It is currently 24 Feb 2018, 02:29

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

For positive integers m and n, is 7+72+73+….+7mn divisible by 14? 1) n

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

Hide Tags

1 KUDOS received
Senior SC Moderator
User avatar
D
Joined: 14 Nov 2016
Posts: 1277
Location: Malaysia
GMAT ToolKit User Premium Member CAT Tests
For positive integers m and n, is 7+72+73+….+7mn divisible by 14? 1) n [#permalink]

Show Tags

New post 31 Mar 2017, 06:16
1
This post received
KUDOS
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

45% (01:58) correct 55% (02:03) wrong based on 47 sessions

HideShow timer Statistics

For positive integers m and n, is \(7+7^2+7^3+….+7^{mn}\) divisible by 14?

1) \(n=even\)

2) \(m = \frac{a}{b}\) , where one of a and b is an odd and the other is an even
[Reveal] Spoiler: OA

_________________

"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."

Rules for posting in verbal forum | Please DO NOT post short answer in your post!

3 KUDOS received
Senior Manager
Senior Manager
avatar
B
Joined: 13 Oct 2016
Posts: 367
GPA: 3.98
Re: For positive integers m and n, is 7+72+73+….+7mn divisible by 14? 1) n [#permalink]

Show Tags

New post 31 Mar 2017, 08:09
3
This post received
KUDOS
2
This post was
BOOKMARKED
ziyuen wrote:
For positive integers m and n, is \(7+7^2+7^3+….+7^{mn}\) divisible by 14?

1) \(n=even\)

2) \(m = \frac{a}{b}\) , where one of a and b is an odd and the other is an even


Hi

Good question +1

\(7+7^2+7^3+….+7^{mn}\) = \(7*(1 + 7 + 7^2 + 7^3 + .... + 7^{mn - 1})\)

The problem is whether the expression \((1 + 7 + 7^2 + 7^3 + .... + 7^{mn - 1})\) is even or odd.

1) \(n=even\)

If n is even then \(mn - 1 = odd\) and we have = 1 + sum of odd number of odd elements (please excuse me for tautology) because \(7^{any power}\) will be odd.

\(1 + odd = even\). Sufficient.

2) \(m = \frac{a}{b}\) , where one of a and b is an odd and the other is an even

So if \(a=odd\) then \(b=even\) and vice versa. But if we want \(m\) to be an integer, first case will be impossible (\(\frac{odd}{even} =/= integer\)).

And we are left with \(m*odd = even\) hence \(m\) is even.

As in previous cae \(mn - 1\) will be odd. Sufficient.

Answer D.
Manager
Manager
avatar
S
Status: GMAT...one last time for good!!
Joined: 10 Jul 2012
Posts: 71
Location: India
Concentration: General Management
GMAT 1: 660 Q47 V34
GPA: 3.5
GMAT ToolKit User Reviews Badge
Re: For positive integers m and n, is 7+72+73+….+7mn divisible by 14? 1) n [#permalink]

Show Tags

New post 01 Apr 2017, 09:35
ziyuen wrote:
For positive integers m and n, is \(7+7^2+7^3+….+7^{mn}\) divisible by 14?

1) \(n=even\)

2) \(m = \frac{a}{b}\) , where one of a and b is an odd and the other is an even


7(1+7+7^2+7^3+….+7^mn-1)
For the above to be divisible by 14. The expression in bracket has to be divisible by 2. So the expression needs to be even. 1 is not divisible by 2, but 1+7 is. So the power of 7 has to be odd.
Therefore question boils down to....is mn-1=odd?
For mn-1 to be odd, mn should be even, for mn to be even either of them or both of needs to be even.

1) n= even; Suff
2)m=a/b. For this to be an integer m has to be even; Suff

Ans:D
_________________

Kudos for a correct solution :)

Re: For positive integers m and n, is 7+72+73+….+7mn divisible by 14? 1) n   [#permalink] 01 Apr 2017, 09:35
Display posts from previous: Sort by

For positive integers m and n, is 7+72+73+….+7mn divisible by 14? 1) n

  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®.