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GMAT Prep PS Question - Sets

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by queenisabella » Sun Mar 11, 2012 12:48 pm
Need help answering this in a timely fashion on the GMAT.

If each term in the sum A1 + A2 + ... + An is either 7 of 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

OA is C
Source: GMAT Prep
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by Mike@Magoosh » Sun Mar 11, 2012 4:31 pm
Hi, there. I'm happy to help with this. :)

If each term in the sum A1 + A2 + ... + An is either 7 of 77 and the sum equals 350, which of the following could be equal to n?

So, 350 = 7*50, so n could be 50 if all the terms are 7, and none are 77.

Suppose we have one term that is 77, and all the others are seven. Well, for the one term of 77, we have replaced eleven terms of 7. What we have is

1 term of 77, and 50 - 11 = 39 terms of 7 ===> 40 terms

Answer = C

Here's a somewhat related question on sequences,

https://gmat.magoosh.com/questions/854

When you submit your answer to that question, the following page will have a complete video explanation.

Do what I've done make sense? If you have any questions on what I've said, please do not hesitate to contact me.

Mike :)
Magoosh GMAT Instructor
https://gmat.magoosh.com/
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by queenisabella » Sun Mar 11, 2012 6:02 pm
very helpful. thanks Mike@Magoosh!
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by Anurag@Gurome » Sun Mar 11, 2012 7:58 pm
queenisabella wrote:Need help answering this in a timely fashion on the GMAT.

If each term in the sum A1 + A2 + ... + An is either 7 of 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

OA is C
Source: GMAT Prep
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.
Anurag Mairal, Ph.D., MBA
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