If each term in the sum a1+a2+a3+...+an is either 7 or 77 and the sum = 350, which of the following could be equal to n?
38
39
40
41
42
Answer is 40
Is this because the only way that the sums of 7 and 77 can come up to 350 is if they add up to a sum that ends in 0, and that the only multiple of 7 that ends in 0 is if it were multiplied by 10?
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
Sequence Problem
This topic has expert replies
GMAT/MBA Expert
-
Rahul@gurome
- GMAT Instructor
- Posts: 1179
- Joined: Sun Apr 11, 2010 9:07 pm
- Location: Milpitas, CA
- Thanked: 447 times
- Followed by:88 members
If each term in the sum a1+a2+a3+...+an is either 7 or 77 and the sum = 350, which of the following could be equal to n?
Let the number of terms which are 77 be x.
So number of terms which are 7 is (n-x).
Or 77x + 7(n-x) = 350.
Or 70x + 7n = 350.
Or n = 50 -10x.
Note that n and x are non negative integers. Also n is more than 0. So 50 -10x > 0 or x < 5.
Now if x is 1, n = 40.
So n can take the value of 40.
Let the number of terms which are 77 be x.
So number of terms which are 7 is (n-x).
Or 77x + 7(n-x) = 350.
Or 70x + 7n = 350.
Or n = 50 -10x.
Note that n and x are non negative integers. Also n is more than 0. So 50 -10x > 0 or x < 5.
Now if x is 1, n = 40.
So n can take the value of 40.
Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
-
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
350/7 = 50. So if each term were 7, we'd have 50 terms. The answer choices are all a little less than 50. So most -- but not all -- of the terms will be 7.vongdn wrote:If each term in the sum a1+a2+a3+...+an is either 7 or 77 and the sum = 350, which of the following could be equal to n?
38
39
40
41
42
Answer is 40
Is this because the only way that the sums of 7 and 77 can come up to 350 is if they add up to a sum that ends in 0, and that the only multiple of 7 that ends in 0 is if it were multiplied by 10?
If 1 term = 77, we have 350-77 = 273 left.
273/7 = 39. This works!
So 1 term = 77, 39 terms = 7.
Total number of terms is 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
-
saurabhmahajan
- Master | Next Rank: 500 Posts
- Posts: 250
- Joined: Thu Jan 07, 2010 2:21 am
- Thanked: 10 times
GMATGuruNY,
I have seen many of your posts where you have solved by plugging numbers and inspired form that i have also solved many of the problems on this forum the same way as you did.
Thanks for helping me and inspiring me.
Keep posting.
I have seen many of your posts where you have solved by plugging numbers and inspired form that i have also solved many of the problems on this forum the same way as you did.
Thanks for helping me and inspiring me.
Keep posting.
Thanks and regards,
Saurabh Mahajan
I can understand you not winning,but i will not forgive you for not trying.
Saurabh Mahajan
I can understand you not winning,but i will not forgive you for not trying.
-
Testluv
- GMAT Instructor
- Posts: 1302
- Joined: Mon Oct 19, 2009 2:13 pm
- Location: Toronto
- Thanked: 539 times
- Followed by:164 members
- GMAT Score:800
...yes!!! That's also the fastest way to solve this problem:Is this because the only way that the sums of 7 and 77 can come up to 350 is if they add up to a sum that ends in 0, and that the only multiple of 7 that ends in 0 is if it were multiplied by 10?
There's eleven 7s in 77. So how can a bunch of 7s sum to 350? Well, since 350 ends in "0", the number of 7s must be a multiple of 10. Only one choice is a multiple of 10--choice C!
Kaplan Teacher in Toronto
-
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
I'm glad that you've been finding my posts helpful. It's my goal -- and that of The Princeton Review -- to use and teach consistent methods that can be applied to many kinds of problems. I plug in my own values or plug in the answer choices in order to solve a majority of GMAT questions.saurabhmahajan wrote:GMATGuruNY,
I have seen many of your posts where you have solved by plugging numbers and inspired form that i have also solved many of the problems on this forum the same way as you did.
Thanks for helping me and inspiring me.
Keep posting.
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
