Author 
Message 
TAGS:

Hide Tags

Manager
Status: Single
Joined: 05 Jun 2011
Posts: 113
Location: Shanghai China

If S is the sum of the first n positive integers, what is [#permalink]
Show Tags
22 Jul 2011, 19:16
1
This post was BOOKMARKED
Question Stats:
61% (01:14) correct 39% (01:58) wrong based on 62 sessions
HideShow timer Statistics
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
Official Answer and Stats are available only to registered users. Register/ Login.



Intern
Joined: 21 Apr 2011
Posts: 3

Re: If S is the sum of the first n positive integers, what is [#permalink]
Show Tags
22 Jul 2011, 23:01
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]



Senior Manager
Joined: 03 Mar 2010
Posts: 413

Re: If S is the sum of the first n positive integers, what is [#permalink]
Show Tags
23 Jul 2011, 00:23
1
This post received KUDOS
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.
_________________
My dad once said to me: Son, nothing succeeds like success.



Manager
Status: Single
Joined: 05 Jun 2011
Posts: 113
Location: Shanghai China

Re: If S is the sum of the first n positive integers, what is [#permalink]
Show Tags
23 Jul 2011, 03:56
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.



Manager
Status: Single
Joined: 05 Jun 2011
Posts: 113
Location: Shanghai China

Re: If S is the sum of the first n positive integers, what is [#permalink]
Show Tags
23 Jul 2011, 03:58
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]



Math Forum Moderator
Joined: 20 Dec 2010
Posts: 1945

Re: If S is the sum of the first n positive integers, what is [#permalink]
Show Tags
23 Jul 2011, 07:01
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"
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



Senior Manager
Joined: 11 Apr 2011
Posts: 263

Re: If S is the sum of the first n positive integers, what is [#permalink]
Show Tags
23 Jul 2011, 13:09
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.
_________________
Powerscore CR Bible Full Chapter Notes  Easily Extend Vocabulary List with Google Dictionary
Please kudo me if you found my post useful. Thanks!!!



Math Expert
Joined: 02 Sep 2009
Posts: 43787

Re: If S is the sum of the first n positive integers, what is [#permalink]
Show Tags
27 Nov 2017, 00:35
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
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Re: If S is the sum of the first n positive integers, what is
[#permalink]
27 Nov 2017, 00:35






