NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 23:14 It is currently 25 Apr 2024, 23:14
Decision Tracker
My Rewards
New posts
New comers' posts

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

If n is a positive integer, is the value of x - y at least

User avatar
L
freedom128
Director
Director
Joined: 30 Sep 2017
Posts: 956
Own Kudos [?]: 1256 [5]
Given Kudos: 402
GMAT 1: 720 Q49 V40
GPA: 3.8
Send PM
Reviews Badge
If n is a positive integer, is the value of x - y at least [#permalink] New post   Updated on: 24 Aug 2019, 22:12
2
Kudos
3
Bookmarks
00:00
A
B
C
D
E

Difficulty:

75% (hard)

Question Stats:

48% (02:11) correct 52% (02:16) wrong based on 44 sessions
Hide Show timer Statistics
If \(n\) is a positive integer, is the value of \(x - y\) at least three times the value of \(5^n−3^n\) ?

(1) \(x=5^{n-1}\) and \(y=3^{n+1}\)

(2) \(n=2\), \((x+y)=32\) and \(xy=135\)

Source: adapted from OG 15

Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
ShowHide Answer
Official Answer
D

Originally posted by freedom128 on 20 Aug 2019, 09:04.
Last edited by freedom128 on 24 Aug 2019, 22:12, edited 7 times in total.
User avatar
L
freedom128
Director
Director
Joined: 30 Sep 2017
Posts: 956
Own Kudos [?]: 1256 [5]
Given Kudos: 402
GMAT 1: 720 Q49 V40
GPA: 3.8
Send PM
Reviews Badge
Re: If n is a positive integer, is the value of x - y at least [#permalink] New post   Updated on: 24 Aug 2019, 22:12
3
Kudos
2
Bookmarks
(1) \(x-y=5^{n-1}-3^{n+1}=3*(5^n-3^n) - \frac{14}{5}*5^n\). Since \(\frac{14}{5}*5^n > 0\), then it must be true that \(x-y < 3*(5^n-3^n)\).
SUFFICIENT

(2) We can calculate the value of \((x-y)\) from:
\((x-y)^2= (x+y)^2-4xy\)
\((x-y)^2= 32^2-4*135 =484\)
\((x-y)=22\) or \(-22\).

Since three times the value of \((5^2-3^2)=16\) is always greater than both possible values of \((x-y)\), then it must be true that \(x-y < 3*(5^n-3^n)\).
SUFFICIENT

Answer is (D)
+1 kudo is appreciated

Originally posted by freedom128 on 20 Aug 2019, 09:13.
Last edited by freedom128 on 24 Aug 2019, 22:12, edited 13 times in total.
avatar
B
arorni
Manager
Manager
Joined: 27 Oct 2017
Posts: 61
Own Kudos [?]: 19 [0]
Given Kudos: 69
Send PM
Re: If n is a positive integer, is the value of x - y at least [#permalink] New post   20 Aug 2019, 18:08
chondro48 wrote:
(1) \(x-y=5^{n-1}-3^{n+1}=3*(5^n-3^n) - \frac{14}{5}*5^n\). Since \(\frac{14}{5}*5^n > 0\), then it must be true that \(x-y < 3*(5^n-3^n)\).
SUFFICIENT

(2) \(x-y=5^{n+1}-3^{n+1}=3*(5^n-3^n) + 2*5^n\). Since \(2*5^n > 0\), then it must be true that \(x-y > 3*(5^n-3^n)\).
SUFFICIENT

Answer is (D)
+1 kudo is appreciated =)


Can you please explain, how you got 14/5 or *5^n in the first equation and 2*5^n in the second?
User avatar
L
freedom128
Director
Director
Joined: 30 Sep 2017
Posts: 956
Own Kudos [?]: 1256 [2]
Given Kudos: 402
GMAT 1: 720 Q49 V40
GPA: 3.8
Send PM
Reviews Badge
Re: If n is a positive integer, is the value of x - y at least [#permalink] New post   Updated on: 21 Aug 2019, 11:39
1
Kudos
1
Bookmarks
arorni wrote:
chondro48 wrote:
(1) \(x-y=5^{n-1}-3^{n+1}=3*(5^n-3^n) - \frac{14}{5}*5^n\). Since \(\frac{14}{5}*5^n > 0\), then it must be true that \(x-y < 3*(5^n-3^n)\).
SUFFICIENT

(2) \(x-y=5^{n+1}-3^{n+1}=3*(5^n-3^n) + 2*5^n\). Since \(2*5^n > 0\), then it must be true that \(x-y > 3*(5^n-3^n)\).
SUFFICIENT

Answer is (D)

Can you please explain, how you got 14/5 or *5^n in the first equation and 2*5^n in the second?


Hi arorni,

(1)
\(x-y=5^{n-1}-3^{n+1}\)
\(=\frac{1}{5}*5^n-3*3^n\)
\(=(\frac{15}{5}*5^n-\frac{14}{5}*5^n)-3*3^n\)
\(=3*5^n-\frac{14}{5}*5^n-3*3^n\)
\(=3*5^n - 3*3^n -\frac{14}{5}*5^n\)
\(=3*(5^n-3^n) -\frac{14}{5}*5^n\)
Then, refer to my previous post for the rest.

(2)
\(x-y=5^{n+1}-3^{n+1}\)
\(=5*5^n-3*3^n\)
\(=2*5^n+3*5^n-3*3^n\)
\(=2*5^n+3*(5^n-3^n)\)
\(=3*(5^n-3^n)+2*5^n\)
Then, refer to my previous post for the rest.

Posted from my mobile device

Originally posted by freedom128 on 20 Aug 2019, 19:28.
Last edited by freedom128 on 21 Aug 2019, 11:39, edited 1 time in total.
User avatar
L
unraveled
CEO
CEO
Joined: 07 Mar 2019
Posts: 2554
Own Kudos [?]: 1813 [1]
Given Kudos: 763
Location: India
WE:Sales (Energy and Utilities)
Send PM
Re: If n is a positive integer, is the value of x - y at least [#permalink] New post   20 Aug 2019, 20:07
1
Kudos
arorni wrote:
chondro48 wrote:
(1) \(x-y=5^{n-1}-3^{n+1}=3*(5^n-3^n) - \frac{14}{5}*5^n\). Since \(\frac{14}{5}*5^n > 0\), then it must be true that \(x-y < 3*(5^n-3^n)\).
SUFFICIENT

(2) \(x-y=5^{n+1}-3^{n+1}=3*(5^n-3^n) + 2*5^n\). Since \(2*5^n > 0\), then it must be true that \(x-y > 3*(5^n-3^n)\).
SUFFICIENT

Answer is (D)
+1 kudo is appreciated =)


Can you please explain, how you got 14/5 or *5^n in the first equation and 2*5^n in the second?


You may try number plug in method also which works smoothly if stuck in algebra.
avatar
B
arorni
Manager
Manager
Joined: 27 Oct 2017
Posts: 61
Own Kudos [?]: 19 [0]
Given Kudos: 69
Send PM
Re: If n is a positive integer, is the value of x - y at least [#permalink] New post   21 Aug 2019, 07:29
chondro48 wrote:
arorni wrote:
chondro48 wrote:
(1) \(x-y=5^{n-1}-3^{n+1}=3*(5^n-3^n) - \frac{14}{5}*5^n\). Since \(\frac{14}{5}*5^n > 0\), then it must be true that \(x-y < 3*(5^n-3^n)\).
SUFFICIENT

(2) \(x-y=5^{n+1}-3^{n+1}=3*(5^n-3^n) + 2*5^n\). Since \(2*5^n > 0\), then it must be true that \(x-y > 3*(5^n-3^n)\).
SUFFICIENT

Answer is (D)

Can you please explain, how you got 14/5 or *5^n in the first equation and 2*5^n in the second?


Hi arorni,
Please give kudos for the explanation below

(1)
\(x-y=5^{n-1}-3^{n+1}\)
\(=\frac{1}{5}*5^n-3*3^n\)
\(=(\frac{15}{5}*5^n-\frac{14}{5}*5^n)-3*3^n\)
\(=3*5^n-\frac{14}{5}*5^n-3*3^n\)
\(=3*5^n - 3*3^n -\frac{14}{5}*5^n\)
\(=3*(5^n-3^n) -\frac{14}{5}*5^n\)
Then, refer to my previous post for the rest.

(2)
\(x-y=5^{n+1}-3^{n+1}\)
\(=5*5^n-3*3^n\)
\(=2*5^n+3*5^n-3*3^n\)
\(=2*5^n+3*(5^n-3^n)\)
\(=3*(5^n-3^n)+2*5^n\)
Then, refer to my previous post for the rest.

Posted from my mobile device


Thanks a lot for the detailed explanation..
avatar
B
arorni
Manager
Manager
Joined: 27 Oct 2017
Posts: 61
Own Kudos [?]: 19 [0]
Given Kudos: 69
Send PM
Re: If n is a positive integer, is the value of x - y at least [#permalink] New post   21 Aug 2019, 07:33
lnm87 wrote:
arorni wrote:
chondro48 wrote:
(1) \(x-y=5^{n-1}-3^{n+1}=3*(5^n-3^n) - \frac{14}{5}*5^n\). Since \(\frac{14}{5}*5^n > 0\), then it must be true that \(x-y < 3*(5^n-3^n)\).
SUFFICIENT

(2) \(x-y=5^{n+1}-3^{n+1}=3*(5^n-3^n) + 2*5^n\). Since \(2*5^n > 0\), then it must be true that \(x-y > 3*(5^n-3^n)\).
SUFFICIENT

Answer is (D)
+1 kudo is appreciated =)


Can you please explain, how you got 14/5 or *5^n in the first equation and 2*5^n in the second?


You may try number plug in method also which works smoothly if stuck in algebra.


Yes..you are right...thanks for the reply, although I solved this question using numbers, I wanted to understand the equation mentioned by chondro48
User avatar
L
unraveled
CEO
CEO
Joined: 07 Mar 2019
Posts: 2554
Own Kudos [?]: 1813 [0]
Given Kudos: 763
Location: India
WE:Sales (Energy and Utilities)
Send PM
Re: If n is a positive integer, is the value of x - y at least [#permalink] New post   21 Aug 2019, 07:43
arorni wrote:

Yes..you are right...thanks for the reply, although I solved this question using numbers, I wanted to understand the equation mentioned by chondro48


Same here, solved using numbers but it takes too much of time generally and getting across algebra solution is best if the method strikes early which in my case is a 50-50 chance :|
User avatar
L
stne
SVP
SVP
Joined: 27 May 2012
Posts: 1680
Own Kudos [?]: 1424 [0]
Given Kudos: 632
Send PM
Re: If n is a positive integer, is the value of x - y at least [#permalink] New post   23 Aug 2019, 02:11
chondro48 wrote:
(1) \(x-y=5^{n-1}-3^{n+1}=3*(5^n-3^n) - \frac{14}{5}*5^n\). Since \(\frac{14}{5}*5^n > 0\), then it must be true that \(x-y < 3*(5^n-3^n)\).
SUFFICIENT

(2) \(x-y=5^{n+1}-3^{n+1}=3*(5^n-3^n) + 2*5^n\). Since \(2*5^n > 0\), then it must be true that \(x-y > 3*(5^n-3^n)\).
SUFFICIENT

Answer is (D)
+1 kudo is appreciated =)



Hi chondro48,
Appreciate your adaptation, but you have been a member of GMAT club for about two years now, you should know that in an actual GMAT question , two statements should never contradict each other. In your first statement you have \(x-y < 3(5^n−3^n)\) and in your second statement you have \(x-y > 3(5^n−3^n)\).

This should not happen in an actual GMAT question !
User avatar
L
freedom128
Director
Director
Joined: 30 Sep 2017
Posts: 956
Own Kudos [?]: 1256 [0]
Given Kudos: 402
GMAT 1: 720 Q49 V40
GPA: 3.8
Send PM
Reviews Badge
Re: If n is a positive integer, is the value of x - y at least [#permalink] New post   Updated on: 24 Aug 2019, 19:32
stne wrote:
chondro48 wrote:
(1) \(x-y=5^{n-1}-3^{n+1}=3*(5^n-3^n) - \frac{14}{5}*5^n\). Since \(\frac{14}{5}*5^n > 0\), then it must be true that \(x-y < 3*(5^n-3^n)\).
SUFFICIENT

(2) \(x-y=5^{n+1}-3^{n+1}=3*(5^n-3^n) + 2*5^n\). Since \(2*5^n > 0\), then it must be true that \(x-y > 3*(5^n-3^n)\).
SUFFICIENT

Answer is (D)
+1 kudo is appreciated =)



Hi chondro48,
Appreciate your adaptation, but you have been a member of GMAT club for about two years now, you should know that in an actual GMAT question , two statements should never contradict each other. In your first statement you have \(x-y < 3(5^n−3^n)\) and in your second statement you have \(x-y > 3(5^n−3^n)\).

This should not happen in an actual GMAT question !


Hi stne,

Thank you for the input. The question has been revised so that the two statements do not contradict each other and the answer key remains the same. After all, the old question is still great for practicing concepts and creativity.

Posted from my mobile device

Originally posted by freedom128 on 23 Aug 2019, 02:52.
Last edited by freedom128 on 24 Aug 2019, 19:32, edited 2 times in total.
User avatar
L
TheNightKing
VP
VP
Joined: 18 Dec 2017
Posts: 1170
Own Kudos [?]: 991 [0]
Given Kudos: 421
Location: United States (KS)
GMAT 1: 600 Q46 V27
Send PM
Re: If n is a positive integer, is the value of x - y at least [#permalink] New post   24 Aug 2019, 07:38
chondro48 wrote:
If \(n\) is a positive integer, is the value of \(x - y\) at least three times the value of \(5^n−3^n\) ?

(1) \(x=5^{n-1}\) and \(y=3^{n+1}\)

(2) \(x=5^{n+1}\) and \(y=3^{n+1}\)

Source: adapted from OG 15
+1 kudo is appreciated.


So if I take value of n as 1, I get 5-3 as 2. So effectively I am checking if x-y >=6.

A. x=1 y=9. x-y becomes a negative value. I mean sure the question does not say x-y is positive but it can't be greater than 6 for sure. And n can be 1 because it is a positive number which means 1 is not sufficient.

Am I doing something wrong?

Thanks for the tag!
User avatar
L
freedom128
Director
Director
Joined: 30 Sep 2017
Posts: 956
Own Kudos [?]: 1256 [0]
Given Kudos: 402
GMAT 1: 720 Q49 V40
GPA: 3.8
Send PM
Reviews Badge
Re: If n is a positive integer, is the value of x - y at least [#permalink] New post   Updated on: 24 Aug 2019, 12:55
TheNightKing wrote:
chondro48 wrote:
If \(n\) is a positive integer, is the value of \(x - y\) at least three times the value of \(5^n−3^n\) ?

(1) \(x=5^{n-1}\) and \(y=3^{n+1}\)

(2) \(x=5^{n+1}\) and \(y=3^{n+1}\)


So if I take value of n as 1, I get 5-3 as 2. So effectively I am checking if x-y >=6.

A. x=1 y=9. x-y becomes a negative value. I mean sure the question does not say x-y is positive but it can't be greater than 6 for sure. And n can be 1 because it is a positive number which means 1 is not sufficient.

Am I doing something wrong?

Thanks for the tag!



Hi TheNightKing,

No, you are not that wrong. If \(n = 1\), then \(x - y = 1 - 9 = -8\), certainly less than three times \((5^1 - 3^1) = 6\). If you try any other value of positive integer n (n = 2, 3, 4, etc), you will find that the value of \(x - y\) is ALWAYS less than three times the value of \(5^n−3^n\). Thus, statement (1) is indeed sufficient.

Similar scheme (pick a number) can also be applied for statement (2).

Btw. The question actually doesn't limit that n has to be 1.

Originally posted by freedom128 on 24 Aug 2019, 07:52.
Last edited by freedom128 on 24 Aug 2019, 12:55, edited 3 times in total.
User avatar
L
TheNightKing
VP
VP
Joined: 18 Dec 2017
Posts: 1170
Own Kudos [?]: 991 [0]
Given Kudos: 421
Location: United States (KS)
GMAT 1: 600 Q46 V27
Send PM
Re: If n is a positive integer, is the value of x - y at least [#permalink] New post   24 Aug 2019, 07:55
chondro48 wrote:
TheNightKing wrote:
chondro48 wrote:
If \(n\) is a positive integer, is the value of \(x - y\) at least three times the value of \(5^n−3^n\) ?

(1) \(x=5^{n-1}\) and \(y=3^{n+1}\)

(2) \(x=5^{n+1}\) and \(y=3^{n+1}\)


So if I take value of n as 1, I get 5-3 as 2. So effectively I am checking if x-y >=6.

A. x=1 y=9. x-y becomes a negative value. I mean sure the question does not say x-y is positive but it can't be greater than 6 for sure. And n can be 1 because it is a positive number which means 1 is not sufficient.

Am I doing something wrong?

Thanks for the tag!


No, you are not wrong. When n=1, it is certain that x-y=1-9=-8 is less than three times (5^1 - 3^1)=6. This applies to any value of n (please try n=2 or n=3). Therefore, statement (1) is deemed sufficient.

Btw. The question actually just asks whether \(x - y\) is at least three times the value of \(5^n−3^n\), not what is the value of n.

generously give kudo to the question. Thanks buddy:)

Posted from my mobile device


As far as I know that is not how DS works, If it doesn't work for n=1 but works for n>1 and the question is saying n is positive number and not n is positive number greater than 1 that means the statement is not sufficient.
avatar
B
DiogoNunes
Intern
Intern
Joined: 03 Aug 2019
Posts: 3
Own Kudos [?]: 0 [0]
Given Kudos: 11
Location: Australia
Concentration: General Management, General Management
Schools: Other Schools Booth '22 Babson '22 CBS '22 Cranfield '21
Send PM
Re: If n is a positive integer, is the value of x - y at least [#permalink] New post   24 Aug 2019, 10:28
chondro48 wrote:
If \(n\) is a positive integer, is the value of \(x - y\) at least three times the value of \(5^n−3^n\) ?

(1) \(x=5^{n-1}\) and \(y=3^{n+1}\)

(2) \(x=5^{n+1}\) and \(y=3^{n+1}\)

Source: adapted from OG 15
+1 kudo is appreciated.

about what level is this question? 600+?
User avatar
L
freedom128
Director
Director
Joined: 30 Sep 2017
Posts: 956
Own Kudos [?]: 1256 [0]
Given Kudos: 402
GMAT 1: 720 Q49 V40
GPA: 3.8
Send PM
Reviews Badge
Re: If n is a positive integer, is the value of x - y at least [#permalink] New post   24 Aug 2019, 12:56
DiogoNunes wrote:
chondro48 wrote:
If \(n\) is a positive integer, is the value of \(x - y\) at least three times the value of \(5^n−3^n\) ?

(1) \(x=5^{n-1}\) and \(y=3^{n+1}\)

(2) \(x=5^{n+1}\) and \(y=3^{n+1}\)

Source: adapted from OG 15
+1 kudo is appreciated.

about what level is this question? 600+?


Just medium, 600-650 level.

Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
GMAT Club Bot
gmatclubot
Re: If n is a positive integer, is the value of x - y at least [#permalink]
24 Aug 2019, 12:56
Moderators:
Bunuel
Math Expert
92915 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts
GMATBusters
GMAT Tutor
1905 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions