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SOLVING EQUATIONS

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SOLVING EQUATIONS

by candela.tartiere » Tue Feb 26, 2013 3:30 am
Is x+y=7 ?
(1) 4x+3y=24
(2) x and y are positive integers

I don't know what I got wrong - it seams crystal clear!
x=7-y (from the equation given)
(using this value of x I input it on the second equation)
4(7-y)+3y=24
28-4y+3y=24
-y=-4
y=4
(using this value of y in the equation given in the question: x+4=7, then x must be 3)
Or it is impossible to say that x=3 since we're not said that it is an integer???
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Source: — Data Sufficiency |

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by Anurag@Gurome » Tue Feb 26, 2013 3:50 am
candela.tartiere wrote:I don't know what I got wrong - it seams crystal clear!
x=7-y (from the equation given)
(using this value of x I input it on the second equation)
4(7-y)+3y=24...
It is not given.
The question asked whether (x + y) = 7 or not.
You are taking that as supplied information, and putting back into the question. You can't do that.
candela.tartiere wrote:Is x+y=7 ?
(1) 4x+3y=24
(2) x and y are positive integers
Statement 1: Consider the following two examples,
x = 0, y = 8 ---> (x + y) ≠ 7
x = 3, y = 4 ---> (x + y) = 7

Not sufficient

Statement 2: Consider the following two examples,
x = 1, y = 8 ---> (x + y) ≠ 7
x = 3, y = 4 ---> (x + y) = 7

Not sufficient

1 & 2 Together: Form statement 2, y = (24 - 4x)/3 = 8 - 4x/3
As y is a positive integer, x must be a multiple of 3.
If x = 3 ---> y = 8 - 4 = 4 ---> (x + y) =7
If x ≥ 6 ---> y ≤ 8 - 4*2 = 0 ---> y negative ---> Not possible

Hence, x = 3 and y = 4 is the only solution.
Hence, (x + y) = 7

Sufficient

The correct answer is C.
Anurag Mairal, Ph.D., MBA
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Gurome, Inc.
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