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GMATPrep: Equal to n?

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GMATPrep: Equal to n? [#permalink]

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New post 01 Apr 2010, 19:21
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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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Re: GMATPrep: Equal to n? [#permalink]

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New post 01 Apr 2010, 21:51
joyseychow 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.40

39*7 + 1*77 = 350. so n = 39 + 1 = 40
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Re: GMATPrep: Equal to n? [#permalink]

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New post 01 Apr 2010, 22:36
Approach the problem like this

first thing is we need a '0' in the units digits of the result ... so when you add a '3' to a '7' you get '0' in the units digit

The only number which provides a '3' in the units digit is that is 39*77 or 39*7 ... since the latter makes sense for a total of 350 we have

39*7 = 273 + 77 = 350
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Re: GMATPrep: Equal to n? [#permalink]

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New post 16 May 2011, 21:22
Step 1:

If all the terms in the sum are 7, then we need 50 terms of 7. But in the solution there is no option of 50.

Step 2:

We have an option of substituting 77 in the terms of the equation.
So, if we have one 77 in the terms of the equation, then we have to have thirty nine terms of 7 i.e
39*7+77=350

We need 40 terms in the equation to equal 350. We have 40 as an option in the list of answers.
If we want to substitute two terms of 77, we need an option, which has less than 29 terms in the list of answers.

So, the obvious choice of answer is (C).
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Re: GMATPrep: Equal to n? [#permalink]

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New post 17 May 2011, 04:24
(7x + 77y) = 350
7(x +11y) = 350
x + 11y = 50

Clearly if we let y = 1, then x = 39. Number of terms is 40. C.

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Re: GMATPrep: Equal to n? [#permalink]

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New post 17 May 2011, 05:30
7-77-problem-solving-27636.html
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Re: GMATPrep: Equal to n? [#permalink]

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New post 17 May 2011, 07:24
39 1's and 40th element is 11.

40
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Re: GMATPrep: Equal to n?   [#permalink] 17 May 2011, 07:24
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