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# Find the value(s) of x such that 8xy - 12y + 2x - 3 = 0 is true for al

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Math Expert
Joined: 02 Sep 2009
Posts: 59589
Find the value(s) of x such that 8xy - 12y + 2x - 3 = 0 is true for al  [#permalink]

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19 Mar 2019, 00:24
00:00

Difficulty:

25% (medium)

Question Stats:

75% (01:48) correct 25% (01:43) wrong based on 32 sessions

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Find the value(s) of x such that 8xy - 12y + 2x - 3 = 0 is true for all values of y.

(A) 2/3
(B) 3/2 or -1/4
(C) -2/3 or -1/4
(D) 3/2
(E) -3/2 or -1/4

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e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3158
Re: Find the value(s) of x such that 8xy - 12y + 2x - 3 = 0 is true for al  [#permalink]

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19 Mar 2019, 00:47

Solution

Given:
• The expression 8xy - 12y + 2x - 3 = 0 is true for all values of y

To find:
• The value(s) of x

Approach and Working:
We can simplify the given expression in the following manner:
• 8xy - 12y + 2x - 3 = 0
Or, 4y (2x – 3) + 1 (2x – 3) = 0
Or, (2x – 3) (4y + 1) = 0

As it is true for all values of y, we can say 2x – 3 = 0, which implies x = 3/2

Hence, the correct answer is option D.

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Senior Manager
Joined: 12 Sep 2017
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Find the value(s) of x such that 8xy - 12y + 2x - 3 = 0 is true for al  [#permalink]

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19 Mar 2019, 19:19
The easiest way I found was:

Given that "true for all values of y" take y as 1.

$$8x(1) - 12(1) + 2x - 3 = 0$$

$$10x - 15 = 0$$

Test the values...

$$10*\frac{3}{2} - 15 = 0$$ ... Only option

D
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9850
Location: Pune, India
Re: Find the value(s) of x such that 8xy - 12y + 2x - 3 = 0 is true for al  [#permalink]

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19 Mar 2019, 20:23
Bunuel wrote:
Find the value(s) of x such that 8xy - 12y + 2x - 3 = 0 is true for all values of y.

(A) 2/3
(B) 3/2 or -1/4
(C) -2/3 or -1/4
(D) 3/2
(E) -3/2 or -1/4

For 8xy - 12y + 2x - 3 = 0 to be true for all value of y, the constant term should be 0 and the y terms should be 0 too.
2x - 3 = 0
which gives x = 3/2
The y terms y(8x - 12) will be 0 too when x = 3/2.

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Karishma
Veritas Prep GMAT Instructor

Re: Find the value(s) of x such that 8xy - 12y + 2x - 3 = 0 is true for al   [#permalink] 19 Mar 2019, 20:23
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