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inequality

by mrinal2100 » Sat Aug 27, 2011 7:37 am
|x+2|=|y+2| what is the value of x+y?
(1) xy<0
(2) x>2 y<2

if mod (X+2) = mod (Y+2)

then (x+2)^2 = (Y+2)^2

there fore x^2 + 4X + 4 = Y^2 + 4Y + 4

X^2 - Y^2 = 4 (Y-X)

(X+Y)(X-Y) = -4(X-Y)

so X + Y = -4 ...

So i coould solve these with out even looking at here statement 1 and 2

Is there any mistake in my solution
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by aplavakarthik » Sun Aug 28, 2011 7:59 am
mrinal2100 wrote:|x+2|=|y+2| what is the value of x+y?
(1) xy<0
(2) x>2 y<2

if mod (X+2) = mod (Y+2)

then (x+2)^2 = (Y+2)^2

there fore x^2 + 4X + 4 = Y^2 + 4Y + 4

X^2 - Y^2 = 4 (Y-X)

(X+Y)(X-Y) = -4(X-Y)

so X + Y = -4 ...

So i coould solve these with out even looking at here statement 1 and 2

Is there any mistake in my solution
Hey,

U r right but u have left the problem unfinished.

U can remember one more thing

if |X|=|Y| it is equal to |X|=+/-(y)

So considering the given data |x+2|=+/-(y+2)

first lets consider x+2=+(y+2)

Which gives u x=y

second lets consider x+2=-(y+2)

which gives u x+y=-4.

U left the problem here.

from above u can understand that one possible value for x+y=-4, but we also have got x=y that mean for every value u take for x (which is equal to y) u get different value for x+y

Eg: if x=2 then y also is 2 and here x+y =4 and not -4.

So u cannot say directly from the given statement.

Now consider Statement 1
1.xy<0

for the above to satisfy one should be +ve and the other should be -ve
ie., x +ve, y -ve or x -ve, y +ve

so taking this from the above got values x=y will not satisfy so value of x+y=-4

Statement 1 is sufficient

Now consider statement 2

x>2,y>2

from given statement x+y=-4 can ruled out since x and y are +ve

Now x=y can have more than one value for x+y since we can have many values to satisfy x>2,y>2

Statement 2 Not sufficient.

Ans A Statement 1 alone is sufficient
Last edited by aplavakarthik on Sun Aug 28, 2011 8:03 am, edited 1 time in total.
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by force5 » Sun Aug 28, 2011 8:02 am
The problem here is that you are overlooking what absolute value means..

when we say |x+2| = |y+2|

we are not sure about the signs of x and y. ie- we dont know whether they are positive or negative

you opened the squares that's fine. but you still don't know whether x+y = -4 or -x+y=-4 or x-y=-4 which makes your conclusion much broader.

hope you understand.
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by aplavakarthik » Sun Aug 28, 2011 8:13 am
force5 wrote:The problem here is that you are overlooking what absolute value means..

when we say |x+2| = |y+2|

we are not sure about the signs of x and y. ie- we dont know whether they are positive or negative

you opened the squares that's fine. but you still don't know whether x+y = -4 or -x+y=-4 or x-y=-4 which makes your conclusion much broader.

hope you understand.
that is the reason i have considered x+2=+/-(y+2)
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by prateek_guy2004 » Sun Aug 28, 2011 2:25 pm
Statement 1 sufficient

A
Don't look for the incorrect things that you have done rather look for remedies....

https://www.beatthegmat.com/motivation-t90253.html
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by force5 » Sun Aug 28, 2011 2:38 pm
Yes correct Answer should be A
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by GmatKiss » Sun Aug 28, 2011 11:47 pm
IMO:A
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by navami » Mon Aug 29, 2011 8:13 am
IMO A.

Option 2 is not needed.
This time no looking back!!!
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by [email protected] » Wed Sep 07, 2011 9:51 am
mrinal2100 wrote:|x+2|=|y+2| what is the value of x+y?
(1) xy<0
(2) x>2 y<2

if mod (X+2) = mod (Y+2)

then (x+2)^2 = (Y+2)^2

there fore x^2 + 4X + 4 = Y^2 + 4Y + 4


X^2 - Y^2 = 4 (Y-X)

(X+Y)(X-Y) = -4(X-Y)

so X + Y = -4 ...

So i coould solve these with out even looking at here statement 1 and 2

Is there any mistake in my solution
I THINK THE ANSWER SHOULD BE D, FROM OPTION B, IF X>2 AND Y<2 AND TO GET |x+2|=|y+2|
WE GET TO KNOW THAT X IS POSITIVE AND Y IS NEGATIVE. IN THIS CASE ALSO X+Y = -4 ALWASYS
SO ACCORDING TO ME ANSWER IS D
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by Ian Stewart » Wed Sep 07, 2011 1:14 pm
mrinal2100 wrote:|x+2|=|y+2| what is the value of x+y?
(1) xy<0
(2) x>2 y<2

if mod (X+2) = mod (Y+2)

then (x+2)^2 = (Y+2)^2

there fore x^2 + 4X + 4 = Y^2 + 4Y + 4

X^2 - Y^2 = 4 (Y-X)

(X+Y)(X-Y) = -4(X-Y)

so X + Y = -4 ...

So i coould solve these with out even looking at here statement 1 and 2

Is there any mistake in my solution
I've highlighted the mistake in your solution above. You've divided by X-Y on both sides of the equation, but you can only do that if you're sure that X-Y is not equal to zero (you can never divide by zero). Since, before reading the statements, it's certainly possible that X=Y, you do need additional information here. Using either statement, however, you can be certain that X is not equal to Y, so your solution proves the answer is D.

There is a different (non-algebraic) way to look at this question. The expression |a-b| is always equal to the distance between a and b on the number line. So |x+2| = |x - (-2)| is just equal to the distance between x and -2 on the number line. So, from the equation |x+2| = |y+2|, we learn that x and y are equally far from -2 on the number line. There are just two possibilities: x and y are on the same side of -2, so x=y, or x and y are on opposite sides of -2, in which case on the number line we would have a picture something like this (where x and y could be in either order of course) :

----x-----(-2)------y-----

In this case, -2 is the midpoint of x and y, so is the average of x and y, and thus x+y = (2)(-2) = -4. Since each statement guarantees that x and y are different, each statement is sufficient and the answer is D.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by sl750 » Thu Sep 08, 2011 6:51 am
This question confuses me. Are we supposed to rephrase the question to read
Does x=y or Does x+y =-4? Because the question is not a yes/no question, how do you know that this question has only one solution?
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