If $3|3 – x| = 7,$ what is the product of all the possible values of $x?$ - The Beat The GMAT Forum

If $3|3 – x| = 7,$ what is the product of all the possible values of $x?$

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Sat Jun 06, 2020 5:16 am

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If $3|3 – x| = 7,$ what is the product of all the possible values of $x?$

A. 1/9
B. 1/3
C. 2/3
D. 16/9
E. 32/9

[spoiler]OA=E[/spoiler]

Source: Manhattan GMAT

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Source: Beat The GMAT — Problem Solving | Sat Jun 06, 2020 5:16 am

RaghavKhanna: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Sun Jun 07, 2020 2:35 am

Re: If $3|3 – x| = 7,$ what is the product of all the possible values of $x?$

by RaghavKhanna » Sun Jun 07, 2020 2:48 am

|x-3| = 7/3
=> x-3 = 7/3, when x-3>0
=> x = 16/3

and,
3-x = 7/3, when x-3<0
x = 2/3

Product of possible values of x = 16/3 * 2/3 = 32/9

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8176; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: If $3|3 – x| = 7,$ what is the product of all the possible values of $x?$

by Scott@TargetTestPrep » Fri Jun 12, 2020 1:53 pm

Gmat_mission wrote: ↑
Sat Jun 06, 2020 5:16 am
If $3|3 – x| = 7,$ what is the product of all the possible values of $x?$

A. 1/9
B. 1/3
C. 2/3
D. 16/9
E. 32/9

[spoiler]OA=E[/spoiler]

Solution:

Case 1. If 3 - x is positive, we have:

3(3 - x) = 7

9 - 3x = 7

-3x = -2

x = 2/3

Case 2. If (3 - x) is negative, we have:

3(-3 + x) = 7

3(x - 3) = 7

3x - 9 = 7

3x = 16

x = 16/3

Therefore, the product of all the possible values of x is 2/3 * 16/3 = 32/9.

Answer: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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