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# If each term in the sum A1+A2+ An is either 7 or 77 and the

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Intern
Joined: 25 Dec 2008
Posts: 41
If each term in the sum A1+A2+ An is either 7 or 77 and the  [#permalink]

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01 Jan 2009, 12:49
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?
A. 38
B. 39
C. 40
D. 41
E. 42

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SVP
Joined: 29 Aug 2007
Posts: 2420

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01 Jan 2009, 13:51
shobuj40 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?
A. 38
B. 39
C. 40
D. 41
E. 42

C. Since 77 = 11(7), n = 50 because 350 = 7n.

1. 77 (0) + 7 (50) = 350 ...........total terms = 50.
2. 77 (1) + 7 (39) = 350 ........... total terms = 40
3. 77 (2) + 7 (28) = 350 ............ total terms = 30.

Since number of terms in ACs are all over 38 but smaller than 50, it should be 39+1 = 40 in C.
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VP
Joined: 17 Jun 2008
Posts: 1474

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02 Jan 2009, 04:48
Another approach:

7x + 77y = 350
or, x + 11y = 50
or, y = (50-x)/11 and in order for y to be aninteger, (50-x) is to be a multiple of 11.

i.e., (50-x) could be 11, 22, 33, 44
or, x could be 39, etc.
and hence, y could be 1, etc.

Hence, n = x + y = 40, etc.
GMAT Tutor
Joined: 24 Jun 2008
Posts: 1345

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02 Jan 2009, 11:36
1
Or just look at the units' digit: we're adding a lot of numbers that end in 7, and we're getting something ending in 0. That could only happen if we're adding 10, or 20, or 30, etc, numbers together; the number of numbers must be a multiple of 10. So 40 must be the answer.

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Re: series &nbs [#permalink] 02 Jan 2009, 11:36
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