Last visit was: 26 Mar 2025, 18:25 It is currently 26 Mar 2025, 18:25
Home
GMAT
Messages
Tests
Schools
Reviews
Rewards
Chat
My Profile
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
avatar
pradeepparihar
avatar
Joined: 14 Nov 2011
Last visit: 01 May 2012
Posts: 5
Own Kudos:
121
 [57]
Posts: 5
Kudos: 121
 [57]
If x and y are positive, what is the value of x? Updated on: 09 Mar 2012, 23:39
Originally posted by pradeepparihar on 09 Mar 2012, 21:22.
Last edited by Bunuel on 09 Mar 2012, 23:39, edited 2 times in total.
Edited the question
4
Kudos
Add Kudos
53
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

15% (low)

Question Stats:

80% (01:45) correct 20% (01:51) wrong based on 1722 sessions

History

Date
Time
Result
Not Attempted Yet
If x and y are positive, what is the value of x?

(1) 200% of x equals to 400% of y.

(2) xy is the square of a positive integer.
ShowHide Answer
Official Answer
E
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 26 Mar 2025
Posts: 100,092
Own Kudos:
711,160
 [15]
Given Kudos: 92,710
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 100,092
Kudos: 711,160
 [15]
If x and y are positive, what is the value of x? 09 Mar 2012, 23:38
4
Kudos
Add Kudos
11
Bookmarks
Bookmark this Post
If x and y are positive, what is the value of x?

Notice that we are not told that \(x\) and \(y\) are integers only, we are just told that they are both positive.

(1) 200% of x equals to 400% of y --> \(\frac{200}{100}*x=\frac{400}{100}*y\) --> \(x=2y\). Not sufficient to get the single numerical value of \(x\).

(2) xy is the square of a positive integer --> \(xy=n^2\), for some positive integer \(n\). Not sufficient to get the single numerical value of \(x\).

(1)+(2) Since from (1) \(x=2y\) then from (2) \(x*\frac{x}{2}=n^2\) --> \(x^2=2n^2\) --> the value of \(x\) (x^2) is determined by the value of integer \(n\), so we still cannot get the single numerical value of \(x\). For example: if \(n=1\) then \(x=\sqrt{2}\) but if \(n=2\) then \(x=2\sqrt{2}\). Not sufficient.

Answer: E.

Hope it's clear.


subhashghosh
(1)
200/100 * x = 400/100 * y
2x = 4y
X = 2y
=> X is even


Since we are not told that \(x\) and \(y\) are integers only, then from \(x=2y\) we cannot say whether \(x\) even:

\(x\) will be even if \(y=integer\);
\(x\) will be odd if \(y=\frac{odd}{2}\), for example if \(y=\frac{3}{2}\) then \(x=3=odd\);
\(x\) may not be an integer at all, for example if \(y=\frac{1}{3}\) then \(x=\frac{2}{3}\neq{integer}\).

In fact if we knew that \(x=even\) then \(x^2=2n^2\), from (1)+(2), would have only one integer solution \(x=0\) and \(n=0\), but this would contradict the given fact that \(x\) is positive.

Hope it's clear.
General Discussion
User avatar
subhashghosh
User avatar
Retired Moderator
Joined: 16 Nov 2010
Last visit: 25 Jun 2024
Posts: 902
Own Kudos:
1,235
 [1]
Given Kudos: 43
Location: United States (IN)
Concentration: Strategy, Technology
Products:
My Reviews
Posts: 902
Kudos: 1,235
 [1]
If x and y are positive, what is the value of x? 09 Mar 2012, 23:17
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
(1)
200/100 * x = 400/100 * y
2x = 4y
X = 2y
=> X is even

(2)
Xy = 1,4,9,16,…

Not Sufficient.

(1) + (2)

Suppose:

2y^2 = 16
Y = 2root(2)
X = 4root(2)
Or
2y^2 = 4
Y = root(2)
X = 2root(2)

Not Sufficient.

So Answer is E.
avatar
raul2011
avatar
Joined: 06 Dec 2011
Last visit: 03 May 2012
Posts: 2
Own Kudos:
2
Posts: 2
Kudos: 2
If x and y are positive, what is the value of x? 11 Mar 2012, 04:44
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If x and y are positive, what is the value of x?

Notice that we are not told that \(x\) and \(y\) are integers only, we are just told that they are both positive.

(1) 200% of x equals to 400% of y --> \(\frac{200}{100}*x=\frac{400}{100}*y\) --> \(x=2y\). Not sufficient to get the single numerical value of \(x\).

(2) xy is the square of a positive integer --> \(xy=n^2\), for some positive integer \(n\). Not sufficient to get the single numerical value of \(x\).

(1)+(2) Since from (1) \(x=2y\) then from (2) \(x*\frac{x}{2}=n^2\) --> \(x^2=2n^2\) --> the value of \(x\) (x^2) is determined by the value of integer \(n\), so we still cannot get the single numerical value of \(x\). For example: if \(n=1\) then \(x=\sqrt{2}\) but if \(n=2\) then \(x=2\sqrt{2}\). Not sufficient.

Answer: E.

Hope it's clear.


subhashghosh
(1)
200/100 * x = 400/100 * y
2x = 4y
X = 2y
=> X is even


Since we are not told that \(x\) and \(y\) are integers only, then from \(x=2y\) we cannot say whether \(x\) even:

\(x\) will be even if \(y=integer\);
\(x\) will be odd if \(y=\frac{odd}{2}\), for example if \(y=\frac{3}{2}\) then \(x=3=odd\);
\(x\) may not be an integer at all, for example if \(y=\frac{1}{3}\) then \(x=\frac{2}{3}\neq{integer}\).

In fact if we knew that \(x=even\) then \(x^2=2n^2\), from (1)+(2), would have only one integer solution \(x=0\) and \(n=0\), but this would contradict the given fact that \(x\) is positive.

Hope it's clear.

Hello Bunuel,

Thanks for this wonderful explanation!

However I'm still not able to figure out the meaning of the following statement

Quote:
In fact if we knew that \(x=even\) then \(x^2=2n^2\), from (1)+(2), would have only one integer solution \(x=0\) and \(n=0\), but this would contradict the given fact that \(x\) is positive.

Can you please provide more clarity and let know which particular number property you are using to deduce the above statement?
User avatar
subhashghosh
User avatar
Retired Moderator
Joined: 16 Nov 2010
Last visit: 25 Jun 2024
Posts: 902
Own Kudos:
1,235
Given Kudos: 43
Location: United States (IN)
Concentration: Strategy, Technology
Products:
My Reviews
Posts: 902
Kudos: 1,235
If x and y are positive, what is the value of x? 11 Mar 2012, 04:49
Kudos
Add Kudos
Bookmarks
Bookmark this Post
raul2011
Bunuel
If x and y are positive, what is the value of x?

Notice that we are not told that \(x\) and \(y\) are integers only, we are just told that they are both positive.

(1) 200% of x equals to 400% of y --> \(\frac{200}{100}*x=\frac{400}{100}*y\) --> \(x=2y\). Not sufficient to get the single numerical value of \(x\).

(2) xy is the square of a positive integer --> \(xy=n^2\), for some positive integer \(n\). Not sufficient to get the single numerical value of \(x\).

(1)+(2) Since from (1) \(x=2y\) then from (2) \(x*\frac{x}{2}=n^2\) --> \(x^2=2n^2\) --> the value of \(x\) (x^2) is determined by the value of integer \(n\), so we still cannot get the single numerical value of \(x\). For example: if \(n=1\) then \(x=\sqrt{2}\) but if \(n=2\) then \(x=2\sqrt{2}\). Not sufficient.

Answer: E.

Hope it's clear.


subhashghosh
(1)
200/100 * x = 400/100 * y
2x = 4y
X = 2y
=> X is even


Since we are not told that \(x\) and \(y\) are integers only, then from \(x=2y\) we cannot say whether \(x\) even:

\(x\) will be even if \(y=integer\);
\(x\) will be odd if \(y=\frac{odd}{2}\), for example if \(y=\frac{3}{2}\) then \(x=3=odd\);
\(x\) may not be an integer at all, for example if \(y=\frac{1}{3}\) then \(x=\frac{2}{3}\neq{integer}\).

In fact if we knew that \(x=even\) then \(x^2=2n^2\), from (1)+(2), would have only one integer solution \(x=0\) and \(n=0\), but this would contradict the given fact that \(x\) is positive.

Hope it's clear.

Hello Bunuel,

Thanks for this wonderful explanation!

However I'm still not able to figure out the meaning of the following statement

Quote:
In fact if we knew that \(x=even\) then \(x^2=2n^2\), from (1)+(2), would have only one integer solution \(x=0\) and \(n=0\), but this would contradict the given fact that \(x\) is positive.

Can you please provide more clarity and let know which particular number property you are using to deduce the above statement?

Which particular number property - I think Bunuel is saying that 0 is neither positive nor negative.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 26 Mar 2025
Posts: 100,092
Own Kudos:
711,160
Given Kudos: 92,710
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 100,092
Kudos: 711,160
If x and y are positive, what is the value of x? 11 Mar 2012, 04:59
Kudos
Add Kudos
Bookmarks
Bookmark this Post
raul2011
Hello Bunuel,

Thanks for this wonderful explanation!

However I'm still not able to figure out the meaning of the following statement

Quote:
In fact if we knew that \(x=even\) then \(x^2=2n^2\), from (1)+(2), would have only one integer solution \(x=0\) and \(n=0\), but this would contradict the given fact that \(x\) is positive.

Can you please provide more clarity and let know which particular number property you are using to deduce the above statement?

Sure. We know that \(n\) is a positive integer. Now, if \(x\) is an even integer, then \(x^2=2n^2\) should be true for some integers \(n\) and \(x\), but it's true only for one integer solution \(x=n=0\), which cannot be valid, since we are given that \(x\) is a positive number (0 is neither positive nor negative).

Hope it's clear.
User avatar
fameatop
User avatar
Joined: 24 Aug 2009
Last visit: 09 Jun 2017
Posts: 385
Own Kudos:
2,393
Given Kudos: 275
Concentration: Finance
Schools:Harvard, Columbia, Stern, Booth, LSB,
Posts: 385
Kudos: 2,393
If x and y are positive, what is the value of x? 11 Sep 2012, 05:45
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If x and y are positive, what is the value of x?

Notice that we are not told that \(x\) and \(y\) are integers only, we are just told that they are both positive.

(1) 200% of x equals to 400% of y --> \(\frac{200}{100}*x=\frac{400}{100}*y\) --> \(x=2y\). Not sufficient to get the single numerical value of \(x\).

(2) xy is the square of a positive integer --> \(xy=n^2\), for some positive integer \(n\). Not sufficient to get the single numerical value of \(x\).

(1)+(2) Since from (1) \(x=2y\) then from (2) \(x*\frac{x}{2}=n^2\) --> \(x^2=2n^2\) --> the value of \(x\) (x^2) is determined by the value of integer \(n\), so we still cannot get the single numerical value of \(x\). For example: if \(n=1\) then \(x=\sqrt{2}\) but if \(n=2\) then \(x=2\sqrt{2}\). Not sufficient.

Answer: E.

Hope it's clear.


subhashghosh
(1)
200/100 * x = 400/100 * y
2x = 4y
X = 2y
=> X is even


Since we are not told that \(x\) and \(y\) are integers only, then from \(x=2y\) we cannot say whether \(x\) even:

\(x\) will be even if \(y=integer\);
\(x\) will be odd if \(y=\frac{odd}{2}\), for example if \(y=\frac{3}{2}\) then \(x=3=odd\);
\(x\) may not be an integer at all, for example if \(y=\frac{1}{3}\) then \(x=\frac{2}{3}\neq{integer}\).

In fact if we knew that \(x=even\) then \(x^2=2n^2\), from (1)+(2), would have only one integer solution \(x=0\) and \(n=0\), but this would contradict the given fact that \(x\) is positive.

Hope it's clear.

Hi Bunuel,

Thanks for the nice explanation . I would like to modify the question a bit & would like to present a twist to the same question.

If the new statement reads "If x and y are positive integers, what is the value of x" rather than "If x and y are positive, what is the value of x"
Now what will be the answer.

As per me the answer should be C because i believe no such value will exist.

Kindly enlighten us all.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 26 Mar 2025
Posts: 100,092
Own Kudos:
711,160
Given Kudos: 92,710
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 100,092
Kudos: 711,160
If x and y are positive, what is the value of x? 11 Sep 2012, 06:03
Kudos
Add Kudos
Bookmarks
Bookmark this Post
fameatop
Bunuel
If x and y are positive, what is the value of x?

Notice that we are not told that \(x\) and \(y\) are integers only, we are just told that they are both positive.

(1) 200% of x equals to 400% of y --> \(\frac{200}{100}*x=\frac{400}{100}*y\) --> \(x=2y\). Not sufficient to get the single numerical value of \(x\).

(2) xy is the square of a positive integer --> \(xy=n^2\), for some positive integer \(n\). Not sufficient to get the single numerical value of \(x\).

(1)+(2) Since from (1) \(x=2y\) then from (2) \(x*\frac{x}{2}=n^2\) --> \(x^2=2n^2\) --> the value of \(x\) (x^2) is determined by the value of integer \(n\), so we still cannot get the single numerical value of \(x\). For example: if \(n=1\) then \(x=\sqrt{2}\) but if \(n=2\) then \(x=2\sqrt{2}\). Not sufficient.

Answer: E.

Hope it's clear.


subhashghosh
(1)
200/100 * x = 400/100 * y
2x = 4y
X = 2y
=> X is even


Since we are not told that \(x\) and \(y\) are integers only, then from \(x=2y\) we cannot say whether \(x\) even:

\(x\) will be even if \(y=integer\);
\(x\) will be odd if \(y=\frac{odd}{2}\), for example if \(y=\frac{3}{2}\) then \(x=3=odd\);
\(x\) may not be an integer at all, for example if \(y=\frac{1}{3}\) then \(x=\frac{2}{3}\neq{integer}\).

In fact if we knew that \(x=even\) then \(x^2=2n^2\), from (1)+(2), would have only one integer solution \(x=0\) and \(n=0\), but this would contradict the given fact that \(x\) is positive.

Hope it's clear.

Hi Bunuel,

Thanks for the nice explanation . I would like to modify the question a bit & would like to present a twist to the same question.

If the new statement reads "If x and y are positive integers, what is the value of x" rather than "If x and y are positive, what is the value of x"
Now what will be the answer.

As per me the answer should be C because i believe no such value will exist.

Kindly enlighten us all.

In this case, for (1)+(2) we would have the same equation: \(x=2n^2\), which has only one integer solution for \(x\) and \(n\): \(x=n=0\) but since we are told that \(x\) is a positive integer then this solution is no good.

But we won't see such question on the real test where no value can satisfy the statements. So, the question in this case would be flawed.
User avatar
suganyam
User avatar
Joined: 19 Jan 2019
Last visit: 01 Oct 2022
Posts: 40
Own Kudos:
9
Given Kudos: 65
Products:
My Reviews
Posts: 40
Kudos: 9
If x and y are positive, what is the value of x? 02 Jan 2020, 06:57
Kudos
Add Kudos
Bookmarks
Bookmark this Post
If x and y are positive, what is the value of x?

(1) 200% of x equals to 400% of y.-NS as we dont know the values of x,y

(2) xy is the square of a positive integer.--NS as we dont know the values of x,y and the new variable used
1& 2 together also will not help
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,103
Own Kudos:
18,321
 [2]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,103
Kudos: 18,321
 [2]
If x and y are positive, what is the value of x? 02 Jan 2020, 10:23
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
pradeepparihar
If x and y are positive, what is the value of x?

(1) 200% of x equals to 400% of y.

(2) xy is the square of a positive integer.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Since we have 2 variables (x and y) and 0 equations, C is most likely the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)

We have \(2x = 4y\) or \(x = 2y\) from condition 1).
Then \(xy = 2y \cdot y = 2y^2\).


If \(x = 2\sqrt{2}, y = \sqrt{2}\), then \(xy = 4 = 2^2\), which is a square of a positive integer \(2\).
If \(x = 6\sqrt{2}, y = 3\sqrt{2}\), then \(xy = 36 = 6^2\), which is a square of a positive integer \(6\).

Since both conditions together do not yield a unique solution, they are not sufficient.

Therefore, E is the answer.

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B, or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D, or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 36,719
Own Kudos:
963
Posts: 36,719
Kudos: 963
If x and y are positive, what is the value of x? 08 Mar 2025, 20:20
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderator:
Bunuel
Math Expert
100092 posts