Find all School-related info fast with the new School-Specific MBA Forum

It is currently 14 Sep 2014, 18:01

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If each term in the sum a1+a2+a3+.....+an is either 7 or 77

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
VP
VP
User avatar
Joined: 20 Sep 2005
Posts: 1023
Followers: 3

Kudos [?]: 24 [1] , given: 0

GMAT Tests User
If each term in the sum a1+a2+a3+.....+an is either 7 or 77 [#permalink] New post 22 Mar 2006, 22:07
1
This post received
KUDOS
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

66% (01:58) correct 34% (01:19) wrong based on 177 sessions
If each term in the sum a1+a2+a3+.....+an is either 7 or 77 and the sum equals 350, which of the following could be equal to n?

A. 38
B. 39
C. 40
D. 41
E. 42

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-each-term-in-the-sum-a1-a2-a3-an-is-either-7-or-93974.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 30 Oct 2013, 06:48, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Kaplan Promo CodeKnewton GMAT Discount CodesManhattan GMAT Discount Codes
3 KUDOS received
SVP
SVP
User avatar
Joined: 05 Apr 2005
Posts: 1736
Followers: 3

Kudos [?]: 33 [3] , given: 0

GMAT Tests User
Re: 7,77....Problem Solving [#permalink] New post 22 Mar 2006, 22:27
3
This post received
KUDOS
lhotseface wrote:
If each term in the sum a1 + a2 + a3.....+ an is either 7 or 77 and the sum is 350, What is n ?

Note: a1,a2 represent the first term,second...and NOT a*1, a*2 !


A. 38
B. 39
C. 40
D. 41
E. 42


350/7=50
77/7=11

so 50-11=39
or 50-2(11)=28
or 50-3(11)=17
or 50-4(11)=6

hence except 39 rest are to small than the answer choices. so go with B.
3 KUDOS received
SVP
SVP
avatar
Joined: 14 Dec 2004
Posts: 1711
Followers: 1

Kudos [?]: 33 [3] , given: 0

GMAT Tests User
 [#permalink] New post 22 Mar 2006, 22:35
3
This post received
KUDOS
I'm getting 40

350 = 50 * 7
& 77 = 11 * 7

50*7 has 50 terms.

we can write it as,
39*7 + 77 = 350 => 40 terms.
9 KUDOS received
SVP
SVP
User avatar
Joined: 24 Sep 2005
Posts: 1898
Followers: 10

Kudos [?]: 104 [9] , given: 0

GMAT Tests User
Re: 7,77....Problem Solving [#permalink] New post 23 Mar 2006, 02:58
9
This post received
KUDOS
lhotseface wrote:
If each term in the sum a1 + a2 + a3.....+ an is either 7 or 77 and the sum is 350, What is n ?

Note: a1,a2 represent the first term,second...and NOT a*1, a*2 !


A. 38
B. 39
C. 40
D. 41
E. 42


Let x and y be the number of term 7 and the number of term 77 respectively. WE have :
7x+ 77y= 350 ---> x+11y = 50 ---> x+y= 50- 10y
we have : x+y= n = 50- 10y ---> n must have the unit digit of 0 because 50 - 10y must be a number which has unit digit of 0

Among the answer choices provided, only C matches.

I go for C.
SVP
SVP
avatar
Joined: 14 Dec 2004
Posts: 1711
Followers: 1

Kudos [?]: 33 [0], given: 0

GMAT Tests User
Re: 7,77....Problem Solving [#permalink] New post 23 Mar 2006, 04:24
HIMALAYA wrote:
lhotseface wrote:
If each term in the sum a1 + a2 + a3.....+ an is either 7 or 77 and the sum is 350, What is n ?

Note: a1,a2 represent the first term,second...and NOT a*1, a*2 !


A. 38
B. 39
C. 40
D. 41
E. 42


350/7=50
77/7=11

so 50-11=39
or 50-2(11)=28
or 50-3(11)=17
or 50-4(11)=6

hence except 39 rest are to small than the answer choices. so go with B.


You just missed the 77 to count ;)
SVP
SVP
User avatar
Joined: 05 Apr 2005
Posts: 1736
Followers: 3

Kudos [?]: 33 [0], given: 0

GMAT Tests User
Re: 7,77....Problem Solving [#permalink] New post 23 Mar 2006, 06:33
vivek123 wrote:
HIMALAYA wrote:
lhotseface wrote:
If each term in the sum a1 + a2 + a3.....+ an is either 7 or 77 and the sum is 350, What is n ?

Note: a1,a2 represent the first term,second...and NOT a*1, a*2 !


A. 38
B. 39
C. 40
D. 41
E. 42


350/7=50
77/7=11

so 50-11=39
or 50-2(11)=28
or 50-3(11)=17
or 50-4(11)=6

hence except 39 rest are to small than the answer choices. so go with B.


You just missed the 77 to count ;)


thats right. yah, i forget to count that. :oops:
Current Student
User avatar
Joined: 29 Jan 2005
Posts: 5252
Followers: 23

Kudos [?]: 128 [0], given: 0

GMAT Tests User Reviews Badge
 [#permalink] New post 25 Mar 2006, 21:52
vivek123 wrote:
I'm getting 40

350 = 50 * 7
& 77 = 11 * 7

50*7 has 50 terms.

we can write it as,
39*7 + 77 = 350 => 40 terms.


Worked it the same way as Vivek. Laxie`s method would be more efficient with much bigger numbers...
Retired Moderator
User avatar
Joined: 02 Sep 2010
Posts: 807
Location: London
Followers: 76

Kudos [?]: 473 [0], given: 25

GMAT ToolKit User GMAT Tests User Reviews Badge
Re: 7,77....Problem Solving [#permalink] New post 18 Oct 2010, 23:50
Merging topics ...

Please try using the forum search feature ... You should be able to find answers to a lot of questions which have been asked before
_________________

Math write-ups
1) Algebra-101 2) Sequences 3) Set combinatorics 4) 3-D geometry

My GMAT story

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Expert Post
4 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23534
Followers: 3483

Kudos [?]: 26092 [4] , given: 2705

Re: ps question [#permalink] New post 19 Oct 2010, 13:02
4
This post received
KUDOS
Expert's post
satishreddy wrote:
if each term in the sum of a1+a2+...................+an is either 7 or 77 and the sum equals to 350, which of the following could be equal to n?

38
39
40
41
42


Alternate solutions from: tough-ps-problem-please-help-100812.html?hilit=term%20equal%20either#p779175

Number of approaches are possible.

For example: as units digit of 350 is zero then # of terms must be multiple of 10. Only answer choice which is multiple of 10 is C (40).

To illustrate consider adding:

*7
*7
...
77
77
----
=350

So, several 7's and several 77's, note that the # of rows equals to the # of terms. Now, to get 0 for the units digit of the sum the # of rows (# of terms) must be multiple of 10. Only answer choice which is multiple of 10 is C (40).

Answer: C.

Or:
7x+77y=350, where x is # of 7's and y is # of 77's, so # of terms n equals to x+y;

7(x+11y)=350 --> x+11y=50 --> now, if x=39 and y=1 then n=x+y=40 and we have this number in answer choices.

Answer: C.

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

6 KUDOS received
Director
Director
User avatar
Status: GMAT Learner
Joined: 14 Jul 2010
Posts: 652
Followers: 34

Kudos [?]: 229 [6] , given: 32

GMAT Tests User
Re: 7,77....Problem Solving [#permalink] New post 27 Jun 2011, 21:26
6
This post received
KUDOS
Since, there is no 50 in the answer choices (350/7 = 50), we know there is at least one 77.

350 - 77 = 273
273/7 = 39
39+1 = 40.

If 40 wasn't there, I would have subtracted 77 from 273 and continued in a similar way.
Ans. C
_________________

I am student of everyone-baten
Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

Intern
Intern
avatar
Joined: 06 Dec 2009
Posts: 3
Followers: 0

Kudos [?]: 0 [0], given: 1

Re: 7,77....Problem Solving [#permalink] New post 28 Jun 2011, 08:51
laxieqv wrote:
lhotseface wrote:
If each term in the sum a1 + a2 + a3.....+ an is either 7 or 77 and the sum is 350, What is n ?

Note: a1,a2 represent the first term,second...and NOT a*1, a*2 !


A. 38
B. 39
C. 40
D. 41
E. 42


Let x and y be the number of term 7 and the number of term 77 respectively. WE have :
7x+ 77y= 350 ---> x+11y = 50 ---> x+y= 50- 10y
we have : x+y= n = 50- 10y ---> n must have the unit digit of 0 because 50 - 10y must be a number which has unit digit of 0

Among the answer choices provided, only C matches.

I go for C.



+1 Kudos to you laxieqv !!
Director
Director
avatar
Joined: 01 Feb 2011
Posts: 770
Followers: 14

Kudos [?]: 82 [0], given: 42

GMAT Tests User
Re: 7,77....Problem Solving [#permalink] New post 29 Jun 2011, 16:15
x+11y = 50

x+y = n = verifying this with answer choices and checking for integer value for y, we can find out x+y = 40.

Answer is C.
Intern
Intern
avatar
Joined: 14 Apr 2011
Posts: 21
Followers: 0

Kudos [?]: 1 [0], given: 0

Re: 7,77....Problem Solving [#permalink] New post 29 Jun 2011, 16:29
laxieqv wrote:
lhotseface wrote:
If each term in the sum a1 + a2 + a3.....+ an is either 7 or 77 and the sum is 350, What is n ?

Note: a1,a2 represent the first term,second...and NOT a*1, a*2 !


A. 38
B. 39
C. 40
D. 41
E. 42


Let x and y be the number of term 7 and the number of term 77 respectively. WE have :
7x+ 77y= 350 ---> x+11y = 50 ---> x+y= 50- 10y
we have : x+y= n = 50- 10y ---> n must have the unit digit of 0 because 50 - 10y must be a number which has unit digit of 0

Among the answer choices provided, only C matches.

I go for C.



I like this method because it attacks the the question dead on by representing each term as x and y and then deductively finding the answer through POE. Hope I can think this quickly on the exam!
Manager
Manager
User avatar
Joined: 05 Jan 2010
Posts: 76
Concentration: Finance, Real Estate
WE: Asset Management (Real Estate)
Followers: 1

Kudos [?]: 12 [0], given: 9

Re: 7,77....Problem Solving [#permalink] New post 28 Jul 2011, 11:57
I used a different method altogether. I observed that since all the numbers are 7s, the total number of sevens has to be a multiple of 5 in order to get to 350. out of the answer choices, only 40 is a multiple of 5, So eliminate everything but choice C. I guess, if there were other multiples of 5 then you could use one of the methods above. But as a quick elimination strategy it helped to do the least amount of work.
Intern
Intern
avatar
Joined: 27 Feb 2011
Posts: 48
Followers: 0

Kudos [?]: 2 [0], given: 9

Re: 7,77....Problem Solving [#permalink] New post 28 Jul 2011, 12:03
Substitution ..

it will take 50 7s to get 350 .. options are less than 50 .. so there should be atleast one 77.. 77/7 = 11 ..

so 39 7s + one 77 = 40
1 KUDOS received
Manager
Manager
avatar
Joined: 29 Apr 2010
Posts: 79
Followers: 1

Kudos [?]: 11 [1] , given: 1

Re: 7,77....Problem Solving [#permalink] New post 29 Jul 2011, 12:43
1
This post received
KUDOS
C it is..
350 = 7x+77y
x+11y=50

x y
39 1 =40
28 2
17 3
6 4

40 fits into our answer choice.


lhotseface wrote:
If each term in the sum a1 + a2 + a3.....+ an is either 7 or 77 and the sum is 350, What is n ?

Note: a1,a2 represent the first term,second...and NOT a*1, a*2 !


A. 38
B. 39
C. 40
D. 41
E. 42
Manager
Manager
User avatar
Status: On...
Joined: 16 Jan 2011
Posts: 189
Followers: 3

Kudos [?]: 35 [0], given: 62

GMAT Tests User
Re: 7,77....Problem Solving [#permalink] New post 30 Jul 2011, 20:58
+1 C
7(50)=350
Since 50 is not there in ANSWERS
so 77 needs to be ther
77=7(11)
So :
number of terms if one 77 is there 50-11+1=50-10=40 --> Check the Ans. C matches..
_________________

Labor cost for typing this post >= Labor cost for pushing the Kudos Button
kudos-what-are-they-and-why-we-have-them-94812.html

Manager
Manager
User avatar
Status: On...
Joined: 16 Jan 2011
Posts: 189
Followers: 3

Kudos [?]: 35 [0], given: 62

GMAT Tests User
Re: 7,77....Problem Solving [#permalink] New post 30 Jul 2011, 21:06
A beautiful variant of this problem -
If each term in the sum a1 + a2 + a3.....+ an is either 7 or 77 and the sum is 350

Note: a1,a2 represent the first term,second...and NOT a*1, a*2 !
n has a value of :
I. 30
II. 45
III. 10
IV. 50
V. 25

Which of the following can be True ?
A - I,II,III
B - II,III,V
C - I,III,IV
D - All
C - None

Apply the same concepts and you can figure out the solution
_________________

Labor cost for typing this post >= Labor cost for pushing the Kudos Button
kudos-what-are-they-and-why-we-have-them-94812.html

SVP
SVP
User avatar
Joined: 09 Sep 2013
Posts: 2378
Followers: 194

Kudos [?]: 38 [0], given: 0

Premium Member
Re: If each term in the sum a1 + a2 + a3.....+ an is either 7 or [#permalink] New post 30 Oct 2013, 03:23
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23534
Followers: 3483

Kudos [?]: 26092 [0], given: 2705

Re: If each term in the sum a1+a2+a3+.....+an is either 7 or 77 [#permalink] New post 30 Oct 2013, 06:49
Expert's post
Re: If each term in the sum a1+a2+a3+.....+an is either 7 or 77   [#permalink] 30 Oct 2013, 06:49
    Similar topics Author Replies Last post
Similar
Topics:
3 Experts publish their posts in the topic If each term in the sum a1+a2+a3+.....+an is either 7 or 77 DSGB 9 10 Sep 2010, 11:02
24 Experts publish their posts in the topic If each term in the sum a1+a2+a3+...+an is either 7 or 77 LM 22 10 May 2010, 08:36
4 Experts publish their posts in the topic If the infinite sequence a1, a2, a3, ..., an, ..., each term alimad 7 16 May 2008, 02:50
Experts publish their posts in the topic In the infinite sequence a1, a2, a3.....an, each term after inwosu 4 04 Jan 2008, 04:07
3/ If each term in the sum a1 + a2 + a3 +....+an is either 7 yezz 5 15 Oct 2006, 08:53
Display posts from previous: Sort by

If each term in the sum a1+a2+a3+.....+an is either 7 or 77

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.