If each term in the sum a1 + a2 + ..... + an is either 7 or 77 and the sum equals 350, which of the following could be equal to n?
1. 38
2. 39
3. 40
4. 41
5. 42
Sum of the numbers
This topic has expert replies
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
7*50 = 350.If each term in the sum a1+a1+a3+a4+...+aN is either 7 or 77 and the sum equals 350, which of the following could be equal to n?
1) 38
2) 39
3) 40
4) 41
5) 42
Thus, if each term is 7, the total number of terms = 50.
The answer choices are all JUST A BIT LESS than 50.
Thus, MOST of the terms must be 7.
ONLY A FEW terms will be 77.
If 1 term = 77, the amount remaining = 350-77 = 273.
273/7 = 39. This works!
So 1 term = 77, 39 terms = 7.
Total number of terms = 1+39 = 40.
The correct answer is C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Looking for a pattern is another possible approach:psm12se wrote:If each term in the sum a1 + a2 + ..... + an is either 7 or 77 and the sum equals 350, which of the following could be equal to n?
1. 38
2. 39
3. 40
4. 41
5. 42
Since both 7 and 77 have 7 as their units digit, we know that if we take any two terms, their sum will have a units digit of 4 (e.g., 7 + 7 = 14, 7 + 77 = 84, 77 + 77 = 154)
Similarly, if we take any three terms, their sum will have a units digit of 1. (e.g., 7 + 7 + 7 = 21, 7 + 7 + 77 = 91, etc.)
Now let's look for a pattern.
The sum of any 1 term will have units digit 7
The sum of any 2 terms will have units digit 4
The sum of any 3 terms will have units digit 1
The sum of any 4 terms will have units digit 8
The sum of any 5 terms will have units digit 5
The sum of any 6 terms will have units digit 2
The sum of any 7 terms will have units digit 9
The sum of any 8 terms will have units digit 6
The sum of any 9 terms will have units digit 3
The sum of any 10 terms will have units digit 0
The sum of any 11 terms will have units digit 7 (at this point, the pattern repeats)
From this, we can conclude that the sum of any 20 terms will have units digit 0
And the sum of any 30 terms will have units digit 0, and so on.
We are told the sum of the terms is 350 (units digit 0), so the number of terms must be 10 or 20 or 30 or . . .
Since C is a multiple of 10, this must be the correct answer.
Cheers,
Brent
Another option is to try some different configurations. If we do, we see that adding 39 7's and 1 77 gives us a total of 350. (39 + 1 = [spoiler]40 = C[/spoiler])
Last edited by Brent@GMATPrepNow on Thu Oct 17, 2013 6:22 am, edited 1 time in total.
I will try to give my 2 cents:
For me it is the best to make an equality:
7x+77y=350
7(x+11y)=350
x+11y=50
From here need to find numbers of x and y that fit into the answer choices? the only choice here is y=1 and x=39
So the overall number of integers is 40!
I hope that helps!
For me it is the best to make an equality:
7x+77y=350
7(x+11y)=350
x+11y=50
From here need to find numbers of x and y that fit into the answer choices? the only choice here is y=1 and x=39
So the overall number of integers is 40!
I hope that helps!