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# Number Properties from GMATPrep (2)

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Manager
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Number Properties from GMATPrep (2) [#permalink]

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28 Sep 2009, 00:37
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75% (01:23) correct 25% (01:27) wrong based on 3 sessions

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Plese help me to solve that problem.
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Manager
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Re: Number Properties from GMATPrep (2) [#permalink]

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28 Sep 2009, 01:18
The correct answer is C: 40.

Let's simplify the question: Since all the terms used are divisible by 7, we can rewrite the question as follows:

If each term in the sum a1 + a2 + ... + an is either 1 or 11 and the sum equals 50, which of the following could be equal to n?

Now, since each term is equal to 1 or 11, let's represent the total number of 1s = x, and the total number of 11s = y.

Therefore:

50 = x + 11y
and
n = x + y

so:

50 = x + 11y = 10y + (x+y)
50 = 10y + n
n = 50 - 10y

Since n = 50 is not an option, it should become apparent that n MUST BE a multiple of 10 since y is an integer. Therefore the only option is C: 40.
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Re: Number Properties from GMATPrep (2) [#permalink]

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28 Sep 2009, 10:16
Let thre be x terms of 77 and y terms of 7.Then we get

77x + 7y = 350

11x + y = 50

So x = 4 & y = 6 (x+y) = 10
x = 3 & y = 17 (x+y) = 20

So it must be a multiple of 10.
I wud go with option 40
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Re: Number Properties from GMATPrep (2) [#permalink]

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28 Sep 2009, 23:20
I used a less algebraic solution by backsolving/simple logic.

350 is divisible by 7 but 50 is not an option. Looking at the options you can estimate that subtractive 77 and dividing will give you something between 38 and 42.

350 – 77 = 273.
273/7 = 39.

Hence (1)77 + (39)7 = 350 Hence Ans = 40.

This may not work for more complex questions but this answer took me <1min solving this way.
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Re: Number Properties from GMATPrep (2) [#permalink]

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29 Sep 2009, 06:45
My approach was somewhat similar to yangsta8's.Looking at the possible answers one can see that you can only have one 77 in the sequence(since 350 -(2x77) = 196 and 196/7=28, which is not in the answer options)
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Re: Number Properties from GMATPrep (2) [#permalink]

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29 Sep 2009, 11:32
great going guys, so many ways to solve..
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Re: Number Properties from GMATPrep (2) [#permalink]

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07 Oct 2009, 12:12
or divide everything by 7 and then think in terms of 1s and 11s... and eliminate all but the right answer...

the answer hits that there would be only one 11 as all the values are circa 40... so it must be 40 39 ones and 1 eleven give you 40.
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Problem on Sequences . Need help [#permalink]

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13 Jun 2010, 00:55
If each term in the sequence a1+a2+a3+....+an is either 7 or 77 and the sum equals 350,which of the following could be equal to n

1) 38
2) 39
3) 40
4) 41
5) 42
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Re: Number Properties from GMATPrep (2) [#permalink]

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05 May 2011, 02:47
350/7 = 50

number of 1's = 39 and number of 11's = 1
hence 40.
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Re: Number Properties from GMATPrep (2) [#permalink]

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05 May 2011, 07:27
Because the sum contains 0 at end, so 7 needs to be multiplied by factor of 10. 40 is the only choice that matches.

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Re: Number Properties from GMATPrep (2) [#permalink]

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07 May 2011, 06:26
7x+77y = 350 => x+11y = 50 (equation 1)

x+y = n (equation 2)

subtracting 2 from 1 , we have

10y = 50-n => $$y = (50-n)/10$$

then by plugging in answers we can see , C is only possible choice. everything else is a non integer.

Re: Number Properties from GMATPrep (2)   [#permalink] 07 May 2011, 06:26
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# Number Properties from GMATPrep (2)

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