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505-555 (Easy)|   Algebra|      
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Mangeshkhuspe
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What is the value of x^2 - y^2? 19 Jun 2016, 12:48
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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15% (low)

Question Stats:

74% (00:41) correct 26% (00:43) wrong based on 146 sessions

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What is the value of x^2 - y^2?

(1) x + y = 16

(2) x - y = 0

Source is Magoosh.
My question is why the answer is not C and why can't we use difference of squares here.
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B
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FacelessMan
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What is the value of x^2 - y^2? 19 Jun 2016, 13:25
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\(x^2 - y^2\) can be factorized as (x+y)*(x-y). Now statement 2 gives us the value of x-y. So that means, irrespective of the values of (x+y), \(x^2 -y^2\) will always be zero,
Thus B is sufficient, and you don't need A. Hope this helps.
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Mangeshkhuspe
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What is the value of x^2 - y^2? 19 Jun 2016, 13:29
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FacelessMan
\(x^2 - y^2\) can be factorized as (x+y)*(x-y). Now statement 2 gives us the value of x-y. So that means, irrespective of the values of (x+y), \(x^2 -y^2\) will always be zero,
Thus B is sufficient, and you don't need A. Hope this helps.
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Thanks for the reply, but if we multiply by X+Y=16 by X-Y=0, then still we get the answer as "0". Which will then come to C?
Whats the logic behind it?
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Mangeshkhuspe
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What is the value of x^2 - y^2? 19 Jun 2016, 13:32
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Mangeshkhuspe
FacelessMan
\(x^2 - y^2\) can be factorized as (x+y)*(x-y). Now statement 2 gives us the value of x-y. So that means, irrespective of the values of (x+y), \(x^2 -y^2\) will always be zero,
Thus B is sufficient, and you don't need A. Hope this helps.

Thanks for the reply, but if we multiply by X+Y=16 by X-Y=0, then still we get the answer as "0". Which will then come to C?
Whats the logic behind it?
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Got the logic, the highlighted sentence gives the answer.
Its really difficult being so aware about it on the GMAT.
But then it is what the GMAT tests.
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What is the value of x^2 - y^2? Updated on: 19 Jun 2016, 13:45
Originally posted by FacelessMan on 19 Jun 2016, 13:39.
Last edited by FacelessMan on 19 Jun 2016, 13:45, edited 1 time in total.
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Actually, this is a classic case of what is referred as the C Trap. Google "C-Trap GMAT". You need to understand the difference between B and C.
For B, only statement 2 is sufficient to answer this question. Statement 1 is not needed to answer.
For C, both statements are necessary for you to derive the answer.

here, statement 2 is enough to answer and thus it will be B.
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What is the value of x^2 - y^2? 19 Jun 2016, 13:45
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FacelessMan
Actually, this is a classic case of what is referred as the C Trap. Google "C-Trap GMAT". You need to answer the difference between B and C.
For B, only statement 2 is sufficient to answer this question. Statement 1 is not needed to answer.
For C, both statements are necessary for you to derive the answer.

here, statement 2 is enough to answer and thus it will be B.
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Sure Will do. When the answer seems to easy and pointing towards "C". Just Double check.
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What is the value of x^2 - y^2? 19 Jun 2016, 13:47
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Mangeshkhuspe
FacelessMan
Actually, this is a classic case of what is referred as the C Trap. Google "C-Trap GMAT". You need to answer the difference between B and C.
For B, only statement 2 is sufficient to answer this question. Statement 1 is not needed to answer.
For C, both statements are necessary for you to derive the answer.

here, statement 2 is enough to answer and thus it will be B.

Sure Will do. When the answer seems to easy and pointing towards "C". Just Double check.
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Check C-Trap Question Collection from our Special Questions's Directory.
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What is the value of x^2 - y^2? 19 Jun 2016, 18:56
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Mangeshkhuspe
What is the value of x^2 - y^2?

(1) x + y = 16

(2) x - y = 0

Source is Magoosh.
My question is why the answer is not C and why can't we use difference of squares here.
Show more


Sometimes, people rush combining two statement to create 2 equations in 2 variables.

Without even factoring the question to (X-Y)(X+Y), Statement 2 tells:

X-Y=0 , simply this means X=Y, Substitute in equation above x^2 - X^2= 0.

value was achieved by Statement 2

Answer: B
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What is the value of x^2 - y^2? 14 Jul 2016, 13:45
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Hello,

I ran into this DS question

What is the value of \(x^2 - y^2\)?
\((1) x + y = 16\)
\((2) x - y = 0\)

I immediately went x=16-y, and plugged it into the statement equation:
\((16^2-32y+y^2)-y^2\)
and solved, resulting in \(y=8\) and \(x=8\)
And thus concluded that statement 1 is sufficient.

I reviewed the solution and saw that statement 1 is NS as shown by counter examples:
\(x=7, y=9; x=8,y=8\) (as well as others)

My question is: in a general sense, how can I know not just to dive and algebraically solve for x as I did? In my mind, I was sure that I was doing it right, because algebraically it was valid.

Thanks
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What is the value of x^2 - y^2? 14 Jul 2016, 14:18
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bzo34
Hello,

I ran into this DS question

What is the value of \(x^2 - y^2\)?
\((1) x + y = 16\)
\((2) x - y = 0\)

I immediately went x=16-y, and plugged it into the statement equation:
\((16^2-32y+y^2)-y^2\)
and solved, resulting in \(y=8\) and \(x=8\)
And thus concluded that statement 1 is sufficient.

I reviewed the solution and saw that statement 1 is NS as shown by counter examples:
\(x=7, y=9; x=8,y=8\) (as well as others)

My question is: in a general sense, how can I know not just to dive and algebraically solve for x as I did? In my mind, I was sure that I was doing it right, because algebraically it was valid.

Thanks
Show more




There are a couple of issues here.

Firstly, think logically. Statement 1: If x+y = 16, then x and y can take many different values. Firstly, its not given that x and y are integers, secondly there are different values like x =2 y=14, x=10, y=6 which will give different answers for x^2 - y^2. Thirdly, when you say you solved (16^2-32y+y^2)-y^2, it means you equated it to zero. Is it mentioned anywhere that x^2 - y^2 = 0 ?

Now coming to statement 2: x - y = 0. This means that x =y and x^2 - y^2 will be zero for all values of x and y, since they are equal. Hence, statement 2 is sufficient.
Answer is B.

You'll learn these basics with more practice. Stay positive. :)

Please give kudos if this helps! :)
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What is the value of x^2 - y^2? 14 Jul 2016, 14:24
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Thanks for the helpful response Raghav. After your explanation, I see that I made a critical error in equating \(x^2 - y^2\) to zero. Thanks for the encouragement as well :)
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What is the value of x^2 - y^2? 31 Jul 2018, 09:16
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Mangeshkhuspe
What is the value of x^2 - y^2?

(1) x + y = 16

(2) x - y = 0

Source is Magoosh.
My question is why the answer is not C and why can't we use difference of squares here.
Show more

OA:B

Question stem : What is value of \(x^2 - y^2 or (x-y)(x+y)\)

Statement1: \(x+y=16\)
\((x-y)(x+y)=(x-y)16\)
We still need value of \(x-y\).
Statement 1 alone is not sufficient

Statement 2: \(x - y = 0\)
\((x-y)(x+y)=0(x+y)=0\)
We are able to get unique value for \(x^2 - y^2 i.e 0\)

Another way \(x - y = 0,x=y\)
\(x^2 - y^2=x^2 - x^2=0\)
Statement 2 alone is sufficient
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What is the value of x^2 - y^2? 21 Jan 2022, 06:59
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