GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 21 Oct 2019, 15:44

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.

Close

Request Expert Reply

Confirm Cancel

If x and y are distinct positive integers, what is the value of ....

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
Joined: 24 Feb 2015
Posts: 45
If x and y are distinct positive integers, what is the value of ....  [#permalink]

Show Tags

New post 10 Sep 2015, 15:00
2
7
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

40% (02:12) correct 60% (02:18) wrong based on 203 sessions

HideShow timer Statistics

If x and y are distinct positive integers, what is the value of \(x^4 - y^4\)?

1. \((y^2 + x^2)(y + x)(x - y) > 100\)
2. \(x^y = y^x\)
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58396
Re: If x and y are distinct positive integers, what is the value of ....  [#permalink]

Show Tags

New post 10 Sep 2015, 22:04
1
1
Intern
Intern
avatar
S
Joined: 24 Jun 2013
Posts: 32
Reviews Badge
Re: If x and y are distinct positive integers, what is the value of ....  [#permalink]

Show Tags

New post 13 Mar 2017, 00:51
Prajat wrote:
If x and y are distinct positive integers, what is the value of \(x^4 - y^4\)?

1. \((y^2 + x^2)(y + x)(x - y) > 100\)
2. \(x^y = y^x\)


Hi,

I could infer the answer to be "E".

1. \((y^2 + x^2)(y + x)(x - y) > 100\)

By solving, \((x^4 - y^4) > 100\). The Value cannot not be decided as the set is infinite (> 100). Hence it is insufficient.

2. \(x^y = y^x\)

x and y being two distinct positive integers, the values can take one of the forms as below,
(a) y=2, x=4
(b) y=4, x=16 etc.
Hence insufficient.

By combining 1 and 2, many values exist,

(a) y=2, x=4, then \((x^4 - y^4) > 100\) becomes 240, which is >100
(b) y=4, x=16, then \((x^4 - y^4) > 100\) becomes 65280, which is also >100.

so no one value can be inferred by combining 1 and 2.

Hence, the answer is E.

Please let me know any other alternative views.

Thanks.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58396
Re: If x and y are distinct positive integers, what is the value of ....  [#permalink]

Show Tags

New post 13 Mar 2017, 01:01
arichinna wrote:
Prajat wrote:
If x and y are distinct positive integers, what is the value of \(x^4 - y^4\)?

1. \((y^2 + x^2)(y + x)(x - y) > 100\)
2. \(x^y = y^x\)


Hi,

I could infer the answer to be "E".

1. \((y^2 + x^2)(y + x)(x - y) > 100\)

By solving, \((x^4 - y^4) > 100\). The Value cannot not be decided as the set is infinite (> 100). Hence it is insufficient.

2. \(x^y = y^x\)

x and y being two distinct positive integers, the values can take one of the forms as below,
(a) y=2, x=4
(b) y=4, x=16etc.
Hence insufficient.

By combining 1 and 2, many values exist,

(a) y=2, x=4, then \((x^4 - y^4) > 100\) becomes 240, which is >100
(b) y=4, x=16, then \((x^4 - y^4) > 100\) becomes 65280, which is also >100.

so no one value can be inferred by combining 1 and 2.

Hence, the answer is E.

Please let me know any other alternative views.

Thanks.


Notice that 4^16 ≠ 16^4.
_________________
Intern
Intern
avatar
B
Joined: 11 Jun 2016
Posts: 4
Re: If x and y are distinct positive integers, what is the value of ....  [#permalink]

Show Tags

New post 16 Mar 2017, 08:33
1
Good question!

While B might look like the answer (I spent a good amount of time trying to understand why it wasn't), C is correct.

Statement 1 gives the lowest limit of the, i.e. x^4-y^4\(\) >100. Basically, the result will be a positive number greater than 100.
Statement B defines a relationship between x and y such that only the numbers 2 and 4 satisfy this relationship. Butwe either X or Y could be 2 or 4. Thus, we do not know the value for each variable. If x = 2 and y = 4, then we get a negative result, but if x is 4 and y is 2, then we get a postive result that is quite large

Combining both statements, we can rule out x=2 and y=4, as we know that the result must be positive and greater than 100.
This gives the correct answer, x=4 and y=2.
Hence C.
Director
Director
avatar
S
Joined: 12 Nov 2016
Posts: 699
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Re: If x and y are distinct positive integers, what is the value of ....  [#permalink]

Show Tags

New post 29 May 2017, 20:06
2
Prajat wrote:
If x and y are distinct positive integers, what is the value of \(x^4 - y^4\)?

1. \((y^2 + x^2)(y + x)(x - y) > 100\)
2. \(x^y = y^x\)


They key words in this problem are "distinct positive integers."

Statement 1

(y^2 + x^2)(y + x)(x - y) > 10
(y^2 + x^2) (xy- y^2 + x^2 -yx)
xy^3- y^4 + x^2y^2 - y^3x + x^3y - x^2y^2 + x^4 -yx^3 ( notice terms that cancel)
-y^4 + x^4
x^4-y^4 >100

Insufficient because there are infinite variables that can satisfy this inequality

Statement 2

x^y=y^x

only 0,1 or 2 and 4 can satisfy this equation; however, the integers must be both positive and distinct. Therefore, the set of integers must be 2 and 4- but x and y cannot be distinguished- x could be 2 or x could be 4

Statement 1 and 2

Using both statements it can be inferred that x must be 4 because x must be greater than 100.

Hence
"C"
Director
Director
User avatar
G
Joined: 09 Aug 2017
Posts: 500
Re: If x and y are distinct positive integers, what is the value of ....  [#permalink]

Show Tags

New post 30 Oct 2018, 20:07
If I am not mistaken, 0 and 1 does't satisfy statement 2.
0^1 not equals to 1^0

Nunuboy1994 wrote:
Prajat wrote:
If x and y are distinct positive integers, what is the value of \(x^4 - y^4\)?

1. \((y^2 + x^2)(y + x)(x - y) > 100\)
2. \(x^y = y^x\)


They key words in this problem are "distinct positive integers."

Statement 1

(y^2 + x^2)(y + x)(x - y) > 10
(y^2 + x^2) (xy- y^2 + x^2 -yx)
xy^3- y^4 + x^2y^2 - y^3x + x^3y - x^2y^2 + x^4 -yx^3 ( notice terms that cancel)
-y^4 + x^4
x^4-y^4 >100

Insufficient because there are infinite variables that can satisfy this inequality

Statement 2

x^y=y^x

only 0,1 or 2 and 4 can satisfy this equation; however, the integers must be both positive and distinct. Therefore, the set of integers must be 2 and 4- but x and y cannot be distinguished- x could be 2 or x could be 4

Statement 1 and 2

Using both statements it can be inferred that x must be 4 because x must be greater than 100.

Hence
"C"
GMAT Club Bot
Re: If x and y are distinct positive integers, what is the value of ....   [#permalink] 30 Oct 2018, 20:07
Display posts from previous: Sort by

If x and y are distinct positive integers, what is the value of ....

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne