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

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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

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Brent Hanneson - Creator of GMATPrepNow.com
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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.
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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

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