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If S is the sum of the first n positive integers, what is [#permalink]
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22 Jul 2011, 20:16
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If S is the sum of the first n positive integers, what is the value of n? (1) S < 20 (2) S^2 >220 OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/ifsisthe ... 93852.html
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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 + (n1)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 + (n1)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]



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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, 01:23
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tracyyahoo wrote: If S is the sum of the first n positive integers, what is the value of n?
1) S < 20 2) S^2 >220 Sum of first n positive integer S = n * (n+1) / 2 Stmt1: S < 20. For n=5 S = 5*6/2 =15 For n=4 S=4*5/2 = 10 Hence n can be 5 or 4 or 3.... Insufficient. Stmt2: S^2 >220 For n=5, S=15 and S^2 = 225 > 220 For n=6, S=21 and S^2 = 441 > 220 Again, two values. Insufficient. Combining, From 1, n can be 5,4,3... From 2, n can be 5,6,7.... Common value is 5. hence sufficient. OA C.
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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, 04:56
S is the sum of n integer, not the averge. Big brother....Stmt1: S < 20. For n=5 S = 5*6/2 =15? jamifahad wrote: tracyyahoo wrote: If S is the sum of the first n positive integers, what is the value of n?
1) S < 20 2) S^2 >220 Sum of first n positive integer S = n * (n+1) / 2 Stmt1: S < 20. For n=5 S = 5*6/2 =15 For n=4 S=4*5/2 = 10 Hence n can be 5 or 4 or 3.... Insufficient. Stmt2: S^2 >220 For n=5, S=15 and S^2 = 225 > 220 For n=6, S=21 and S^2 = 441 > 220 Again, two values. Insufficient. Combining, From 1, n can be 5,4,3... From 2, n can be 5,6,7.... Common value is 5. hence sufficient. OA C.



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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, 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 + (n1)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 + (n1)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]



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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, 08:01
tracyyahoo wrote: If S is the sum of the first n positive integers, what is the value of n?
1) S < 20 2) S^2 >220
Pls tell me why? THANK U~~ Sum of n natural number = n(n+1)/2 1) n(n+1)/2<20 n(n+1)<40 {1, 2}=2 {2, 3}=6 {3, 4}=12 {4, 5}=20 {5, 6}=30 {6, 7}=42>40. Ignore & Stop. 1<=n<=5 Not Sufficient. 2) S^2 >220 Square root both sides: S >14 n(n+1)/2>14 n(n+1)>28 {5,6}=30 {6,7}=42 . . . n>=5 Not Sufficient. Together: n=5 Ans: "C"
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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, 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.
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Re: If S is the sum of the first n positive integers, what is [#permalink]
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27 Nov 2017, 01:35
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. Answer: C. OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/ifsisthe ... 93852.html
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Re: If S is the sum of the first n positive integers, what is
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