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equations DS

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equations DS

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Does (x + a)^2 = y^2?

(1) x = y - a

(2) x = y + a

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got A here
it is more clear while using a^2-b^2=(a-b)(a+b)
second can be true if a=0 but the value is unknown

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A for me as well

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Hi there,

(1) Sufficient:

x+a = y therefore (x+a)^2 = y^2

(2) Insufficient:

Take a = 0 then x=y hence (x+a)^2 = x^2 = y^2
Take y = a = 1 and x = 2, then 3^2 = (x+a)^2 is different from y^2 = 1

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Night reader wrote:
Does (x + a)^2 = y^2?

(1) x = y - a

(2) x = y + a
IMO A
what's the OA?

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IMO A as well as per explanation provided above.

whats the OA?

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ashforgmat wrote:
IMO A as well as per explanation provided above.

whats the OA?
good question.
without offense - I was not satisfied with the expert's answer at this time Sad too mechanical approach

anyways my best try was

Quote:
Does (x + a)^2 = y^2?

(1) x = y - a

(2) x = y + a
question stem -> |x+a|=|y| OR |x+a|-|y|=0 -> |x+a-y|=0 where i) x+a-y=0, ii) -x-a+y=0 -> both equate x=y-a which is equivalent to -x=a-y
st(1) x= y-a is Sufficient
st(2) x= y+a is Not Sufficient

answer is A.

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I think the expert reply was short and to the point.....I think you just over analyzed the question. I understand you're trying to see the trick with the absolute values, but it really just leads to the same answer. Maybe the question was just testing to see if you'd over think the question lol!

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chendawg wrote:
I think the expert reply was short and to the point.....I think you just over analyzed the question. I understand you're trying to see the trick with the absolute values, but it really just leads to the same answer. Maybe the question was just testing to see if you'd over think the question lol!
The problem is testing what it does. OA was A. I pointed out the expert's solution above and followed with my (last) solution to help us see the "if-s" -->
(x+a)^2=y^2 is deconstructed into (x+a)(x+a)=y*y where (x+a) can OR can not be equal to y. Because the official answer suggested A, I left this untouched. We had discussion with another fellow in private about this question too. I think the question itself creates an ambiguity.

As for over-analysis per DS questions - I'd rather do over- than under- Smile

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Don't over-analyze.

If x = y + a then the stem would become:

((y + a) + a)^2 = y^2
(y + 2a)^2 = y^2

Which only makes sense if a = 0 but is false for any other value. Insufficient.

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hey_deep wrote:
Don't over-analyze.

If x = y + a then the stem would become:

((y + a) + a)^2 = y^2
(y + 2a)^2 = y^2

Which only makes sense if a = 0 but is false for any other value. Insufficient.
is your comment re the 2nd statement?
the earlier post was about the 1st statement - I am copying/pasting for clarity purpose: (x+a)^2=y^2 is deconstructed into (x+a)(x+a)=y*y where (x+a) can OR can not be equal to y. When mods are given we should easily spot that difference in values.
...

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Night reader wrote:
chendawg wrote:
I think the expert reply was short and to the point.....I think you just over analyzed the question. I understand you're trying to see the trick with the absolute values, but it really just leads to the same answer. Maybe the question was just testing to see if you'd over think the question lol!
The problem is testing what it does. OA was A. I pointed out the expert's solution above and followed with my (last) solution to help us see the "if-s" -->
(x+a)^2=y^2 is deconstructed into (x+a)(x+a)=y*y where (x+a) can OR can not be equal to y. Because the official answer suggested A, I left this untouched. We had discussion with another fellow in private about this question too. I think the question itself creates an ambiguity.

As for over-analysis per DS questions - I'd rather do over- than under- Smile
I like your point about the deconstruction, as I can see many questions where that would be relevant. However, I think you can tell by looking at this question that it isn't one of them; because the expressions in the Statements are so similar to the expressions in the Prompt, you know that Substitution would be your best option. If you saw something strange like "x
I agree that a full analysis of the question is necessary, however, I want to suggest two things to you for greater success on test day:

1) Overanalysis is NOT better than underanalysis. They are both bad. You want to do exactly the right analysis! Remember it's a timed, adaptive test, so you should not be over-analyzing.

2) Analyze the entire question. The Statements often give you a little hint about what kind of question it is. Yes, of course, we should break down the Prompt before actually looking at the Statements carefully, but it's all on one big screen in front of you, and that's okay -- use everything you can see to determine the correct approach.

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go on with A

Since

x=y-a
x+a=y

squaring on both sides we get

(x+a)^2=y^2


go on with B
x=y+a
x-a=y
squaring on both sides we get
not possible to get

(x+a)^2=y^2


opt A is correct Mr. Green

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Only option A can help determine if the eqation holds true or not as value of variable a can be "Zero".

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the answer should be A.just substitute the value of x=y-a form first statetment in the question that is (y-a+a)^2which is equal to y^2 hence proved.

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