It is currently 18 Nov 2017, 13:12

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If m and n are non-negative integers, mn=?

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

Hide Tags

Expert Post
Math Revolution GMAT Instructor
User avatar
P
Joined: 16 Aug 2015
Posts: 4314

Kudos [?]: 3035 [0], given: 0

GPA: 3.82
Premium Member CAT Tests
If m and n are non-negative integers, mn=? [#permalink]

Show Tags

New post 01 Aug 2017, 00:59
Expert's post
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

58% (00:59) correct 42% (01:19) wrong based on 48 sessions

HideShow timer Statistics

If m and n are non-negative integers, mn=?

1) \(9^n=3^m\)
2) \(2^n=5^m\)
[Reveal] Spoiler: OA

_________________

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.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself
See our Youtube demo

Kudos [?]: 3035 [0], given: 0

1 KUDOS received
BSchool Forum Moderator
User avatar
D
Joined: 26 Feb 2016
Posts: 1597

Kudos [?]: 671 [1], given: 17

Location: India
Concentration: General Management, Leadership
WE: Sales (Retail)
Premium Member CAT Tests
Re: If m and n are non-negative integers, mn=? [#permalink]

Show Tags

New post 01 Aug 2017, 01:31
1
This post received
KUDOS
1. \(9^n=3^m\)
This is possible when the values of n and m are as follows:
a) n=1,m=2 nm=2
b) n=2,m=4, nm=8

We are not able to come up with an unique value for the expression mn(Insufficient)

2. \(2^n=5^m\)
This is possible if and only if n=m=0.

The value of nm=0 (Sufficient)(Option B)
_________________

Stay hungry, Stay foolish

2017-2018 MBA Deadlines

Class of 2020: Rotman Thread | Schulich Thread
Class of 2019: Sauder Thread

Kudos [?]: 671 [1], given: 17

Expert Post
Math Revolution GMAT Instructor
User avatar
P
Joined: 16 Aug 2015
Posts: 4314

Kudos [?]: 3035 [0], given: 0

GPA: 3.82
Premium Member CAT Tests
Re: If m and n are non-negative integers, mn=? [#permalink]

Show Tags

New post 03 Aug 2017, 01:25
==> In the original condition, there are 2 variables (m,n) and in order to match the number of variables to the number of equations, there must be 2 equations. Since there is 1 for con 1) and 1 for con 2), C is most likely to be the answer. By solving con 1) and con 2), from con 1), you get \(9^n=(3^2)^n=3^{2n}=3^m\), which becomes \(2n=m\). In order for con 2) to satisfy as well, you only get m=n=0, hence it is unique and sufficient. The answer is C. However, this is an integer question, one of the key questions, so you apply CMT 4 (A: if you get C too easily, consider A or B). For con 1), the way to satisfy \(9^n=(3^2)^n=3^{2n}=3^m\) to \(2n=m\) is not unique and not sufficient. For con 2), from \(2^n=5^m\), you get \(2^n=even\) and \(5^m=odd\), so even≠odd. Only m=n=0 satisfies this, hence it is unique and sufficient.

Therefore, the answer is B, not C.
Answer: B
_________________

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.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself
See our Youtube demo

Kudos [?]: 3035 [0], given: 0

Re: If m and n are non-negative integers, mn=?   [#permalink] 03 Aug 2017, 01:25
Display posts from previous: Sort by

If m and n are non-negative integers, mn=?

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


GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.