if each term in the sum a1 + a2 + ... is either 7 or 77
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
GMAT/MBA Expert
- Jeff@TargetTestPrep
- GMAT Instructor
- Posts: 1462
- Joined: Thu Apr 09, 2015 9:34 am
- Location: New York, NY
- Thanked: 39 times
- Followed by:22 members
Solution:lunarpower wrote:courtesy of user 'karenmeow'
if each term in sum a1+a2+...+an is either 7 or 77, and the sum equals 350, which can be n?
choices: 38, 39, 40, 41, 42
We can let x be the number of terms that are 7 and y be the number of terms that are 77. Notice that x + y = n, the total number of terms. We can also set up the following equation
7x + 77y = 350
Dividing both sides by 7 we have:
x + 11y = 50
11y = 50 - x
y = (50 - x)/11
Because y is an integer, we know that (50 - x) must be a multiple of 11.
Thus, to make that true, variable x can only be 6, 17, 28 or 39.
If x = 6, y = 4, so n = 10.
If x = 17, y = 3, so n = 20.
If x = 28, y = 2, so n = 30.
If x = 39, y = 1, so n = 40.
We see that answer choice C is the only one that matches our possibilities for n.
Note: In looking at the equation x + 11y = 50, we also could have taken a units digit approach. We know that the units digit of x + 11y is a zero. We also know that 11 times any number will result in the same units digit as the original number. As an example let's take the number 2. 2 has a units digit of 2 and 2 x 11 = 22 also has a units digit of 2.
Thus, we can say that x + 11y will result in the same units digit as x + y. Since we know that x + 11y = 50, we know that x + 11y has a units digit of zero. This means that x + y (or "n" in this case) also has a units digit of zero. Since 40 is the only answer choice with a units digit of zero we know that is the correct answer.
The answer is C
Jeffrey Miller
Head of GMAT Instruction
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
- akshaydhande
- Newbie | Next Rank: 10 Posts
- Posts: 8
- Joined: Thu Jun 16, 2016 7:06 am
- Location: Navi Mumbai
- GMAT Score:630
I would suggest u directly take options and start to check
lets start with
38*7=266+77 near 350 but does not end in 0, next 77 will be too much
39*7=273+77 ==350 bingo 39 times 7 and 1 time 77 that is total 39+1=40 terms.
lets start with
38*7=266+77 near 350 but does not end in 0, next 77 will be too much
39*7=273+77 ==350 bingo 39 times 7 and 1 time 77 that is total 39+1=40 terms.
700 in reach.
-
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
That works too! Since the answers are so clustered around 40, I'd start there: 40 * 7 is 280, and if we drop one 7, we've got 39*7 + 77, or ... 350! What luck.akshaydhande wrote:I would suggest u directly take options and start to check
lets start with
38*7=266+77 near 350 but does not end in 0, next 77 will be too much
39*7=273+77 ==350 bingo 39 times 7 and 1 time 77 that is total 39+1=40 terms.