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Is 2/x + 2/y = 30?

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Is 2/x + 2/y = 30? [#permalink] New post   Updated on: 17 Nov 2013, 23:25
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Is 2/x + 2/y = 30?

(1) x + y = 15xy

(2) x = y

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File comment: Hi,

I think the correct answer to the question #04032 is D.

Here is my explanation for the option B.
Since we have x=y and by manipulating the original equation we get is x + y = 15xy?
substitute y with x and we get 2x=15x^2 -----------> 15x^2-2x = 0 ------------> x(15x - 2)=0 so we have x=0 or x=2/15. Now we can't have x=0 because x is in denominator, therefore, the only plausible option we get here x=2/15.

Now substitute this in the question and see if we get 2/x + 2/y = 30 ---------> 2*15/2 + 2*15/2 = 30 ----------> 30/2 + 30/2 = 30 ------> 60/2 =30 and the equation holds here.

Please correct me if I have done anything wrong here. Thank you.
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Originally posted by vaishnogmat on 17 Nov 2013, 16:30.
Last edited by Bunuel on 17 Nov 2013, 23:25, edited 2 times in total.
Edited the question.
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Re: Is 2/x + 2/y = 30? [#permalink] New post   17 Nov 2013, 21:57
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vaishnogmat wrote:
Is 2/x+2/y=30?

1) x + y = 15xy

2) x = y


a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c) Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient
d) EACH statement ALONE is sufficient to answer the question asked
e) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed


I think the correct answer to the question #04032 is D.

Here is my explanation for the option B.
Since we have x=y and by manipulating the original equation we get is x + y = 15xy?
substitute y with x and we get 2x=15x^2 -----------> 15x^2-2x = 0 ------------> x(15x - 2)=0 so we have x=0 or x=2/15. Now we can't have x=0 because x is in denominator, therefore, the only plausible option we get here x=2/15.

Now substitute this in the question and see if we get 2/x + 2/y = 30 ---------> 2*15/2 + 2*15/2 = 30 ----------> 30/2 + 30/2 = 30 ------> 60/2 =30 and the equation holds here.

Please correct me if I have done anything wrong here. Thank you.


From where did you get the value x = 2/15? You got it by assuming that the original equation holds. But that is what the question is. "Does the original equation hold?" i.e. "Is x + y = 15xy?". The original equation is not given to you. The question doesn't say that it holds. The questions asks you whether it holds.

We cannot assume that it holds, find the value of x and then put it back in the equation. Obviously since we get x = 2/15 from the assumed equation, it will fit the equation when you put it back.

To give you a simple example of the error, think:

Question: Is x + y = 2?
Statement 1: x = y
Since x = y, x = y = 1 (from the equation x + y = 2)
Now put x = y = 1 in x+y = 2. It obviously satisfies the equation. It doesn't mean that x+y is 2. You got x = y = 1 USING x+y = 2. You cannot use it because it is not given to you. It is asked. All you know is x = y. It doesn't imply that x + y = 2. x and y could take any values. x = y = 4, x = y = 19 etc. x+y is not necessarily 2 in every case.
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Re: Is 2/x + 2/y = 30? [#permalink] New post   18 Nov 2013, 14:33
VeritasPrepKarishma wrote:
vaishnogmat wrote:
Is 2/x+2/y=30?

1) x + y = 15xy

2) x = y


a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c) Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient
d) EACH statement ALONE is sufficient to answer the question asked
e) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed


I think the correct answer to the question #04032 is D.

Here is my explanation for the option B.
Since we have x=y and by manipulating the original equation we get is x + y = 15xy?
substitute y with x and we get 2x=15x^2 -----------> 15x^2-2x = 0 ------------> x(15x - 2)=0 so we have x=0 or x=2/15. Now we can't have x=0 because x is in denominator, therefore, the only plausible option we get here x=2/15.

Now substitute this in the question and see if we get 2/x + 2/y = 30 ---------> 2*15/2 + 2*15/2 = 30 ----------> 30/2 + 30/2 = 30 ------> 60/2 =30 and the equation holds here.

Please correct me if I have done anything wrong here. Thank you.


From where did you get the value x = 2/15? You got it by assuming that the original equation holds. But that is what the question is. "Does the original equation hold?" i.e. "Is x + y = 15xy?". The original equation is not given to you. The question doesn't say that it holds. The questions asks you whether it holds.

We cannot assume that it holds, find the value of x and then put it back in the equation. Obviously since we get x = 2/15 from the assumed equation, it will fit the equation when you put it back.

To give you a simple example of the error, think:

Question: Is x + y = 2?
Statement 1: x = y
Since x = y, x = y = 1 (from the equation x + y = 2)
Now put x = y = 1 in x+y = 2. It obviously satisfies the equation. It doesn't mean that x+y is 2. You got x = y = 1 USING x+y = 2. You cannot use it because it is not given to you. It is asked. All you know is x = y. It doesn't imply that x + y = 2. x and y could take any values. x = y = 4, x = y = 19 etc. x+y is not necessarily 2 in every case.





Thanks Karishma. I had a feeling I was doing something wrong here but just needed an expert's explanation I guess.
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Re: Is 2/x + 2/y = 30? [#permalink] New post   19 Nov 2013, 02:38
I have a little concern with A as answer-
it says, x + y = 15xy. Since nothing is mentioned about x and y, this equation
holds true when both x =y = 0. In this case 2/x + 2/y is undefined.
why have we ignored this case ?
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Re: Is 2/x + 2/y = 30? [#permalink] New post   19 Nov 2013, 03:01
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zerosleep wrote:
I have a little concern with A as answer-
it says, x + y = 15xy. Since nothing is mentioned about x and y, this equation
holds true when both x =y = 0. In this case 2/x + 2/y is undefined.
why have we ignored this case ?


Yes, it would be better if it were mentioned in the stem that \(xy\neq{0}\).
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Re: Is 2/x + 2/y = 30? [#permalink] New post   19 Nov 2013, 15:41
Bunuel wrote:
zerosleep wrote:
I have a little concern with A as answer-
it says, x + y = 15xy. Since nothing is mentioned about x and y, this equation
holds true when both x =y = 0. In this case 2/x + 2/y is undefined.
why have we ignored this case ?


Yes, it would be better if it were mentioned in the stem that \(xy\neq{0}\).




Aren't we supposed to assume this since both x and y are in denominator? And as we all know if x or y were 0 then it wouldn't be a valid GMAT question.
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Re: Is 2/x + 2/y = 30? [#permalink] New post   19 Nov 2013, 15:42
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vaishnogmat wrote:
Bunuel wrote:
zerosleep wrote:
I have a little concern with A as answer-
it says, x + y = 15xy. Since nothing is mentioned about x and y, this equation
holds true when both x =y = 0. In this case 2/x + 2/y is undefined.
why have we ignored this case ?


Yes, it would be better if it were mentioned in the stem that \(xy\neq{0}\).




Aren't we supposed to assume this since both x and y are in denominator? And as we all know if x or y were 0 then it wouldn't be a valid GMAT question.


Usually in such cases GMAT still mentions that \(xy\neq{0}\).
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Re: Is 2/x + 2/y = 30? [#permalink] New post   19 Nov 2013, 20:24
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vaishnogmat wrote:
Aren't we supposed to assume this since both x and y are in denominator? And as we all know if x or y were 0 then it wouldn't be a valid GMAT question.


That is true but to be thorough, GMAT does mention that x and y cannot be 0. Doesn't the original source have this bit of information? If not, let me know the source and I will get it updated.
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Re: Is 2/x + 2/y = 30? [#permalink] New post   20 Nov 2013, 14:32
VeritasPrepKarishma wrote:
vaishnogmat wrote:
Aren't we supposed to assume this since both x and y are in denominator? And as we all know if x or y were 0 then it wouldn't be a valid GMAT question.


That is true but to be thorough, GMAT does mention that x and y cannot be 0. Doesn't the original source have this bit of information? If not, let me know the source and I will get it updated.




This is a question from Veritas Prep Test. Question ID: 04032
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Is 2/x + 2/y = 30? [#permalink] New post   02 Mar 2016, 13:07
Is \(\frac{2}{x} + \frac{2}{y} = 30?\)

1) \(x+y = 15xy\)
2) \(x = y\)

I'm questioning the OA on this one.
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Re: Is 2/x + 2/y = 30? [#permalink] New post   02 Mar 2016, 13:14
speedilly wrote:
Is \(\frac{2}{x} + \frac{2}{y} = 30?\)

1) \(x+y = 15xy\)
2) \(x = y\)

I'm questioning the OA on this one.


Please search for a question before starting a new thread. Refer above for the solution. Topics merged.

Why do you say that the OA is incorrect? Clearly if you manipulate the given question, \(\frac{2}{x} + \frac{2}{y} = 30?\) ---> 1/x + 1/y = 15 ---> In effect the question is asking whether x+y=15xy ? Statement 1 is directly providing you "yes" for the question asked. Hence it is sufficient.

Statement 2 is clearly NOT sufficient. With x=y=5 , will you get 1/x+1/y = 30? NO. But if x=y=2/15, then you will get 1/x + 1/y = 30. Ambiguity of the answer for this statement, makes this statement not sufficient.

Hope this helps.
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Re: Is 2/x + 2/y = 30? [#permalink] New post   02 Mar 2016, 13:23
Engr2012 wrote:
speedilly wrote:
Is \(\frac{2}{x} + \frac{2}{y} = 30?\)

1) \(x+y = 15xy\)
2) \(x = y\)

I'm questioning the OA on this one.


Please search for a question before starting a new thread. Refer above for the solution. Topics merged.

Why do you say that the OA is incorrect? Clearly if you manipulate the given question, \(\frac{2}{x} + \frac{2}{y} = 30?\) ---> 1/x + 1/y = 15 ---> In effect the question is asking whether x+y=15xy ? Statement 1 is directly providing you "yes" for the question asked. Hence it is sufficient.

Statement 2 is clearly NOT sufficient. With x=y=5 , will you get 1/x+1/y = 30? NO. But if x=y=2/15, then you will get 1/x + 1/y = 30. Ambiguity of the answer for this statement, makes this statement not sufficient.

Hope this helps.


I was questioning the OA of A. If I saw this question on the GMAT, I would consider the case where x = y = 0. Clearly, 2/x and 2/y are undefined in this case, but 1) and 2) could still hold. Bunuel addressed this concern; a better question would say that xy does not equal 0.
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Re: Is 2/x + 2/y = 30? [#permalink] New post   02 Mar 2016, 13:26
speedilly wrote:
Engr2012 wrote:
speedilly wrote:
Is \(\frac{2}{x} + \frac{2}{y} = 30?\)

1) \(x+y = 15xy\)
2) \(x = y\)

I'm questioning the OA on this one.


Please search for a question before starting a new thread. Refer above for the solution. Topics merged.

Why do you say that the OA is incorrect? Clearly if you manipulate the given question, \(\frac{2}{x} + \frac{2}{y} = 30?\) ---> 1/x + 1/y = 15 ---> In effect the question is asking whether x+y=15xy ? Statement 1 is directly providing you "yes" for the question asked. Hence it is sufficient.

Statement 2 is clearly NOT sufficient. With x=y=5 , will you get 1/x+1/y = 30? NO. But if x=y=2/15, then you will get 1/x + 1/y = 30. Ambiguity of the answer for this statement, makes this statement not sufficient.

Hope this helps.


I was questioning the OA of A. If I saw this question on the GMAT, I would consider the case where x = y = 0. Clearly, 2/x and 2/y are undefined in this case, but 1) and 2) could still hold. Bunuel addressed this concern; a better question would say that xy does not equal 0.


Sure. GMAT questions will specifically mention that variables in denominator can not be = 0. But for non official questions, you can keep this information as 'implied'.
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Re: Is 2/x + 2/y = 30? [#permalink] New post   02 Mar 2016, 23:02
Expert Reply
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 2/x + 2/y = 30?

(1) x + y = 15xy

(2) x = y


When you modify the original condition and the question, they become 2(y+x)/xy=30?, y+x=30/2=15?. Since 1) is yes, it is sufficient.
Thus, A is the answer.


-> Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
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Re: Is 2/x + 2/y = 30? [#permalink] New post   20 Dec 2016, 10:46
VeritasPrepKarishma wrote:
vaishnogmat wrote:
Is 2/x+2/y=30?

1) x + y = 15xy

2) x = y


a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c) Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient
d) EACH statement ALONE is sufficient to answer the question asked
e) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed


I think the correct answer to the question #04032 is D.

Here is my explanation for the option B.
Since we have x=y and by manipulating the original equation we get is x + y = 15xy?
substitute y with x and we get 2x=15x^2 -----------> 15x^2-2x = 0 ------------> x(15x - 2)=0 so we have x=0 or x=2/15. Now we can't have x=0 because x is in denominator, therefore, the only plausible option we get here x=2/15.

Now substitute this in the question and see if we get 2/x + 2/y = 30 ---------> 2*15/2 + 2*15/2 = 30 ----------> 30/2 + 30/2 = 30 ------> 60/2 =30 and the equation holds here.

Please correct me if I have done anything wrong here. Thank you.


From where did you get the value x = 2/15? You got it by assuming that the original equation holds. But that is what the question is. "Does the original equation hold?" i.e. "Is x + y = 15xy?". The original equation is not given to you. The question doesn't say that it holds. The questions asks you whether it holds.

We cannot assume that it holds, find the value of x and then put it back in the equation. Obviously since we get x = 2/15 from the assumed equation, it will fit the equation when you put it back.

To give you a simple example of the error, think:

Question: Is x + y = 2?
Statement 1: x = y
Since x = y, x = y = 1 (from the equation x + y = 2)
Now put x = y = 1 in x+y = 2. It obviously satisfies the equation. It doesn't mean that x+y is 2. You got x = y = 1 USING x+y = 2. You cannot use it because it is not given to you. It is asked. All you know is x = y. It doesn't imply that x + y = 2. x and y could take any values. x = y = 4, x = y = 19 etc. x+y is not necessarily 2 in every case.


Mam'
Pl comment on my approach:
1) Statement 1 is sufficient as it simply reiterating what has been asked for. For example if the question is "Is 1+1=2?" and one of the option is 2=2, so it is basically answering the question....So 1 is sufficient.
2) When info in statement 2 is substituted in the equation in question, we get 2 answers y=infinity and y =some finite number (no need to solve completely, to save time). But as soon as we get infinity I am sure not to get a definite answer...

Pl comment.
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