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Re: If S is the sum of the first n positive integers, what is [#permalink]

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23 Jul 2011, 00:01

To find the sum of evenly spaced set of finite numbers, you can use the arithmetic progression formula: Sn = (n/2)[A1 + (n-1)d], where, n = the number of terms A1= the first term d = the common difference In the question, we're asked for n.

Stat. 1: S<20 (n/2)[A1 + (n-1)d] <20 solving for n shall give you: note that d=1 n <\sqrt{40} This means n can be 6,5,4,3,2 or 1. So insufficient. Stat. 2: S^2 >220 S> \sqrt{220} So S >14 Here note that \sqrt{220}is between 14 and 15. Therefore, using the previous formula n > \sqrt{28} This means n can be 6,7,8,9,10....So insufficient Combining statement 1 and statement 2 leaves us with only number 6 as a valid value for n; therefore, it is sufficient. The answer is, thus, [spoiler=]C/spoiler]

Re: If S is the sum of the first n positive integers, what is [#permalink]

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23 Jul 2011, 04:58

Too complicated, hard to understand~~

yefetarisira wrote:

To find the sum of evenly spaced set of finite numbers, you can use the arithmetic progression formula: Sn = (n/2)[A1 + (n-1)d], where, n = the number of terms A1= the first term d = the common difference In the question, we're asked for n.

Stat. 1: S<20 (n/2)[A1 + (n-1)d] <20 solving for n shall give you: note that d=1 n <\sqrt{40} This means n can be 6,5,4,3,2 or 1. So insufficient. Stat. 2: S^2 >220 S> \sqrt{220} So S >14 Here note that \sqrt{220}is between 14 and 15. Therefore, using the previous formula n > \sqrt{28} This means n can be 6,7,8,9,10....So insufficient Combining statement 1 and statement 2 leaves us with only number 6 as a valid value for n; therefore, it is sufficient. The answer is, thus, [spoiler=]C/spoiler]

Re: If S is the sum of the first n positive integers, what is [#permalink]

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23 Jul 2011, 14:09

Answer is C.

1) S < 20.

1+2+3+4+5+6 = 21. 21 is greater than 20. Therefore, statement 1 tells us that 1<=n<=5

2) S^2 > 220. S > 15.

Statement 2 tells us that the sum is greater than or equal to 15. This also tells us that n has to be greater than or equal to 5.

Combined: We get statement 1 which states that n is less than or equal to 5 and statement 2 which states n is greater than or equal to 5.Therefore, N is equal to 5. Hence Sufficient from both statements 1 and 2. _________________

If S is the sum of the first n positive integers, what is the value of n ?

The sum of the first n positive integers \(S=\frac{n(n+1)}{2}\).

(1) \(S < 20\) --> \(\frac{n(n+1)}{2}< 20\) --> \(n(n+1)<40\) --> \(0<n<6\) (n can 1, 2, 3, 4, 5). Not sufficient

(2) \(S^2 > 220\) --> \((\frac{n(n+1)}{2})^2> 220\) --> \(n(n+1)>\sqrt{880}\) --> \(\sqrt{880}\) is slightly less than 30 --> \(n(n+1)>29\) --> \(n>4\) (n can be 5, 6, 7, ...). Not sufficient.

(1)+(2) Intersection of values of n from (1) and (2) is n=5. Sufficient.

Answer: C.

OR, just write down several values of S. S= 1, 3, 6, 10, 15, 21, 28, ...

(1) \(S < 20\). S=1, 3, 6, 10, 15. Not sufficient

(2) \(S^2 > 220\). S=15, 21, ... Not sufficient.

(1)+(2) Intersection of values of n from (1) and (2) is S=15 --> n=5. Sufficient.