December 15, 2018 December 15, 2018 07:00 AM PST 09:00 AM PST Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT. December 15, 2018 December 15, 2018 10:00 PM PST 11:00 PM PST Get the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299)
Author 
Message 
TAGS:

Hide Tags

Manager
Status: Single
Joined: 05 Jun 2011
Posts: 98
Location: Shanghai China

If S is the sum of the first n positive integers, what is
[#permalink]
Show Tags
22 Jul 2011, 19:16
Question Stats:
67% (01:55) correct 33% (02:04) wrong based on 82 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: 377

Re: If S is the sum of the first n positive integers, what is
[#permalink]
Show Tags
23 Jul 2011, 00:23
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: 98
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: 98
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]



Retired Moderator
Joined: 20 Dec 2010
Posts: 1820

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: 254

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: 51218

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 &nbs
[#permalink]
27 Nov 2017, 00:35






