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If S is the sum of the first n positive integers, what is the value of
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08 May 2010, 02:11
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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 DS84302.01
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Re: If S is the sum of the first n positive integers, what is the value of
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08 May 2010, 05:03
abhi758 wrote: If S is the sum of the first n positive integers, what is the value of n ? (1) \(S < 20\) (2) \(s^2 > 220\) 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.
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Re: If S is the sum of the first n positive integers, what is the value of
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08 May 2010, 12:28
Thanks Bunnel. Very well explained!



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Re: If S is the sum of the first n positive integers, what is the value of
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16 May 2010, 13:08
easy one this time s<20 so N could be 2 to 5 (N greater than 5 will exceed the limit s<20) this condition alone not sufficient. statement B  S^2 > 220 N clould be 5,6,7,8 anything equal or greater than 5 hence not sufficient. combining the two , we get N=5 which is the answer hence C



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Re: If S is the sum of the first n positive integers, what is the value of
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29 Jul 2014, 15:24
abhi758 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 First n positive intergers: 1, 2, 3, 4, 5, 6, 7. Sum of them could be: 3,6,10,15,21 (1) S < 20 > n could be 1, 2, 3, 4, 5, > insufficient (2) S^2 > 220 220 = 11*2*10 = 11*4*5 > S > square root of 220 = 2 * sqrt(55) 7^2 < 55 < 8^2 > S > (about) 14 > C ( S =15) That is everything on my note in 1 min 20 sec.



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Re: If S is the sum of the first n positive integers, what is the value of
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18 Dec 2014, 06:55
2. Properties of Integers For more check Ultimate GMAT Quantitative Megathread Hope it helps.
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Re: If S is the sum of the first n positive integers, what is the value of
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18 Dec 2014, 07:53
1.S<20 (n(n+1)/2)<20 for n = 1 to 5 the above equation is valid. so we cant say the exact valeu of n . Insufficient
2. (n^2(n+1)^2)/4>220 for n>4 the above equation is valid. so we cant say the exact valeu of n . Insufficient
1+2>> there is only one value that satisfies both the equations i.e n=5 from 1, 1<=n<=5 and from 2, n>4 common value is 5. Sufficinet
Ans C



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Re: If S is the sum of the first n positive integers, what is the value of
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19 Dec 2014, 10:51
If S is the sum of the first n positive integers, what is the value of n ?
(1) S < 20 (2) S^2 > 220
Solution: Sum of first positive n numbers is defined as S= n*(n+1)/2
Statement 1: S < 20 Five distinct values of n satisfies this condition (n={1,2,3,4,5})  Insufficient
Statement 2: S^2 > 220 Since S is sum of positive integers (ignoring negative values), S > 14. Again multiple values of n satisfies this condition (n>=5)  Insufficient
Combining Statement 1 and 2: Unique solution n = 5
Answer C



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Re: If S is the sum of the first n positive integers, what is the value of
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20 Dec 2014, 17:08
S = sum of first positive integers = n(n+1)/2
(1) S < 20 if the number of integers are 4, S = 4*5/2 = 10 if the number of integers are 5, S = 5*6/2 = 15. Insufficient (2) S^2 > 220 S^2 goes till infinite. Insufficient.
If considered, 1 and 2, then S = 15. Sufficient.
Ans = C.



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Re: If S is the sum of the first n positive integers, what is the value of
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08 Feb 2015, 06:11
Hey,
Great, you reminded me of this formula!
However, in this case, we don't really need it.
[1] S<20 This means that the numbers are: 1,2,3,4,5 = 15. NS, because there is a range of possible sums using these values.
[2] s^2>220 This is not sufficient on its own, again becase there is a range of possible sums.
[1,2] Sufficient. 15^2 = 225 (1+2+3+4+5). 10^2 = 100 (1+2+3+4)
So, only 15^2 = 225 can be the case.



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Re: If S is the sum of the first n positive integers, what is the value of
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11 Dec 2016, 11:26
Excellent Question. Here is what i did in this Question >
From 1 => S=1,3,6,10,15 Not sufficient From 2=> N can be 1000 or 10000 or anything basically with s^2>220 restriction.
Hence insufficient
Combing the two statements S must be 15 Hence n must be 5
Hence C
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Re: If S is the sum of the first n positive integers, what is the value of
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16 Dec 2016, 18:34
This is a great Official Question. Here is what i did in this one => WE need the value of n
Statement 1> S<20
n=1=>S=1 n=2=>S=3 n=3=>S=6 n=4=>S=10 n=5=>S=15
Hence n can be {1,2,3,4,5} Not sufficient
Statement 2> Here n can take infinite values. E.g=> n=1000902439380 n=1489312843 etc. Not sufficient
Combining the two statements> S=15 is the only value that would satisfy both the conditions
Hence S=15 n=5
Hence sufficient
Hence C
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Re: If S is the sum of the first n positive integers, what is the value of
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07 Feb 2019, 03:55
abhi758 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 n can be 3, 4, 5 From 1, sum can be 10,15(for n =4 and n=5) From 2, n can be any value after 5,6,7,8 Combination will give only one value for n n = 5, sum = 15, 225> 220 C
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Re: If S is the sum of the first n positive integers, what is the value of
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