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DS: (x+y)

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by ikaplan » Sun Sep 11, 2011 2:34 am
If x+xy+y=-1, then what is the value of x+y?

(1) y=-1
(2) x=2

Source: NOVA's GMAT DS Prep Course, p.65
"Commitment is more than just wishing for the right conditions. Commitment is working with what you have."
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Source: — Data Sufficiency |
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by gmatclubmember » Sun Sep 11, 2011 4:12 am
ikaplan wrote:If x+xy+y=-1, then what is the value of x+y?

(1) y=-1
(2) x=2

Source: NOVA's GMAT DS Prep Course, p.65
The answer would be B. Second statement alone is sufficient.
What is OA?
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by rohit_gmat » Sun Sep 11, 2011 8:17 am
ikaplan wrote:If x+xy+y=-1, then what is the value of x+y?

(1) y=-1
(2) x=2

Source: NOVA's GMAT DS Prep Course, p.65
trick Q?

stmnt 1) y = -1 ... putting this in our equation gives us :
x + x(-1) + (-1) = -1
x - x -1 = -1
-1 = -1 ==> this doesn't give us any value for x, so we cant find out what x+y equals to
INSUFF

stmnt 2) x = 2 ... putting this in our equation gives us :
2 + 2y + y = -1
3y = -1 -2
3y = -3
y = -1
x =2 & y=-1 ... so x+y = 1

SUFF

Answer B
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by ikaplan » Sun Sep 11, 2011 12:20 pm
OA: B
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by Brent@GMATPrepNow » Sun Sep 11, 2011 4:07 pm
ikaplan wrote:If , then what is the value of x+y?

(1) y=-1
(2) x=2

Source: NOVA's GMAT DS Prep Course, p.65
I'll offer another approach here, since it's always nice to have several options when solving a question.

For me, when I see a given equation like x+xy+y=-1, I consider whether there's a way to rearrange it such that I can gain some information about x and y.

Here, we can rewrite the given equation as x+xy+1+y=0. Then we can factor it in parts (a useful technique when dealing with 4-term algebraic expressions).
When we factor it in parts we get: x(1+y) + 1(1+y)=0
We can now simplify this as (x+1)(1+y)=0
This tells us that x= -1 or y= -1 (or they both equal -1)

Okay, now let's examine the statements:

Statement 1: y= -1
If y= -1, we can see that x can have any value, which means x+y can have any value.
As such, statement 1 is not sufficient.

Statement 2: x = 2
If x = 2, then it must be true that y=-1 (since we already concluded that x= -1 or y= -1 (or they both equal -1))
So we know that x=2 and we know that y must equal -1.
As such, we can find the value of x+y (it equals 1), so statement 2 is sufficient, and the answer is B

Of course, rohit_gmat's solution is quicker, but I thought I'd post another approach nonetheless.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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