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# value of N

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VP
Joined: 18 May 2008
Posts: 1258

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29 Jan 2009, 04:28
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SVP
Joined: 17 Jun 2008
Posts: 1534

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29 Jan 2009, 05:20
7x + 77(n-x) = 350
or, x + 11(n-x) = 50
or, 11n - 10x = 50
or, n = (50 + 10x)/11

For n to be an integer, numerator has to be 110, 220, 330, etc.
Accordingly, n will be a multiple of 10, i.e. 10, 20, 30, 40, etc.

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SVP
Joined: 07 Nov 2007
Posts: 1792

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Location: New York

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29 Jan 2009, 09:27
to make sum 350 with combinations of 7 and 77 ( unit digit is 7 )
number n must be multiple of 10

only option that is multiple of 10 is 40
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Senior Manager
Joined: 30 Nov 2008
Posts: 485

Kudos [?]: 361 [0], given: 15

Schools: Fuqua

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29 Jan 2009, 14:45
IMO 40. But here is my approach.

Each term can be multipleof 7 / 77 ie 7 / 7*11

Given Sum of the terms = 350 ==> which is nothing but 7 * 50

I tried out the possibilities

When 77 is selected, means we are already used 7 * 11 from the sum, so the rest of the terms with 7 will be 39(FYI 50-11) = total number of terms = 1 + 39 = 40

When two 77 are selected, then we are already used 7 * 22 from the sum, so the rest of the terms will 7 will be 28(FYI 50-22) = total number of terms will be 2 + 28 = 30 This is the next possible combination.

Hence I concluded that of the given options, only 40 is possible.

Kudos [?]: 361 [0], given: 15

Re: value of N   [#permalink] 29 Jan 2009, 14:45
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