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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

If 2^x + 2^y = x^2 + y^2, where x and y are nonnegative inte [#permalink]

Show Tags

15 Dec 2009, 15:48

10

This post received KUDOS

40

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

22% (02:50) correct
78% (02:47) wrong based on 1103 sessions

HideShow timer Statistics

If 2^x + 2^y = x^2 + y^2, where x and y are nonnegative integers, what is the greatest possible value of |x – y|?

(A) 0 (B) 1 (C) 2 (D) 3 (E) 4

This is a challenge problem on MGMAT. I do not have the answer to the question... But on solving the problem I got the answer of 2 (not sure if it is right)

If 2^x + 2^y = x^2 + y^2, where x and y are nonnegative integers, what is the greatest possible value of |x – y|? (A) 0 (B) 1 (C) 2 (D) 3 (E) 4

This is a challenge problem on MGMAT. I do not have the answer to the question... But on solving the problem I got the answer of 2 (not sure if it is right)

Suppose you got the answer of 2 for the values of \(x\) and \(y\) as 4 and 2.

4 can not be the greatest value as when you increase \(x\) so as \(x-y\) to be \(4\), \(2^x+2^y\) will always be more than \(x^2+y^2\). _________________

Re: If 2^x + 2^y = x^2 + y^2, where x and y are nonnegative inte [#permalink]

Show Tags

21 Mar 2013, 21:56

12

This post received KUDOS

Expert's post

1

This post was BOOKMARKED

surya167 wrote:

Brunel and all,

Is it a rule to apply one value as zero whenever it is given:

1) Both x and y are non-negative integers 2) we need to find the max value of x-y

What if we are asked to find the min ? how do we solve those questions and also, what would be the approach for min and max value of x+y ? Can u guys pls advise?

Usually, when you are checking for numbers, you do check for 0. It's often a transition point for patterns. Secondly, the question used the term 'non-negative integers' instead of 'positive integers' - this means 0 would probably have a role to play. There are no such rules but common sense says that we must not ignore 0.

Now, when we look at the equation, 2^x + 2^y = x^2 + y^2, some things come to mind: 1. It is not very easy to find values that satisfy this equation. 2. But there must be some values which satisfy since we are looking for a value of |x – y| 3. If x = y = 2, the equation is satisfied since all terms become equal and |x – y| = 0 which is the minimum value of |x – y|.

Usually, the left hand side will be greater than the right hand side (as discussed in the post, 2^n will usually be greater than x^2 except in very few cases). So we must focus on those 'very few cases'. Also, we need to make x and y unequal.

We know (from the post) that 2^4 = 4^2 is one solution so we could put x = 4 while keeping y = 2. The equation will be satisfied and |x – y| = 2

Now, we also know that 2^x < x^2 when x = 3. So is there a solution there as well? The difference between 2^3 and 3^2 is of 1 so can we create a difference of 1 between the other two terms? Sure! If y = 0, then 2^0 = 1 but 0^2 = 0. So another solution is 2^3 + 2^0 = 3^2 + 0^2. Here, |x – y| = 3 which is the maximum difference.

The reason we can be sure that there are no other values is that as you go ahead of 4 on the number line, 2^n will be greater than n^2 (again, discussed in the post). So both left hand side terms will be greater than the right hand side terms i.e. 2^x > x^2 and 2^y > y^2. So, for no other values can we satisfy this equation.

Re: If 2^x + 2^y = x^2 + y^2, where x and y are nonnegative inte [#permalink]

Show Tags

08 Feb 2013, 09:27

6

This post received KUDOS

1

This post was BOOKMARKED

axl_oz wrote:

If 2^x + 2^y = x^2 + y^2, where x and y are nonnegative integers, what is the greatest possible value of |x – y|?

(A) 0 (B) 1 (C) 2 (D) 3 (E) 4

This is a challenge problem on MGMAT. I do not have the answer to the question... But on solving the problem I got the answer of 2 (not sure if it is right)

Since we need to maximize the value of |x – y|, we can do that in two ways...1)make y negative, which is not possible as per the question...2)make y= 0..putting y=0 you will get an equation in x and on hit and trial method u will get the value of x as 3, which will satisfy the equation.... putting x=3 and y=0, we will get the value of |x – y| as 3.

Re: If 2^x + 2^y = x^2 + y^2, where x and y are nonnegative inte [#permalink]

Show Tags

07 Dec 2013, 05:52

1

This post received KUDOS

Expert's post

misanguyen2010 wrote:

Bunuel wrote:

misanguyen2010 wrote:

my answer: |x – y| for x and y 2^x + 2^y = x^2 + y^2 A. x= y x=y=1 2 + 2 = 1 + 1 wrong B. 1 x=2, y=1 4 + 2 = 4 + 1 wrong C. 2 x=3, y=1 8 + 2 = 9 + 1 right D. 3 x=4, y =1 16 + 2 = 16 + 1 wrong E. 4 x=5, y =1 32 + 2 = 25 + 1 wrong

My answer is C.

Please note that the correct answer is D, not C.

Hi thank you for your reply. I explained what i confused. Of course I read previous answers and all chose D. However, from what i found, i chose C. That s why i posted here. I dont know which is wrong in my answer. Please help!

To get the greatest value of |x-y| as 3 consider x=3 and y=0. Notice that these values satisfy \(2^x + 2^y = x^2 + y^2\) --> \(2^3 + 2^0 =9= 3^2 + 0^2\).

Great Problem! Since your trying to find the greatest value of X-Y, you just have to assume that Y=0, like Bunel said and then use the "hit and trial" approach like xcusem... Said. The algebratic approach is great too, but I know for me personally it opens up the opportunity for me to make silly mistakes. So I try to not use it unless necessary.

Re: If 2^x + 2^y = x^2 + y^2, where x and y are nonnegative inte [#permalink]

Show Tags

21 Mar 2013, 09:34

Brunel and all,

Is it a rule to apply one value as zero whenever it is given:

1) Both x and y are non-negative integers 2) we need to find the max value of x-y

What if we are asked to find the min ? how do we solve those questions and also, what would be the approach for min and max value of x+y ? Can u guys pls advise? _________________

Re: If 2^x + 2^y = x^2 + y^2, where x and y are nonnegative inte [#permalink]

Show Tags

06 Dec 2013, 00:37

axl_oz wrote:

If 2^x + 2^y = x^2 + y^2, where x and y are nonnegative integers, what is the greatest possible value of |x – y|?

(A) 0 (B) 1 (C) 2 (D) 3 (E) 4

This is a challenge problem on MGMAT. I do not have the answer to the question... But on solving the problem I got the answer of 2 (not sure if it is right)

my answer: |x – y| for x and y 2^x + 2^y = x^2 + y^2 A. x= y x=y=1 2 + 2 = 1 + 1 wrong B. 1 x=2, y=1 4 + 2 = 4 + 1 wrong C. 2 x=3, y=1 8 + 2 = 9 + 1 right D. 3 x=4, y =1 16 + 2 = 16 + 1 wrong E. 4 x=5, y =1 32 + 2 = 25 + 1 wrong

Re: If 2^x + 2^y = x^2 + y^2, where x and y are nonnegative inte [#permalink]

Show Tags

06 Dec 2013, 02:52

Expert's post

misanguyen2010 wrote:

axl_oz wrote:

If 2^x + 2^y = x^2 + y^2, where x and y are nonnegative integers, what is the greatest possible value of |x – y|?

(A) 0 (B) 1 (C) 2 (D) 3 (E) 4

This is a challenge problem on MGMAT. I do not have the answer to the question... But on solving the problem I got the answer of 2 (not sure if it is right)

my answer: |x – y| for x and y 2^x + 2^y = x^2 + y^2 A. x= y x=y=1 2 + 2 = 1 + 1 wrong B. 1 x=2, y=1 4 + 2 = 4 + 1 wrong C. 2 x=3, y=1 8 + 2 = 9 + 1 right D. 3 x=4, y =1 16 + 2 = 16 + 1 wrong E. 4 x=5, y =1 32 + 2 = 25 + 1 wrong

My answer is C.

Please note that the correct answer is D, not C. _________________

Re: If 2^x + 2^y = x^2 + y^2, where x and y are nonnegative inte [#permalink]

Show Tags

06 Dec 2013, 10:47

1

This post was BOOKMARKED

Bunuel wrote:

misanguyen2010 wrote:

axl_oz wrote:

If 2^x + 2^y = x^2 + y^2, where x and y are nonnegative integers, what is the greatest possible value of |x – y|?

(A) 0 (B) 1 (C) 2 (D) 3 (E) 4

This is a challenge problem on MGMAT. I do not have the answer to the question... But on solving the problem I got the answer of 2 (not sure if it is right)

my answer: |x – y| for x and y 2^x + 2^y = x^2 + y^2 A. x= y x=y=1 2 + 2 = 1 + 1 wrong B. 1 x=2, y=1 4 + 2 = 4 + 1 wrong C. 2 x=3, y=1 8 + 2 = 9 + 1 right D. 3 x=4, y =1 16 + 2 = 16 + 1 wrong E. 4 x=5, y =1 32 + 2 = 25 + 1 wrong

My answer is C.

Please note that the correct answer is D, not C.

Hi thank you for your reply. I explained what i confused. Of course I read previous answers and all chose D. However, from what i found, i chose C. That s why i posted here. I dont know which is wrong in my answer. Please help!

Re: If 2^x + 2^y = x^2 + y^2, where x and y are nonnegative inte [#permalink]

Show Tags

28 Dec 2013, 04:25

Here is how I done it:

1) If |x-y| needs to be max then Y=0, because Y² is only positive 2) Check the answers, those are only integers, you are therefore looking for an integer 3) You have the equation 2^x +1 = X² 4) Use the different choices and you will see that only 3 matches.

Re: If 2^x + 2^y = x^2 + y^2, where x and y are nonnegative inte [#permalink]

Show Tags

17 Feb 2015, 07:44

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. _________________

http://blog.ryandumlao.com/wp-content/uploads/2016/05/IMG_20130807_232118.jpg The GMAT is the biggest point of worry for most aspiring applicants, and with good reason. It’s another standardized test when most of us...

I recently returned from attending the London Business School Admits Weekend held last week. Let me just say upfront - for those who are planning to apply for the...