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# Is x = y ?

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Manager
Joined: 26 Nov 2014
Posts: 106
Is x = y ? [#permalink]

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11 Nov 2015, 00:27
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Difficulty:

55% (hard)

Question Stats:

51% (01:06) correct 49% (01:02) wrong based on 132 sessions

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Is x = y ?

(1) x + y = 100

(2) $$(x − 50)^2 = (y − 50)^2$$
[Reveal] Spoiler: OA

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Re: Is x = y ? [#permalink]

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11 Nov 2015, 02:32
1
KUDOS
is x=y?

1. x+y=100
x=y=50 , =>x=y
or x and y can take any other value
x= 100 , y = 0 =>x ≠ y
Not sufficient

2. $$(x-50)^2$$=$$(y-50)^2$$
x=y=0 => x=y
x and y can take other values as well , equation 2 will hold as long as x=y
x=25 , y=75 =>x ≠ y

Not sufficient
Combining ,
We still get x=y=50 =>x=y
or x=25 , y=75 =>x ≠ y

Not sufficient

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Re: Is x = y ? [#permalink]

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15 Nov 2015, 09:45
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Is x = y ?

(1) x + y = 100

(2) (x−50) 2 =(y−50) 2

There are 2 variables (x,y) and 2 equations are given from the conditions, so there is high chance (C) will be our answer.
Combining the 2 conditions,
1) x+y=100, 2) x-50=y-50, or x-50=-y+50, that is, x+y=100. The only satisfying situation is x+y=100.
the answer is 'yes' for x=y=50, but 'no' for x=40, y=60. Therefore the answer is E

For cases where we need 2 more equation, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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Intern
Joined: 11 Oct 2015
Posts: 5
Re: Is x = y ? [#permalink]

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15 Nov 2015, 11:31
Why is B not the answer for this problem?

Given information in 2), I solved as follows:

Step 1. Square root both sides -> x - 50 = y - 50
Step 2. Add 50 to both sides -> x=y
Therefore 2 is sufficient and B is the answer
Intern
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Posts: 9
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Re: Is x = y ? [#permalink]

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15 Nov 2015, 12:41
ChiLeafsFan wrote:
Why is B not the answer for this problem?

Given information in 2), I solved as follows:

Step 1. Square root both sides -> x - 50 = y - 50
Step 2. Add 50 to both sides -> x=y
Therefore 2 is sufficient and B is the answer

Hi,

You are only considering the result to be positive when doing the square root on both sides e.g. sqrt(4) can be either 2 or -2.

Although I think the method you have chosen is not the quickest one, if you still want to go with that you will have to consider all the cases.

Case 1: sqrt of (x-50)^2 = +(x-50) and sqrt of (y-50)^2 = +(y-50) => x = y
Case 2: sqrt of (x-50)^2 = -(x-50) and sqrt of (y-50)^2 = +(y-50) => x + y = 100 ( x may or may not be equal to y)
Case 3: sqrt of (x-50)^2 = +(x-50) and sqrt of (y-50)^2 = -(y-50) => x + y = 100 ( x may or may not be equal to y)
Case 4: sqrt of (x-50)^2 = -(x-50) and sqrt of (y-50)^2 = -(y-50) => x = y

Therefore, statement 2 is insufficient.

Hope this helps.

I would suggest to simplify the equation.

(x-50)^2 = (y-50)^2
x^2 -100x + 2500 = y^2 -100y + 2500
x^2 - 100x = y^2 -100y
x^2 - y^2 -100x -100y = 0
x+y-100 = 0 or x-y = 0
x+y = 100 or x = y

Therefore, insufficient.
Intern
Joined: 11 Oct 2015
Posts: 5
Re: Is x = y ? [#permalink]

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16 Nov 2015, 04:13
ChiLeafsFan wrote:
Why is B not the answer for this problem?

Given information in 2), I solved as follows:

Step 1. Square root both sides -> x - 50 = y - 50
Step 2. Add 50 to both sides -> x=y
Therefore 2 is sufficient and B is the answer

Hi,

You are only considering the result to be positive when doing the square root on both sides e.g. sqrt(4) can be either 2 or -2.

Although I think the method you have chosen is not the quickest one, if you still want to go with that you will have to consider all the cases.

Case 1: sqrt of (x-50)^2 = +(x-50) and sqrt of (y-50)^2 = +(y-50) => x = y
Case 2: sqrt of (x-50)^2 = -(x-50) and sqrt of (y-50)^2 = +(y-50) => x + y = 100 ( x may or may not be equal to y)
Case 3: sqrt of (x-50)^2 = +(x-50) and sqrt of (y-50)^2 = -(y-50) => x + y = 100 ( x may or may not be equal to y)
Case 4: sqrt of (x-50)^2 = -(x-50) and sqrt of (y-50)^2 = -(y-50) => x = y

Therefore, statement 2 is insufficient.

Hope this helps.

I would suggest to simplify the equation.

(x-50)^2 = (y-50)^2
x^2 -100x + 2500 = y^2 -100y + 2500
x^2 - 100x = y^2 -100y
x^2 - y^2 -100x -100y = 0
x+y-100 = 0 or x-y = 0
x+y = 100 or x = y

Therefore, insufficient.

Thank you! I see what I wasn't thinking though now.
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Re: Is x = y ? [#permalink]

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19 Nov 2015, 17:51
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Hi All,

This DS prompt is based around the 'thoroughness' of your thinking. You can likely see an 'obvious' answer when dealing with each of the two Facts, but can you see any OTHER possibiilties... We can TEST VALUES to get to the solution.

We're asked if X equals Y. This is a YES/NO question.

Fact 1: X + Y = 100

IF...
X = 50
Y = 50
Then the answer to the question is YES.

IF...
X = 0
Y = 100
Then the answer to the question is NO.
Fact 1 is INSUFFICIENT.

Fact 1:$$(X - 50)^{2}$$ = $$(Y - 50)^{2}$$

IF...
X = 50
Y = 50
Then the answer to the question is YES.

IF...
X = 0
Y = 100
Then the answer to the question is NO.
Fact 2 is INSUFFICIENT.

Combined, we have two TESTS that already fit BOTH Facts and provide 2 different answers (one YES and one NO), so there's no more work required.
Combined, INSUFFICIENT.

[Reveal] Spoiler:
E

GMAT assassins aren't born, they're made,
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# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Director Joined: 23 Jan 2013 Posts: 601 Schools: Cambridge'16 Re: Is x = y ? [#permalink] ### Show Tags 29 Dec 2016, 03:50 St1. x+y=100, INSUFF St2. just say |x-50|=|y-50|, so distance from x to 50 is equal to distance from y to 50, so INSUFF. St1+St2. Can be multiple options where x=y and x not equal y. INSUFF E Senior Manager Status: Countdown Begins... Joined: 03 Jul 2016 Posts: 308 Location: India Concentration: Technology, Strategy Schools: IIMB GMAT 1: 580 Q48 V22 GPA: 3.7 WE: Information Technology (Consulting) Re: Is x = y ? [#permalink] ### Show Tags 23 Feb 2017, 06:16 GoLeafsGo wrote: Why is B not the answer for this problem? Given information in 2), I solved as follows: Step 1. Square root both sides -> x - 50 = y - 50 Step 2. Add 50 to both sides -> x=y Therefore 2 is sufficient and B is the answer Because A can be 75 and B 25, still the squares will match. _________________ Need Kudos to unlock GMAT Club tests Intern Joined: 08 Mar 2016 Posts: 36 Re: Is x = y ? [#permalink] ### Show Tags 27 Feb 2017, 07:25 shyind wrote: Is x = y ? (1) x + y = 100 (2) $$(x − 50)^2 = (y − 50)^2$$ Kindly help me understand where am I going wrong here? For (2) (x-50)^2=(y-50)^2 or, (x-50)^2-(y-50)^2=0 or, (x-50+y-50) (x-50-y+50)=0 or, (x+y-100)(x-y)=0 so, either x=y or x=100-y. From (1) & (2) X=100-y. Suff (C). Where am I going wrong? Please Help!! EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 11036 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Re: Is x = y ? [#permalink] ### Show Tags 27 Feb 2017, 15:21 Hi SOUMYAJIT, In DS questions, you have to make sure that you're not missing any of the 'possibilities' and that you're answering the question that is ASKED. You did enough work to determine that Fact 1 and Fact 2 were both insufficient on their own, but when combined, there is more than one answer to the question "Is X = Y?" Here are two solutions to the equations given: X=50 Y=50 and the answer to the question is YES. X=0 Y=100 and the answer to the question is NO. The are two different answers to the given question, so combined/insufficient (E) is the answer. GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Joined: 08 Mar 2016
Posts: 36
Re: Is x = y ? [#permalink]

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27 Feb 2017, 22:25
EMPOWERgmatRichC wrote:
Hi SOUMYAJIT,

In DS questions, you have to make sure that you're not missing any of the 'possibilities' and that you're answering the question that is ASKED.

You did enough work to determine that Fact 1 and Fact 2 were both insufficient on their own, but when combined, there is more than one answer to the question "Is X = Y?"

Here are two solutions to the equations given:
X=50
Y=50
and the answer to the question is YES.

X=0
Y=100
and the answer to the question is NO.

The are two different answers to the given question, so combined/insufficient (E) is the answer.

GMAT assassins aren't born, they're made,
Rich

Got it thanks!!

I seem to have this problem, where in :

(1) I do not forget the first options condition when I goto solve the second DS point, thereby actually checking for C and not B.

or

(2) In the process of thinking, I forget the question that was asked to me in the first place.

Sometimes, even in geometry when I make transformations in a figure to solve a question, I forget the real figure that was there in the question in the first place.

Do you have a way that I can handle this?
Re: Is x = y ?   [#permalink] 27 Feb 2017, 22:25
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