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Which of the following could equal n??

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by gmatpup » Tue Dec 27, 2011 10:22 am
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 equal n?

A. 38
B. 39
C. 40
D. 41
E. 42


Please help! Thanks again! :)
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by user123321 » Tue Dec 27, 2011 10:56 am
gmatpup 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 equal n?

A. 38
B. 39
C. 40
D. 41
E. 42


Please help! Thanks again! :)
rewrite the question, say we have x number of 7's and y number of 77's which make up 350
so 7x + 77y = 350
and question is asking for x+y
=> 7x + 77y = 350
=> x + 11y = 50
put values by trail and error.
i can see if y = 1 then x = 39 => x+y = 40 in one of the choices given. so it should be the answer.

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by pemdas » Tue Dec 27, 2011 12:56 pm
another way, 350 isn't divisible by 77
possible coefficients for 77 are 1,2,3,4 and (350-77*coefficient) must be divisible by 7
let's check (350-77)=273 which is divisible by 7 and returns 39

mark B away, as only one correct answer exists in multiple choice
gmatpup 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 equal n?

A. 38
B. 39
C. 40
D. 41
E. 42


Please help! Thanks again! :)
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by ronnie1985 » Tue Dec 27, 2011 7:55 pm
(c) 40
x= 7s
y = 77s
7x+77y = 350
x+11y = 50
y = 1 => x = 39
x + y = 40
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by Anurag@Gurome » Tue Dec 27, 2011 8:32 pm
gmatpup 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 equal n?

A. 38
B. 39
C. 40
D. 41
E. 42

Please help! Thanks again! :)
Let x and y be the number of 7's and the number of 77's respectively.
Then 7x + 77y = 350 implies x + 11y = 50
x + y = 50 - 10y
So, x + y = n = 50 - 10y implies n must have the unit digit of 0 because 50 - 10y must be a number which has units digit as 0. C is the only option in which the units digit is 0.

The correct answer is C.
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