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# What is the value of x?

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Math Expert
Joined: 02 Sep 2009
Posts: 47112
What is the value of x?  [#permalink]

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14 Apr 2015, 04:48
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15% (low)

Question Stats:

73% (00:43) correct 27% (00:29) wrong based on 112 sessions

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What is the value of x?

(1) 5x + 3y = 15
(2) y = 5 – (5/3)x

Kudos for a correct solution.

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Re: What is the value of x?  [#permalink]

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14 Apr 2015, 05:53
Bunuel wrote:
What is the value of x?

(1) 5x + 3y = 15
(2) y = 5 – (5/3)x

Kudos for a correct solution.

1. 5x+3y=15

Not Sufficient

2. 3y=15-5x
5x+3y=15

Not Sufficient

1 and 2:
Both equations are the same so there can be unlimited solutions.

Manager
Joined: 17 Mar 2015
Posts: 121
Re: What is the value of x?  [#permalink]

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14 Apr 2015, 07:37
#1 - no info about y so we can't find x, insufficient
#2 - same thing. insufficient
#1 + #2.
Transforming 2nd equation into 3y+5x = 15 and noticing that whichever pair of (x;y) you choose to complete the equation #2, it will also complete the equation in #1 (coz they are equal afterall) thus making it impossible to determine the value of x.

Manager
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Re: What is the value of x?  [#permalink]

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14 Apr 2015, 09:56
St 1) 5x + 3y = 15 -> We get 2 values x=0 y=5 or y=0 x=3 so value of x can be 0 or 5 -> NS
St 2) y = 5 – (5/3)x -> solving this we get the same eq. as st 1's (5x + 3y = 15) so again two values of x 0 or 5 -> NS
Combining St1 and ST2 -> No unique solution!

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Re: What is the value of x?  [#permalink]

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14 Apr 2015, 09:57
1
(1) 5x + 3y = 15

Clearly insufficient.

(2) y = 5 – (5/3)x

Solve:
y/5= 1-x/3
x/3+y/5=1
therefore
5x+3y=15
This equation is same as equation 1)
So equation 1 and equation 2 are same and insufficient. So E
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Re: What is the value of x?  [#permalink]

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14 Apr 2015, 10:16
(1) 5x + 3y = 15
no info is given on y
insufficient

(2) y = 5 – (5/3)x
If this expression is multiplied by 3, it is identical to statement 1
Insufficient

Director
Joined: 21 May 2013
Posts: 651
Re: What is the value of x?  [#permalink]

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15 Apr 2015, 08:02
Bunuel wrote:
What is the value of x?

(1) 5x + 3y = 15
(2) y = 5 – (5/3)x

Kudos for a correct solution.

1. 5x+5y=15. Insufficient
2.y=5-(5/3)x
3y=15-5x. Insuffcient

Using both statements, data is still insufficient to find value of x
Math Expert
Joined: 02 Sep 2009
Posts: 47112
Re: What is the value of x?  [#permalink]

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20 Apr 2015, 06:30
Bunuel wrote:
What is the value of x?

(1) 5x + 3y = 15
(2) y = 5 – (5/3)x

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION

Since (1) is a linear equation with two variables, it will allow you to solve for x only in terms of y. So that statement is insufficient by itself, eliminate answers A and D. This leaves B, C, and E.

Since (2) is also a linear equation with two variables, it will allow you to solve for x only in terms of y. So that statement is insufficient by itself, eliminate B. This leaves C and E.

You might be tempted to choose C, because (1) and (2) together give you two linear equations with the same two variables. As we’ve seen though, we must first make sure that the two equations are distinct. To see whether they are in fact the same equation in different guises, rewrite one of them—say Statement (1)—in the form that other already has.

So let’s solve for y using (1).

5x + 3y = 15

Subtract 5x from each side.

3y=15-5x

Divide each side by 3.

y = 5 – (5/3)x

So (1) and (2) are in fact the same equation.

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Re: What is the value of x?  [#permalink]

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30 Oct 2017, 06:10
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