re: Given the inequalities above, which of the following CANNOT be the value of r?

by Scott@TargetTestPrep » Fri Mar 20, 2020 6:00 am
BTGModeratorVI wrote: ↑
Sat Mar 14, 2020 6:28 am
 3r ≤ 4s + 5
|s| ≤ 5

Given the inequalities above, which of the following CANNOT be the value of r?

A. –20
B. –5
C. 0
D. 5
E. 20

Answer: E
Source: Official Guide
We rewrite the absolute value inequality for s as -5 ≤ s ≤ 5. If s = -5 (i.e., the smallest value it can be), then we have:

3r ≤ 4(-5) + 5

3r ≤ -15

r ≤ -5

If s = 5 (i.e., the largest value it can be), then we have:

3r ≤ 4(5) + 5

3r ≤ 25

r ≤ 25/3 = 8⅓

Therefore, we see that r can be any of the values in the given choices except 20.

Answer: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Post new topic Post Reply
• Page 1 of 1