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

 It is currently 27 Jun 2016, 16:09

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

VP
Joined: 20 Sep 2005
Posts: 1021
Followers: 3

Kudos [?]: 33 [1] , given: 0

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

### Show Tags

22 Mar 2006, 23:07
1
KUDOS
8
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

67% (01:58) correct 33% (01:05) wrong based on 329 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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, 07:48, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
SVP
Joined: 05 Apr 2005
Posts: 1731
Followers: 5

Kudos [?]: 58 [4] , given: 0

### Show Tags

22 Mar 2006, 23:27
4
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.
SVP
Joined: 14 Dec 2004
Posts: 1702
Followers: 2

Kudos [?]: 94 [3] , given: 0

### Show Tags

22 Mar 2006, 23:35
3
KUDOS
1
This post was
BOOKMARKED
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.
SVP
Joined: 24 Sep 2005
Posts: 1890
Followers: 17

Kudos [?]: 228 [11] , given: 0

### Show Tags

23 Mar 2006, 03:58
11
KUDOS
2
This post was
BOOKMARKED
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
Joined: 14 Dec 2004
Posts: 1702
Followers: 2

Kudos [?]: 94 [0], given: 0

### Show Tags

23 Mar 2006, 05:24
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
Joined: 05 Apr 2005
Posts: 1731
Followers: 5

Kudos [?]: 58 [0], given: 0

### Show Tags

23 Mar 2006, 07:33
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.
Current Student
Joined: 29 Jan 2005
Posts: 5239
Followers: 23

Kudos [?]: 293 [0], given: 0

### Show Tags

25 Mar 2006, 22:52
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
Joined: 02 Sep 2010
Posts: 805
Location: London
Followers: 99

Kudos [?]: 807 [0], given: 25

### Show Tags

19 Oct 2010, 00:50
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 Expert
Joined: 02 Sep 2009
Posts: 33528
Followers: 5938

Kudos [?]: 73635 [3] , given: 9903

### Show Tags

19 Oct 2010, 14:02
3
KUDOS
Expert's post
3
This post was
BOOKMARKED
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

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).

*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).

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.

Hope it helps.
_________________
Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 650
Followers: 37

Kudos [?]: 659 [7] , given: 39

### Show Tags

27 Jun 2011, 22:26
7
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
_________________

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
Joined: 06 Dec 2009
Posts: 3
Followers: 0

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

### Show Tags

28 Jun 2011, 09:51
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
Joined: 01 Feb 2011
Posts: 757
Followers: 14

Kudos [?]: 95 [0], given: 42

### Show Tags

29 Jun 2011, 17:15
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.

Intern
Joined: 14 Apr 2011
Posts: 21
Followers: 0

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

### Show Tags

29 Jun 2011, 17:29
1
This post was
BOOKMARKED
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
Joined: 05 Jan 2010
Posts: 76
Concentration: Finance, Real Estate
WE: Asset Management (Real Estate)
Followers: 1

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

### Show Tags

28 Jul 2011, 12:57
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
Joined: 27 Feb 2011
Posts: 48
Followers: 0

Kudos [?]: 3 [0], given: 9

### Show Tags

28 Jul 2011, 13:03
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
Manager
Joined: 30 Apr 2010
Posts: 77
Followers: 1

Kudos [?]: 47 [1] , given: 1

### Show Tags

29 Jul 2011, 13:43
1
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
Status: On...
Joined: 16 Jan 2011
Posts: 189
Followers: 3

Kudos [?]: 54 [0], given: 62

### Show Tags

30 Jul 2011, 21:58
+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
Status: On...
Joined: 16 Jan 2011
Posts: 189
Followers: 3

Kudos [?]: 54 [0], given: 62

### Show Tags

30 Jul 2011, 22:06
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

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 10214
Followers: 481

Kudos [?]: 124 [0], given: 0

Re: If each term in the sum a1 + a2 + a3.....+ an is either 7 or [#permalink]

### Show Tags

30 Oct 2013, 04:23
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.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 33528
Followers: 5938

Kudos [?]: 73635 [0], given: 9903

Re: If each term in the sum a1+a2+a3+.....+an is either 7 or 77 [#permalink]

### Show Tags

30 Oct 2013, 07:49
Expert's post
OPEN DISCUSSION OF THIS QUESTION IS HERE: if-each-term-in-the-sum-a1-a2-a3-an-is-either-7-or-93974.html
_________________
Re: If each term in the sum a1+a2+a3+.....+an is either 7 or 77   [#permalink] 30 Oct 2013, 07:49
Similar topics Replies Last post
Similar
Topics:
8 If the infinite sequence a1, a2, a3, ..., an, ..., each term 8 18 Jun 2012, 01:24
4 If each term in the sum a1+a2+a3+.....+an is either 7 or 77 9 10 Sep 2010, 12:02
110 If each term in the sum a1+a2+a3+...+an is either 7 or 77 30 10 May 2010, 09:36
8 In the infinite sequence a1, a2, a3, ..., an, each term after the firs 5 21 Apr 2010, 06:49
4 If the infinite sequence a1, a2, a3, ..., an, ..., each term 7 16 May 2008, 03:50
Display posts from previous: Sort by