Modulus inequality --Veritas question

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Mo2men: Legendary Member; Posts: 712; Joined: Fri Sep 25, 2015 4:39 amFollowed by: 5 members; Thanked: 14 times

by Mo2men » Sun Jan 14, 2018 7:28 am

If |12xâˆ’5|>|7âˆ’6x|, which of the following CANNOT be the product of two possible values of x?

A. -12
B. -7/5
C. -2/9
D. 4/9
E. 17

OA: C

Source: Veritas

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Source: Beat The GMAT — Problem Solving | Sun Jan 14, 2018 7:28 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Jan 14, 2018 7:37 am

I posted a solution here: https://www.beatthegmat.com/value-of-x-t268225.html

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Mon Jan 29, 2018 10:22 am

Mo2men wrote:If |12xâˆ’5|>|7âˆ’6x|, which of the following CANNOT be the product of two possible values of x?

A. -12
B. -7/5
C. -2/9
D. 4/9
E. 17

Let's first solve for when (12x - 5) and (7 - 6x) are both positive.

12x - 5 > 7 - 6x

18x > 12

x > 12/18

x > 2/3

Now let's solve for when (12x - 5) is negative and (7 - 6x) is positive.

-(12x - 5) > 7 - 6x

-12x + 5 > 7 - 6x

-2 > 6x

-1/3 > x

So we have x < -1/3 or x > 2/3.

If x were -1/3 or 2/3, then the product would be -2/9. However, the inequalities specify that x can be neither -1/3 nor 2/3, so we know the product of two possible values of x cannot be -2/9.

Answer: C

Jeffrey Miller
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