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

 It is currently 07 Feb 2016, 20:22

### 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:
Director
Joined: 03 Sep 2006
Posts: 878
Followers: 6

Kudos [?]: 471 [4] , given: 33

If each term in the sum a1+a2+a3+...+an is either 7 or 77 [#permalink]  10 May 2010, 08:36
4
KUDOS
28
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

70% (02:18) correct 30% (01:33) wrong based on 985 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
[Reveal] Spoiler: OA
Intern
Joined: 10 May 2010
Posts: 11
Followers: 1

Kudos [?]: 9 [6] , given: 1

Re: PS3 [#permalink]  10 May 2010, 18:41
6
KUDOS
3
This post was
BOOKMARKED
7x + 77(n-x) = 350 --> where x is the number of times 7 repeats
7x + 7(11)(n-x) = 350
dividing both sides by 7
x + 11 (n-x) = 50

trying different options

now (n-x) has to be 1 because if its more than 1 (ex. 2) then 11(n-x) = 22 and x will be 37 or more which takes the total beyond 50.

Therefore now trying options we get

38 --> 37 + 11(1) = 48
39 --> 38 + 11(1) = 49
40 --> 39 + 11(1) = 50 ... this is the right answer
Director
Joined: 23 Apr 2010
Posts: 583
Followers: 2

Kudos [?]: 49 [0], given: 7

Re: PS3 [#permalink]  26 Dec 2010, 01:29
Can I ask someone to take a look at it as I don't understand the solutions provided (or rather I don't understand how they came up with the solutions)? Thanks.
Math Expert
Joined: 02 Sep 2009
Posts: 31286
Followers: 5345

Kudos [?]: 62128 [26] , given: 9440

Re: PS3 [#permalink]  26 Dec 2010, 01:36
26
KUDOS
Expert's post
17
This post was
BOOKMARKED
nonameee wrote:
Can I ask someone to take a look at it as I don't understand the solutions provided (or rather I don't understand how they came up with the solutions)? 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

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
Joined: 23 Apr 2010
Posts: 583
Followers: 2

Kudos [?]: 49 [0], given: 7

Re: PS3 [#permalink]  26 Dec 2010, 02:25
Thank you, Bunuel. Your first solution is a good one (the second one is rather non-deterministic for me).
Director
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 538
Location: United Kingdom
GMAT 1: 730 Q49 V40
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 49

Kudos [?]: 1842 [0], given: 217

Re: If each term in the sum a1+a2+a3+...+an is either 7 or 77 [#permalink]  13 Jan 2012, 22:35
Thanks Bunuel for both the solutions. Very much appreciated.
_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

Current Student
Joined: 03 Sep 2012
Posts: 339
Location: United States
Concentration: Healthcare, Strategy
GMAT 1: 730 Q48 V42
GPA: 3.88
WE: Medicine and Health (Health Care)
Followers: 13

Kudos [?]: 136 [0], given: 31

If each term in the sum a1+a2+a3+.....+an is either 7 or 77 and [#permalink]  28 Sep 2012, 04:51
I used the answer choices to figure this one out ...

Given that we have 77 and 7 , therefore out of all the options we can get exactly 40 options that will yield 350 if we use 7 , 39 times and 77 ones ... 7 x 39 = 273 , adding 77 we get 350..

It took me about two and half minutes to do this by testing each answer out ..
_________________

"When you want to succeed as bad as you want to breathe, then you’ll be successful.” - Eric Thomas

Senior Manager
Joined: 28 Aug 2006
Posts: 304
Followers: 12

Kudos [?]: 118 [8] , given: 0

Re: If each term in the sum a1+a2+a3+...+an is either 7 or 77 [#permalink]  30 Sep 2012, 05:33
8
KUDOS
1
This post was
BOOKMARKED
LM wrote:
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

This is as good as saying all the numbers are either 1 or 11 and the sum equals 50
Let 1s be x and 11s be y, thus making n = x+y
x + 11y = 50
(x+y)+10y = 50
x+y = 10(5-y)
Hence x+y must be a multiple of 10 i.e. n must be multiple of 10. Only choice C

In case if the question asks the possible values of n, we can conclude that n could be 10,20,30,40,50
_________________
Current Student
Joined: 01 Jun 2012
Posts: 21
Location: United States
Concentration: Nonprofit
GMAT 1: 720 Q48 V43
GPA: 3.83
Followers: 0

Kudos [?]: 8 [0], given: 15

Re: PS3 [#permalink]  04 Nov 2012, 12:02
Bunuel wrote:
nonameee wrote:
Can I ask someone to take a look at it as I don't understand the solutions provided (or rather I don't understand how they came up with the solutions)? 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

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.

Hi Bunuel,

Thanks for all your help, as usual. I answered the question using the second approach but would love to understand the first approach better. I must be missing something simple, but could you further explain why the number off terms must be a multiple of 10 to get a "0" in the units digit? That statement is tripping me up.
Math Expert
Joined: 02 Sep 2009
Posts: 31286
Followers: 5345

Kudos [?]: 62128 [3] , given: 9440

Re: PS3 [#permalink]  06 Nov 2012, 02:03
3
KUDOS
Expert's post
egiles wrote:
Hi Bunuel,

Thanks for all your help, as usual. I answered the question using the second approach but would love to understand the first approach better. I must be missing something simple, but could you further explain why the number off terms must be a multiple of 10 to get a "0" in the units digit? That statement is tripping me up.

Consider this 7+7+7+7+7+7+7+7+7+7=10*7=70 (the sum of ten 7's equals to 10 times that term).

Hope it helps.
_________________
Intern
Joined: 20 Jan 2013
Posts: 40
Location: India
Concentration: Finance, Entrepreneurship
GMAT Date: 03-14-2014
GPA: 3.42
Followers: 0

Kudos [?]: 5 [0], given: 67

Re: If each term in the sum a1 + a2 + a3 + ... +an is either 7 [#permalink]  04 Feb 2014, 11:35
7(1+1 + ... 11+11+.. n terms)=350
1+1 + ... 11+11+.. n terms=50
try out various combinations.
Like 11*4+6 (10 terms)
The options are bigger numbers. So you decrease 11's and increase 1's.
11*1+39 (40 terms) which is our answer.
Hope it helped..
_________________

collection-of-the-best-gmat-resources-167295.html#p1329720

May we all emerge victorious

Intern
Joined: 01 Apr 2013
Posts: 1
Followers: 0

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

Re: If each term in the sum a1+a2+a3+...+an is either 7 or 77 [#permalink]  06 Feb 2014, 03:19
LM wrote:
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

let us suppose there are all 7's then there must be 50 7's for the sum to be 350 . but it is not one of the answer choices .
so let us suppose there is one 77 so there must be 39 7's => total terms 40 which is answer choice c.
Intern
Joined: 01 Aug 2006
Posts: 35
Followers: 0

Kudos [?]: 22 [0], given: 0

Re: If each term in the sum a1+a2+a3+...+an is either 7 or 77 [#permalink]  07 Feb 2014, 16:33
77 is the equivalent of eleven 7s.
Look at answer choices. Clearly, the number of 7s should be much more than 77s.
Take choice 1: 38. If there are 37 7s and 1 77, we get 37*7 + 77 = 336.
To get 350, we need 2 more 7s.
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1854
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 31

Kudos [?]: 1355 [1] , given: 193

Re: If each term in the sum a1+a2+a3+...+an is either 7 or 77 [#permalink]  07 Mar 2014, 01:49
1
KUDOS
$$\frac{350}{7} = 50$$;

As all the options are below 50, there should be atleast one 77 present

To add one 77, we require to remove eleven 7's (7 x 11)

50 - 11 + 1 = 40 = Answer = C

If 40 wasn't there, then again same method:

40 - 11 + 1 = 30
_________________

Kindly press "+1 Kudos" to appreciate

Intern
Joined: 29 Dec 2013
Posts: 10
Followers: 0

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

Re: If each term in the sum a1+a2+a3+...+an is either 7 or 77 [#permalink]  26 Mar 2014, 19:00
Thank you so much Brunel. This is such a simple question but my mind went blank when I was trying to attempt in the practice test! After the test got over, I used the same approach as approach1. It was so simple! Damn
Manager
Joined: 20 Dec 2013
Posts: 125
Followers: 6

Kudos [?]: 76 [0], given: 1

Re: If each term in the sum a1+a2+a3+...+an is either 7 or 77 [#permalink]  26 Mar 2014, 20:44
LM wrote:
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

We will start with the bigger numbers. There can be maximum of 50 Sevens and one 77 will replace 11 Sevens.

For there to be 50 terms: there will be One 77 (11 sevens) and 39 sevens. Hence 39 + 11 = 50 sevens.

Intern
Joined: 04 Jul 2013
Posts: 39
Schools: ISB '16
Followers: 0

Kudos [?]: 11 [3] , given: 26

Re: If each term in the sum a1+a2+a3+...+an is either 7 or 77 [#permalink]  17 Apr 2014, 00:28
3
KUDOS
350= 7a + 77b (a= no of 7s & b = no of 77s)

If b=0 then a=50
If a=0 then b=4 (+some remainder)

both these answers are not in the options.And looking at the options and above range we can conclude that the sum contains atleast 1 term as 77

put b=1,

350= 7a + 77(1)
350 - 77 = 7a

50-11 = a

a=39

a+b = 39+1 = 40 which is in the options

hence C
Intern
Joined: 17 Jul 2013
Posts: 39
Location: India
WE: Information Technology (Health Care)
Followers: 0

Kudos [?]: 7 [0], given: 183

Re: If each term in the sum a1+a2+a3+...+an is either 7 or 77 [#permalink]  12 Jun 2014, 06:43
I think we can frame another question out of this one..

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 the minimum value of n?

A)10 b) 20 c) 30 d)40 e) 50
_________________

I'm on 680... 20 days to reach 700 +

Intern
Joined: 08 Jun 2014
Posts: 3
Followers: 0

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

Re: If each term in the sum a1+a2+a3+...+an is either 7 or 77 [#permalink]  13 Jun 2014, 03:21
Well, I tried it the following way:

a series of 7's and 77's would add up to 350.
So only 1 77 should be enough and rest 7's.
350 -77 - 273
273/9 = 39

So 39 * 7 + 1 * 77 = 350

Senior Manager
Joined: 15 Aug 2013
Posts: 328
Followers: 0

Kudos [?]: 34 [0], given: 23

Re: If each term in the sum a1+a2+a3+...+an is either 7 or 77 [#permalink]  21 Jun 2014, 12:12
Bunuel wrote:
nonameee wrote:
Can I ask someone to take a look at it as I don't understand the solutions provided (or rather I don't understand how they came up with the solutions)? 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

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.

Hi Bunuel,

I noticed that you tried to clarify method 1 below but still not connecting.

How are you drawing the conclusion that it has to be a multiple of 10? Why can't it be 2*175 which is NOT a multiple of 10 or 1*350 etc?

Thanks!
Re: If each term in the sum a1+a2+a3+...+an is either 7 or 77   [#permalink] 21 Jun 2014, 12:12

Go to page    1   2    Next  [ 31 posts ]

Similar topics Replies Last post
Similar
Topics:
2 In the sequence a1,a2,a3...an, each term an is defined as an 3 25 Aug 2014, 11:01
4 If each term in the sum a1+a2+a3+.....+an is either 7 or 77 9 10 Sep 2010, 11:02
7 In the infinite sequence a1, a2, a3, ..., an, each term after the firs 5 21 Apr 2010, 05:49
4 If the infinite sequence a1, a2, a3, ..., an, ..., each term 7 16 May 2008, 02:50
40 If each term in the sum a1+a2+a3+.....+an is either 7 or 77 19 22 Mar 2006, 22:07
Display posts from previous: Sort by