Does (x+y)^2 + (x-y)^2 = 170?

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chipbmk: Senior | Next Rank: 100 Posts; Posts: 70; Joined: Mon Oct 05, 2009 9:33 am

Does (x+y)^2 + (x-y)^2 = 170?

by chipbmk » Fri Nov 20, 2009 4:15 pm

Does (x+y)^2 + (x-y)^2 = 170?

1) x^2 + y^2= 85
2) x=y+1

OA: A

[spoiler]Please be detailed in your responses, especially for statement 2, I think I have proven that statement 2 can work. Will show later once people have given this a try.
[/spoiler]
Thanks!

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Source: Beat The GMAT — Data Sufficiency | Fri Nov 20, 2009 4:15 pm

sunnyjohn: Master | Next Rank: 500 Posts; Posts: 344; Joined: Mon Sep 14, 2009 5:40 am; Thanked: 28 times; Followed by:3 members; GMAT Score:700

by sunnyjohn » Fri Nov 20, 2009 6:58 pm

Answer has to be A.

please explain how u can drive
x = y + 1 ==> (x+y)^2 + (x-y)^2 = 170 OR 2(X^2 + Y^2) = 170

maximum u can do:

(X- Y)^2 = 1

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chipbmk: Senior | Next Rank: 100 Posts; Posts: 70; Joined: Mon Oct 05, 2009 9:33 am

by chipbmk » Fri Nov 20, 2009 11:22 pm

This is what I did, let me know where I went wrong ... it looks right to me.

First: I reduced the main statement to X^2+Y^2 = 85

Statement 2: x=y+1

I plugged this in to the statement above and got:

-- (y+1)^2+Y^2=85
--> Y^2+2Y+1+Y^2=85
--> 2Y^2+2Y-84=0
--> Y^2+Y-42=0
--> (Y-6)(Y+7)=0
--> Y= 6, -7

From there, I plugged those values of Y back into statement 2: x=y+1
Y=6 --> x=6+1=7
Y=-7 --> x=-7+1=-6

If you plug these values into x^2+Y^2=85, it works for both values of Y.

What did I do wrong?

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TRANGZON: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Mon Apr 14, 2008 3:36 pm; Location: California; Thanked: 1 times

by TRANGZON » Sat Nov 21, 2009 6:41 am

Plug x=y+1 into (x+y)^2 + (x-y)^2
(y+1+y)^2 + (y+1-y)^2 = (2y+1)^2 + 1
Cannot conclude: (2y+1)^2 + 1=170 -> B insufficient

While (x+y)^2 + (x-y)^2 = x^2 + 2xy + y^2 + x^2 - 2xy + y^2 = 2(x^2+y^2) = 2*85=170 -> A sufficient

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chipbmk: Senior | Next Rank: 100 Posts; Posts: 70; Joined: Mon Oct 05, 2009 9:33 am

by chipbmk » Sat Nov 21, 2009 9:58 am

Can someone please look at my work for statement 2 and tell me why it is incorrect?

Moderators? Teachers?

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chipbmk: Senior | Next Rank: 100 Posts; Posts: 70; Joined: Mon Oct 05, 2009 9:33 am

by chipbmk » Mon Nov 23, 2009 3:53 pm

No one has explained why my work for statement 2 is incorrect. Anyone? Please!!

Thanks!

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mridul_dave: Senior | Next Rank: 100 Posts; Posts: 41; Joined: Tue Oct 06, 2009 9:49 am; Thanked: 4 times

by mridul_dave » Mon Nov 23, 2009 5:49 pm

chipbmk wrote:This is what I did, let me know where I went wrong ... it looks right to me.

First: I reduced the main statement to X^2+Y^2 = 85

Statement 2: x=y+1

I plugged this in to the statement above and got:

-- (y+1)^2+Y^2=85
--> Y^2+2Y+1+Y^2=85
--> 2Y^2+2Y-84=0
--> Y^2+Y-42=0
--> (Y-6)(Y+7)=0
--> Y= 6, -7

From there, I plugged those values of Y back into statement 2: x=y+1
Y=6 --> x=6+1=7
Y=-7 --> x=-7+1=-6

If you plug these values into x^2+Y^2=85, it works for both values of Y.

What did I do wrong?

how did uget this :
First: I reduced the main statement to X^2+Y^2 = 85
this is wrong

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

by Stuart@KaplanGMAT » Mon Nov 23, 2009 7:17 pm

chipbmk wrote:This is what I did, let me know where I went wrong ... it looks right to me.

First: I reduced the main statement to X^2+Y^2 = 85

Statement 2: x=y+1

I plugged this in to the statement above and got:

.
.
.

What did I do wrong?

The bolded sentence is what you did wrong.

There is no "statement", there is only a question.

To show that statement (2) was sufficient, you assumed that the answer to the original question was "yes". Of course if you assume that the answer is "yes", you'll always get a "yes" answer.

The question reduces to "Does x^2 + y^2 = 85?"

If all we know is that x = y +1, i.e. x - y = 1, there's no way to answer the above question.

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
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chipbmk: Senior | Next Rank: 100 Posts; Posts: 70; Joined: Mon Oct 05, 2009 9:33 am

by chipbmk » Mon Nov 23, 2009 7:38 pm

mridul_dave wrote:
chipbmk wrote:This is what I did, let me know where I went wrong ... it looks right to me.

First: I reduced the main statement to X^2+Y^2 = 85

Statement 2: x=y+1

I plugged this in to the statement above and got:

-- (y+1)^2+Y^2=85
--> Y^2+2Y+1+Y^2=85
--> 2Y^2+2Y-84=0
--> Y^2+Y-42=0
--> (Y-6)(Y+7)=0
--> Y= 6, -7

From there, I plugged those values of Y back into statement 2: x=y+1
Y=6 --> x=6+1=7
Y=-7 --> x=-7+1=-6

If you plug these values into x^2+Y^2=85, it works for both values of Y.

What did I do wrong?
Stuart, If I rephrase the above to: Does X^2+Y^2 = 85?

Then take all I did for Statement 2 and plug in to figure out if it does equal 85 and you get a definitive yes, dont you?

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

by Stuart@KaplanGMAT » Mon Nov 23, 2009 10:22 pm

chipbmk wrote:Stuart, If I rephrase the above to: Does X^2+Y^2 = 85?

Then take all I did for Statement 2 and plug in to figure out if it does equal 85 and you get a definitive yes, dont you?

Statement (2) says:

x = y + 1

If we substitute it in as you did, we get:

DOES (y+1)^2+Y^2=85?
--> DOES Y^2+2Y+1+Y^2=85?
--> DOES 2Y^2+2Y-84=0?
--> DOES Y^2+Y-42=0?
--> DOES (Y-6)(Y+7)=0?
--> DOES Y= 6 or -7?

Well, here's the problem - we have no clue what the value of y is, so there's no way to answer the question definitively.

Again, the mistake you made (and it's a very common mistake in DS) was to treat the question as though it were a statement of fact rather than just a question.

Let's illustrate with a much simpler example:

Q: Does x = y?

(1) y = 4

If we sub in y=4 to the original, we get:

x = 4

Now if we plug back in y=4, we get 4=4, which is true! That's a definite yes!

Whooooaaaa... of course it's true, since we assumed that x=y to find the value of x. However, if we think about the statement and the question, there's no way that knowing that y=4 is sufficient to know whether x=y, since we have absolutely no information about x at all. If we treat the original as a question instead, we simply end up with a new question:

Does x = 4?

and since we have no info at all about x, (1) is insufficient to answer that question.

Basically, if part of your scratchwork involves assuming that the original question is a statement of fact, you'll always end up proving that it's true.