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by smackmartine » Sat Aug 13, 2011 10:15 am
IMO C

x^2+y^2 = (x+y)^2-(2xy)
so we can rephrase whether (x+y)^2-(2xy) >100

1)2xy < 100
However, we don't know the value of (x+y)^2 and can't know the value of (x+y) unless we know the signs , which can be both +ve or both -ve.--- Insufficient.

2)(x+y)^2 >200

Using same logic as above we can't decide the values of 2xy. --Insufficient.

Combining both, we get

(x+y)^2-(2xy)
or GT(200)-LT(100) = LT(200) or GT(200) [GT--greater than , LT--less than]

eg. 201 - 99 = 102 -->LT(200), but

201-(-99) = 300 --> GT(200) , Both case GT(100) Sufficient
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by biswa123 » Sat Aug 13, 2011 11:10 am
Can you give example of two numbers where (x+y)^2 > 200 and x^2+Y^2 <100 ??
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by Frankenstein » Sat Aug 13, 2011 11:14 am
Hi,
From(1): 2xy<100
if x=10, y=1, x^2+y^2 = 101 >100
if x=5, y=5, x^2+y^2 = 50 < 100
Not sufficient

From(2):
(x-y)^2 >= 0
So, x^2+y^2-2xy>=0
So, x^2+y^2 >= 2xy
x^2+y^2+x^2+y^2 >= 2xy+x^2+y^2
2(x^2+y^2) >= (x+y)^2 > 200
So, x^2+y^2 > 100
Sufficient

Hence, B
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by smackmartine » Sat Aug 13, 2011 11:44 am
Frankenstein wrote: From(2):
(x-y)^2 >= 0
So, x^2+y^2-2xy>=0
So, x^2+y^2 >= 2xy
x^2+y^2+x^2+y^2 >= 2xy+x^2+y^2
2(x^2+y^2) >= (x+y)^2 > 200
So, x^2+y^2 > 100
Sufficient
Hmm..Interesting!!
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by smackmartine » Sun Aug 14, 2011 12:13 am
What's the OA?
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by Frankenstein » Sun Aug 14, 2011 12:43 am
Smack..Still not convinced with B?
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by smackmartine » Sun Aug 14, 2011 12:49 am
Frankenstein wrote:Smack..Still not convinced with B?
Actually I am. Just wanted to know the final answer :). If you know the OA , please confirm.
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by ronaldramlan » Sun Aug 14, 2011 3:37 am
This question is taken from Veritas free test. According to Veritas, the OA is C.
I personally believe that the answer is B. Therefore, I'd be very happy if someone from Veritas can clarify.
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by akhilsuhag » Sun Aug 14, 2011 4:57 am
Hey,

From statement 2 how did you get from:

(x+y)^2 > 200 to (x-y)^2 >= 0
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by akhilsuhag » Sun Aug 14, 2011 5:00 am
Hats off!!
Got it now.. I cud nevva have done it this way!!
But why does the OA differ!!
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by GMATGuruNY » Sun Aug 14, 2011 5:57 am
ronaldramlan wrote:Is x^2 + y^2 > 100?

(1) 2xy < 100
(2) (x+y)^2 > 200
Statement 2: (x+y)^2 > 200
Since the square of any value cannot be negative, (x-y)^2 ≥ 0.
Adding the two inequalities, we get:
(x+y)^2 + (x-y)^2 > 200+0.
x^2 + 2xy + y^2 + x^2 - 2xy + y^2 > 200.
2x^2 + 2y^2 > 200.
x^2 + y^2 > 100.
Sufficient.

The correct answer is B.
Last edited by GMATGuruNY on Sun Aug 14, 2011 11:57 am, edited 1 time in total.
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by Frankenstein » Sun Aug 14, 2011 6:04 am
ronaldramlan wrote:This question is taken from Veritas free test. According to Veritas, the OA is C.
I personally believe that the answer is B. Therefore, I'd be very happy if someone from Veritas can clarify.
Hi,
Now, I remember this. I have marked B but the OA was C. I have sent PM to a Veritas expert on July18th. But, I didn't get any reply. But, don't worry, I am sure answer is B. Last month, I have found 3-4 mistakes in Quant in all 5 Veritas tests taken together and I sent PM to them about all those mistakes, and I received reply for only one of them. I hope they will update other things as well.
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by ronaldramlan » Sun Aug 14, 2011 6:47 am
GMATGuruNY wrote: A sneaky way to evaluate statement 2:
The two statements cannot directly contradict each other.
Since statement 1 states that 2xy < 100, it must at least be possible that 2xy < 100 in statement 2.

Statement 2: (x+y)^2 > 200
x^2 + 2xy + y^2 > 200.
x^2 + y^2 > 200 - 2xy
x^2 + y^2 > 200 - (less than 100)
x^2 + y^2 > 100.
In order for it to be possible that 2xy < 100, it MUST be true that x^2 + y^2 > 100.
Sufficient.

The correct answer -- at least on the GMAT -- would have to be B.

If the OA is C, then the question is flawed.
Indeed a tricky thought, using what's commonly accepted in GMAT.
However, don't you think that in doing so, you actually imply that the answer is C, as you seem to evaluate both statements to come to a definite answer?
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by ronaldramlan » Sun Aug 14, 2011 7:10 am
Frankenstein wrote: Hi,
Now, I remember this. I have marked B but the OA was C. I have sent PM to a Veritas expert on July18th. But, I didn't get any reply. But, don't worry, I am sure answer is B. Last month, I have found 3-4 mistakes in Quant in all 5 Veritas tests taken together and I sent PM to them about all those mistakes, and I received reply for only one of them. I hope they will update other things as well.
Well, they certainly have not fixed the mistake if they believe that it is a mistake :)
I just took the simulation a couple of days ago and still got the same OA. If what you said about a number of mistakes in Veritas tests is true, it is horrible. I mean, with the free simulation test available for free and highly featured in many GMAT related websites including Beat The GMAT, such mistake, if exists, should not be left uncorrected. Otherwise, its tests would be misleading to those who struggle to prepare for the GMAT ... truly irresponsible manner if proven to be true.

I know that Veritas is one of the most reputable GMAT prep companies, and what you said about those mistakes was at first incomprehensible for me. But, if your claim is true, Veritas should take immediate actions as its name is at stake.
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