It is currently 26 Jun 2017, 14:23

### 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

# Events & Promotions

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

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

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

### Hide Tags

Intern
Joined: 06 Sep 2010
Posts: 17
Schools: HBS
WE 1: Management Consulting- 2 years
WE 2: Private Equity- 2 years
If each term in the sum a1+a2+a3+.....+an is either 7 or 77 [#permalink]

### Show Tags

10 Sep 2010, 12:02
4
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

78% (01:50) correct 22% (01:33) wrong based on 105 sessions

### HideShow timer Statistics

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 08 Nov 2012, 03:31, edited 2 times in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 39702
Re: Tough PS problem- please help! [#permalink]

### Show Tags

10 Sep 2010, 12:15
1
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
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

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.
_________________
Senior Manager
Joined: 20 Jul 2010
Posts: 263
Re: Tough PS problem- please help! [#permalink]

### Show Tags

11 Sep 2010, 08:05
Nice explanation. I was clueless after reading question and was not able to decide on how to create the equation. I like first deduction which needs some presence of mind
_________________

If you like my post, consider giving me some KUDOS !!!!! Like you I need them

Retired Moderator
Joined: 02 Sep 2010
Posts: 803
Location: London
Re: Tough PS problem- please help! [#permalink]

### Show Tags

11 Sep 2010, 08:16
Same concept alternate solution

Let the number of 77's be X, we know $$X>=0$$

$$7*(n-X) + 77*X = 350$$
$$7*(n-X) + 7*X + 70*X = 350$$
$$7*n + 70*X = 350$$

Since $$X>=0$$, $$X$$ can be $$0,1,2,3,4,5$$ .... Correspondingly the value of n would be $$50,40,30,20,10,0$$ (always a multiple of 10)

So the answer in this case is 40.
_________________
Joined: 31 Dec 1969
Location: Russian Federation
Concentration: Entrepreneurship, International Business
GMAT 3: 740 Q40 V50
GMAT 4: 700 Q48 V38
GMAT 5: 710 Q45 V41
GMAT 6: 680 Q47 V36
GMAT 9: 740 Q49 V42
GMAT 11: 500 Q47 V33
GMAT 14: 760 Q49 V44
WE: Supply Chain Management (Energy and Utilities)
Re: Tough PS problem- please help! [#permalink]

### Show Tags

11 Sep 2010, 21:23
1
This post received
KUDOS
Let a be the no. of 7s & b be the no. of 77s

7*a+77*b=350
a+11b=50

So, possible values for (a,b) are (39,1);(28,2);(17,3);(6,4)
The no. of terms is (a+b) so, no. of terms can be (40,30,20,10)

After comparing with the given options, 40 is the answer.
Manager
Joined: 08 Sep 2010
Posts: 226
Location: India
WE 1: 6 Year, Telecom(GSM)
Re: ps question [#permalink]

### Show Tags

19 Oct 2010, 03:05
1
This post received
KUDOS
satishreddy wrote:
in each in the sum 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

Let the number of terms having value 7 is x ,and the number of terms having value 77 is y.

Now according to question,

7x+77y=350
or, 7x + 11*7 y =350
or, 7(x+11y) =350
or x+11y = 50

If y =1 and x = 39 , x+11y=50 (this is the only case we can take otherwise in all other case (x+y) will be less than or equal to 29 and their is no option in answer which is having less than 29 value.

Hence answer is x+y=40 i.e D.

Consider KUDOS if it helped u in some way.
Retired Moderator
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 1657
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs
in the sum a1 + a2 + a3 + ... + an [#permalink]

### Show Tags

22 Dec 2010, 22:20
Is there an algebraic way to solve this question rather than picking numbers? Thanks!

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
_________________

"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."

My Integrated Reasoning Logbook / Diary: http://gmatclub.com/forum/my-ir-logbook-diary-133264.html

GMAT Club Premium Membership - big benefits and savings

Intern
Joined: 01 Jun 2010
Posts: 4
Re: Tough PS problem- please help! [#permalink]

### Show Tags

23 Dec 2010, 01:43
thanks metallicafan for you supportive help.
Retired Moderator
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 1657
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs
Re: Tough PS problem- please help! [#permalink]

### Show Tags

28 Dec 2010, 12:25
Hi Bunuel,

Could you provide links to more problems like this?
Thanks!
_________________

"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."

My Integrated Reasoning Logbook / Diary: http://gmatclub.com/forum/my-ir-logbook-diary-133264.html

GMAT Club Premium Membership - big benefits and savings

Intern
Joined: 02 Nov 2012
Posts: 35
Re: Tough PS problem- please help! [#permalink]

### Show Tags

07 Nov 2012, 16:40
You know that there have to be a lot of 7ns in the answer, because the answer choices are significant. You also know that 350 = 50*7 however this is not an answer choice. But this is the key to the answer 350 - 11*7 or 77 = 39*7 so the answer has to be 39*7 and 1*77 40!
Re: Tough PS problem- please help!   [#permalink] 07 Nov 2012, 16:40
Similar topics Replies Last post
Similar
Topics:
2 If each term in the sum a1+a2+a3+...+an 5 15 Dec 2016, 02:52
175 If each term in the sum a1+a2+a3+...+an is either 7 or 77 34 12 Feb 2017, 08:12
9 In the infinite sequence a1, a2, a3, ..., an, each term after the firs 7 12 Jun 2017, 19:19
3 If each term in the sum a1+a2+a3+...+an is either 7 or 77 13 24 Jul 2016, 02:08
4 If the infinite sequence a1, a2, a3, ..., an, ..., each term 7 25 Mar 2014, 08:46
Display posts from previous: Sort by

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

 post reply Question banks Downloads My Bookmarks Reviews Important topics

 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®.