GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 23 Jun 2018, 20:42

### 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

Intern
Joined: 05 Mar 2014
Posts: 4
Re: If each term in the sum a1+a2+a3+...+an is either 7 or 77 [#permalink]

### Show Tags

28 Sep 2014, 09:22
Hi Bunel,

In a hurry I tried to solve it by Arithmetic progression method.

(7+7) x n/2 = 350 i got n = 50 here..

(also i did tried some few like: (7 +77) x n/2 = 350 and (77+77) x n/2 = 350. )

Am I totally wrong as I approached it by Arithmetic progression method
Manager
Status: Please do not forget to give kudos if you like my post
Joined: 19 Sep 2008
Posts: 107
Location: United States (CA)
Re: If each term in the sum a1+a2+a3+...+an is either 7 or 77 [#permalink]

### Show Tags

29 Nov 2014, 14:44
fastest way to solve this IMHO:

350 = 7x50 that mean the sum of term should be 50 if 7 is factored out == 7 (a1+a2+...+an) this can happen if and only if its a factors are multiple of 10 and only C works.

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

_________________

Manager
Joined: 20 Feb 2013
Posts: 76
Location: India
GMAT 1: 690 Q49 V34
WE: Information Technology (Computer Software)
Re: If each term in the sum a1+a2+a3+...+an is either 7 or 77 [#permalink]

### Show Tags

19 Dec 2014, 10:25
Started with Algebraic way:
7x + 77(n-x)=350
x + 11(n-x)=50 --> this can give multiple solutions like x=6, n=10 or x=17, n=20 ...

Observe all solutions leading to n = multiples of 10. Only Option C (40) is a multiple of 10.
_________________

If my post is helpful/correct, consider giving Kudos..

Intern
Joined: 18 Apr 2011
Posts: 43
Location: United States
WE: Information Technology (Computer Software)
Re: If each term in the sum a1+a2+a3+...+an is either 7 or 77 [#permalink]

### Show Tags

21 Mar 2015, 05:43
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

You can look at it this way also -
cyclicity of 7:
$$7^1 = 7$$
$$7^2 = 9(last digit)$$
$$7^3 = 3(last digit)$$
$$7^4 = 1(last digit)$$

Sum of the last digits ends with = ..0

so the answer choices must match the $$4*n + 4$$ figure, only 40 matches, hence C.
Intern
Joined: 07 Jul 2015
Posts: 1
Re: If each term in the sum a1+a2+a3+...+an is either 7 or 77 [#permalink]

### Show Tags

09 Sep 2015, 04:39
I took a while to figure this out on my own but here is how I approached this problem:

Since the answer choices were all over 35, there is a very slight possibility that there will be more than 1 multiple of 77.,
Therefore I subtracted 77 (multiple of 7) from 350 (multiple of 7) to get 273 (multiple of 7). Divided 273 by 7 to get 39. Getting 40 as the answer. 39*7 + 1*77 = 350.
Intern
Joined: 17 Aug 2015
Posts: 7
Re: If each term in the sum a1+a2+a3+...+an is either 7 or 77 [#permalink]

### Show Tags

27 Sep 2015, 02:23
paranoidvik
The minimum N would be A) 10.

4*77+ 6*7= 350
VP
Status: It's near - I can see.
Joined: 13 Apr 2013
Posts: 1057
Location: India
GMAT 1: 480 Q38 V22
GPA: 3.01
WE: Engineering (Consulting)
Re: If each term in the sum a1+a2+a3+...+an is either 7 or 77 [#permalink]

### Show Tags

10 Oct 2015, 00:31
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

My Solution:

Consider if we have only 7's then 350 must have 50 number of 7's i.e 350/7=50

But we know we have some 77's too.

Say we have only one "77".

Then one 77 has 7+7+7+7+7+7+7+7+7+7+7 i.e 11 numbers of "7's".

So to accommodate one 77 we must subtract 11 number of 7's.

So we have 50-11=39 number of 7's and 01 number of 77 i.e 39+1=40 Answer C

_________________

"Success is not as glamorous as people tell you. It's a lot of hours spent in the darkness."

Intern
Joined: 21 Dec 2014
Posts: 31
GMAT 1: 710 Q49 V37
Re: If each term in the sum a1+a2+a3+...+an is either 7 or 77 [#permalink]

### Show Tags

19 Oct 2015, 22:47
350=40*7+10*7=39*7+77.
Because a1 to an is either 7 or 77. Therefore, n can be40.

C
Intern
Joined: 09 Oct 2015
Posts: 44
If each term in the sum a1+a2+a3+...+an is either 7 or 77 [#permalink]

### Show Tags

04 Aug 2016, 22:16
Hi All,

Trying to solve the problem by using just one more variable in addition to 'n' which is already a part of the question stem.

Total number of terms: n
Now lets assume the number of terms of 7's and 77's:
7's : x
77's : (n-x)

using the information in the question, we get the following statement:

7(x) + 77( n-x) = 350
7x + 77n - 77x = 350
77n - 70x= 350
7(11n-10x)= 350

11n-10x = 50

Even though plugging in the values will not take too much time, however I suggest we try to understand the statement we just derived:

After subtracting the two values, we should have a '0' in the units place ( 50). To get a '0' we need the units place values of both the terms ( 11n and 10x) to be the same.

10x : this term will always have a '0' in the units place irrespective of the value of x --> this means 11n should have a '0' as well and which is possible is 'n' is a multiple of 10.

40--> multiple of 10.

Hope this helps!

Regards,
SVP
Joined: 08 Jul 2010
Posts: 2115
Location: India
GMAT: INSIGHT
WE: Education (Education)
Re: If each term in the sum a1+a2+a3+...+an is either 7 or 77 [#permalink]

### Show Tags

23 Aug 2016, 21:27
LM wrote:
If each term in the sum $$a_1+a_2+a_3+...+a_n$$ 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

Check the solution in attachment
Attachments

File comment: www.GMATinsight.com

SOl3.jpg [ 100.56 KiB | Viewed 1122 times ]

_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Intern
Joined: 22 Jul 2016
Posts: 24
If each term in the sum a1+a2+a3+...+an is either 7 or 77 [#permalink]

### Show Tags

08 Jan 2017, 08:52
I came up with solution using PoE:

let , number of occurrences of 7 is x ,
number of occurrences of 77 is y ,
total number of terms is n

7x+77y=350 >> x=50-11y -----(1)

we have , x+y=n

substituting value of x from (1)
50-11y+y=n
50-10y=n
As we are subtracting a multiple of 10 from 50
i.e. a number ending with 0 is being subtracted from two digit number ending with 0
Hence , the result should also end with 0

We only have answer choice (C) with such value i.e. 40

Ans : C
Intern
Joined: 19 Sep 2012
Posts: 13
Re: If each term in the sum a1+a2+a3+...+an is either 7 or 77 [#permalink]

### Show Tags

12 Feb 2017, 08:12
I have found the following approach more direct and less time-comsuming:
7(n-x) + 77x = 350
7n-7x+77x = 350
7(n+10x)=350
n+10x=50
n=50-10x
If x=1, then n=50-10=40 (The right option)
If x=2, then n=50-20=30
If x=3, then n=50-30=20
If x=4, then n=50-40=10

Am I missing something?
Intern
Joined: 27 Dec 2016
Posts: 14
Re: If each term in the sum a1+a2+a3+...+an is either 7 or 77 [#permalink]

### Show Tags

02 Jul 2017, 22:53
I solved it a bit differently.
total number of 7's and 77s = 350
Looking at answer choices we can ensure that total number of 7's must be greater than 77's to achieve the range from 38 to 42.
Here is next math part:
350 - 77=273.
273/7 = 39
39 (7s)+1 (77) = 40
Manager
Joined: 16 Jan 2011
Posts: 102
Re: If each term in the sum a1+a2+a3+...+an is either 7 or 77 [#permalink]

### Show Tags

02 Sep 2017, 11:43
From the question stem we know that
a) x+y=n
b) 77x+7y=350 --> 11x+y=50

So, combining these two equations (system of equations) we will get 10x=50-n.

Only C satisfies the equation, since C (e.g.40) is the only answer choice, which has the units digit of 0.
Re: If each term in the sum a1+a2+a3+...+an is either 7 or 77   [#permalink] 02 Sep 2017, 11:43

Go to page   Previous    1   2   [ 34 posts ]

Display posts from previous: Sort by