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# If -17 ≤ 3 - 4q ≤ 47, what is the difference between the max and min

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Intern
Joined: 06 Nov 2018
Posts: 2
Concentration: Economics, Finance
If -17 ≤ 3 - 4q ≤ 47, what is the difference between the max and min  [#permalink]

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04 Aug 2019, 01:00
00:00

Difficulty:

25% (medium)

Question Stats:

75% (01:12) correct 25% (01:21) wrong based on 28 sessions

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If -17 ≤ 3 - 4q ≤ 47, what is the difference between the maximum and minimum possible values of q?

A. 5
B. 6
C. 11
D.15
E. 16
Intern
Joined: 06 Nov 2018
Posts: 2
Concentration: Economics, Finance
Re: If -17 ≤ 3 - 4q ≤ 47, what is the difference between  [#permalink]

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04 Aug 2019, 01:14
What is the difference between the maximum and minimum possible values of x?
1. Solve the inequality the same way as you solve a one-variable equation.
So, 3 should be moved to left and right sides with opposite sign: -20<=-4q<=44

2. Divide the inequality by (-4), keeping in mind that if you multiply or divide an inequality by a negative number, flip the inequality sign.
Hence, -11<=q<=5

3. Between -11 and 5 on the number line there are 16 points.
Director
Joined: 28 Jul 2016
Posts: 546
Location: India
Concentration: Finance, Human Resources
GPA: 3.97
WE: Project Management (Investment Banking)
Re: If -17 ≤ 3 - 4q ≤ 47, what is the difference between the max and min  [#permalink]

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04 Aug 2019, 05:14
-17 ≤ 3 - 4q ≤ 47
or
-20<-4q<44
or
-5<-q<11
now multiple everyside by -
thus 5>q>-11
henec max q<5
and min q is >-11
point in betwwen
5-(-11) = 16
thus E
Director
Joined: 20 Jul 2017
Posts: 636
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Concentration: Entrepreneurship, Marketing
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Re: If -17 ≤ 3 - 4q ≤ 47, what is the difference between the max and min  [#permalink]

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04 Aug 2019, 11:31
Asssel wrote:
If -17 ≤ 3 - 4q ≤ 47, what is the difference between the maximum and minimum possible values of q?

A. 5
B. 6
C. 11
D.15
E. 16

-17 ≤ 3 - 4q ≤ 47
—> -3 - 17 ≤ 3 - 4q - 3 ≤ 47 - 3
—> -20 ≤ -4q ≤ 44
—> -20/-4 ≥ q ≥ 44/-4
—> 5 ≥ q ≥ -11
—> -11 ≤ q ≤ 5

Maximum value of q = 5
Minimum value of q = -11

Difference = 5 - (-11) = 16

IMO Option E

Pls Hit kudos if you like the solution

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Re: If -17 ≤ 3 - 4q ≤ 47, what is the difference between the max and min   [#permalink] 04 Aug 2019, 11:31
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# If -17 ≤ 3 - 4q ≤ 47, what is the difference between the max and min

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