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

It is currently 20 Sep 2018, 21:33

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 m, n and p are positive integers such that (p^m)^n=256

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

Hide Tags

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6221
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
If m, n and p are positive integers such that (p^m)^n=256  [#permalink]

Show Tags

New post 08 Jan 2018, 01:28
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

80% (00:51) correct 20% (00:56) wrong based on 64 sessions

HideShow timer Statistics

[GMAT math practice question]

If \(m, n\) and \(p\) are positive integers such that \((p^m)^n=256\), which of the following could be the value of \(n\)?

I. 1
II. 2
III. 4

A. I and II
B. I and III
C. II and III
D. II only
E. I, II and III

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Senior Manager
Senior Manager
User avatar
G
Joined: 17 Oct 2016
Posts: 323
Location: India
Concentration: Operations, Strategy
GPA: 3.73
WE: Design (Real Estate)
GMAT ToolKit User Premium Member
Re: If m, n and p are positive integers such that (p^m)^n=256  [#permalink]

Show Tags

New post 08 Jan 2018, 01:32
Let p=16, m=2, n=1. Then (p^m)^n=256. n=1
Let p=4, m=2, n=2. Then (p^m)^n=256. n=2
Let p=2, m=2, n=4. Then (p^m)^n=256. n=4

Hence I, II, III are right. Option E

Posted from my mobile device
_________________

Help with kudos if u found the post useful. Thanks

examPAL Representative
User avatar
G
Joined: 07 Dec 2017
Posts: 593
Re: If m, n and p are positive integers such that (p^m)^n=256  [#permalink]

Show Tags

New post 08 Jan 2018, 01:55
MathRevolution wrote:
[GMAT math practice question]

If \(m, n\) and \(p\) are positive integers such that \((p^m)^n=256\), which of the following could be the value of \(n\)?

I. 1
II. 2
III. 4

A. I and II
B. I and III
C. II and III
D. II only
E. I, II and III


Since we're asked 'which of the following could be' we'll use the answers.
This is an Alternative approach.

If n = 1 then p^m = 256. This works with p=m=4.
If n = 2 then p^m = 16. This works with p=4 and m=2
If n = 4 then p^m = 4. this works with p=m=2.

Therefore (E) is correct.
_________________

Image
Image
Sign up for 7-day free trial

Watch free GMAT tutorials in Math, Verbal, IR, and AWA.

GMAT test takers: Watch now the GMAC interview with the people who write the GMAT test!
We discussed the chances of improving a GMAT score; how important the first questions on the test are; what to do if you don’t have enough time to complete a whole section; and more.

You can watch all the action from the interview here.

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6221
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: If m, n and p are positive integers such that (p^m)^n=256  [#permalink]

Show Tags

New post 10 Jan 2018, 01:03
=>

Since \(256 = 2^8\), \((p^m)^n = p^{mn} = 2^8.\)
So, \(p = 2\)and \(mn = 8\).
Since \(n\) is a factor of \(8\), \(n\) could be any of the values \(1, 2, 4\), and \(8\).

Therefore, the answer is E.
Answer: E
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Intern
Intern
avatar
B
Joined: 15 Aug 2017
Posts: 15
Re: If m, n and p are positive integers such that (p^m)^n=256  [#permalink]

Show Tags

New post 10 Jan 2018, 01:15
1
256=2^8
So mXn has following combination
8X1
4X2
2X4
1X8

So n can take the value 1, 2, 4, 8
So E
Board of Directors
User avatar
P
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4031
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member
Re: If m, n and p are positive integers such that (p^m)^n=256  [#permalink]

Show Tags

New post 10 Jan 2018, 08:58
MathRevolution wrote:
[GMAT math practice question]

If \(m, n\) and \(p\) are positive integers such that \((p^m)^n=256\), which of the following could be the value of \(n\)?

I. 1
II. 2
III. 4

A. I and II
B. I and III
C. II and III
D. II only
E. I, II and III


\(256^1 = 256\)

\(2^8 = 256\)

Or, \(4^4 = 256\)

Or, \(16^2 = 256\)

Thus, the possible values of n are all 1 , 2 and 4, answer will be (E)
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

VP
VP
User avatar
V
Status: It's near - I can see.
Joined: 13 Apr 2013
Posts: 1262
Location: India
Concentration: International Business, Operations
GMAT 1: 480 Q38 V22
GPA: 3.01
WE: Engineering (Consulting)
Premium Member Reviews Badge CAT Tests
If m, n and p are positive integers such that (p^m)^n=256  [#permalink]

Show Tags

New post 10 Jan 2018, 09:21
MathRevolution wrote:
[GMAT math practice question]

If \(m, n\) and \(p\) are positive integers such that \((p^m)^n=256\), which of the following could be the value of \(n\)?

I. 1
II. 2
III. 4

A. I and II
B. I and III
C. II and III
D. II only
E. I, II and III


\((256^1)^1\) = 256 ; Eliminate (C) and (D)

\((4^2)^2\) = 256 ; Eliminate (B)

\((4^1)^4\) = 256 ; Eliminate (A)

So (E)
_________________

"Do not watch clock; Do what it does. KEEP GOING."

If m, n and p are positive integers such that (p^m)^n=256 &nbs [#permalink] 10 Jan 2018, 09:21
Display posts from previous: Sort by

If m, n and p are positive integers such that (p^m)^n=256

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

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.