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If 3y = 2x + 6, what is the value of x?

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Bunuel
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If 3y = 2x + 6, what is the value of x? [#permalink] New post   14 Aug 2016, 07:16
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If 3y = 2x + 6, what is the value of x?

(1) 6y = 4x + 12
(2) 2y = 3x − 3
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B
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B
LogicGuru1
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If 3y = 2x + 6, what is the value of x? [#permalink] New post   14 Aug 2016, 08:18
Bunuel wrote:
If 3y = 2x + 6, what is the value of x?

(1) 6y = 4x + 12
(2) 2y = 3x − 3


B is the correct answer

(1) 6y = 4x + 12
This equation cannot be used to solve for variable x or y as it will give us infinite many solutions when used in conjunction with the equation given in the stimulus.

\(\frac{a1}{a1}=\frac{b1}{b2}=\frac{c1}{c2}\)

\(\frac{3}{6}=\frac{2}{4}=\frac{6}{12}\)

\(\frac{1}{2}=\frac{1}{2}=\frac{1}{2}\)===>Infinite many solution

(2) 2y = 3x − 3
Gives us unique solution
Sufficient
ANSWER IS B
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Re: If 3y = 2x + 6, what is the value of x? [#permalink] New post   12 Dec 2017, 20:26
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If you multiply the eqn in the qn by 2 you get the same eqn as statement 1.
2 * (3y = 2x + 6) = 6y = 4x + 12
So statement 1 is not sufficient.

If you solve statement 2 , you can get the values of x and y by simultaneous method.
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Re: If 3y = 2x + 6, what is the value of x? [#permalink] New post   19 May 2019, 18:32
Expert Reply
Given

3y = 2x + 6 ......... Equation A

To Find = The value of x

Statement 1

6y = 4x + 12

2*(3y) = 2*(4x +12)

3y = 2x + 6

Since the above equation is the same as the Equation A, it has got infinitely many solutions (Lines for both the equation are overlapping)

Since we have not got one unique value of x, Statement 1 is not sufficient alone.

Statement 2

2y = 3x -3

Let's multiply the equation by 3

6y = 9x - 9 ......... Equation B

Let's multiply the given equation by 2

6y = 4x + 12 ......... Equation C

Let's subtract Equation C from Equation B

( 6y - 6y ) = ( 9x - 9 ) - ( 4x + 12 )

0 = 5x + 3

x = -3/5

Since we have got one unique value of x, Statement 2 is independently sufficient.

Hence, the correct answer is B
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Re: If 3y = 2x + 6, what is the value of x? [#permalink]
19 May 2019, 18:32
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Bunuel
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