Last visit was: 14 Dec 2024, 00:46 It is currently 14 Dec 2024, 00:46
Home
GMAT
Messages
Tests
Schools
Reviews
Social
Chat
My Profile
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
avatar
shreya717
avatar
Joined: 01 Aug 2011
Last visit: 24 Sep 2012
Posts: 12
Own Kudos:
15
 []
Given Kudos: 15
Posts: 12
Kudos: 15
 []
If n > 2, then the sum, S, of the integers from 1 through n can be cal Updated on: 16 Sep 2022, 06:20
Originally posted by shreya717 on 07 Jun 2012, 04:53.
Last edited by Bunuel on 16 Sep 2022, 06:20, edited 2 times in total.
2
Kudos
Add Kudos
6
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

35% (medium)

Question Stats:

67% (01:40) correct 33% (01:27) wrong based on 202 sessions

History

Date
Time
Result
Not Attempted Yet
If n > 2, then the sum, S, of the integers from 1 through n can be calculated by the following formula: S = n(n + 1)/2. Which one of the following statements about S must be true?

A. S is always odd.
B. S is always even.
C. S must be a prime number
D. S must not be a prime number
E. S must be a perfect square
ShowHide Answer
Official Answer
D
User avatar
Swoosh617
User avatar
Joined: 19 Mar 2012
Last visit: 24 Aug 2015
Posts: 131
Own Kudos:
187
 []
Given Kudos: 13
Location: United States
Concentration: Finance, General Management
Schools: HBS '16 (D) CBS '16 (D) Wharton '16 (D) Booth '16 (A) Anderson '16 (A) Stanford '16 (D)
GMAT 1: 750 Q50 V42
GPA: 3.69
WE:Analyst (Mutual Funds and Brokerage)
Schools: HBS '16 (D) CBS '16 (D) Wharton '16 (D) Booth '16 (A) Anderson '16 (A) Stanford '16 (D)
GMAT 1: 750 Q50 V42
Posts: 131
Kudos: 187
 []
If n > 2, then the sum, S, of the integers from 1 through n can be cal 07 Jun 2012, 05:41
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
S does not necessarily have to be even. For example, when n=5, you have:

S = [(5)(5+1)]/2 = 15, an odd number
User avatar
cyberjadugar
User avatar
Joined: 29 Mar 2012
Last visit: 28 May 2024
Posts: 266
Own Kudos:
1,585
Given Kudos: 23
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
GMAT 3: 730 Q50 V38
Posts: 266
Kudos: 1,585
If n > 2, then the sum, S, of the integers from 1 through n can be cal 07 Jun 2012, 05:49
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi,

S = n(n + 1)/2, n > 2
for ex, n = 3, S = 6
n=5, S = 15 = 3*5 and so on

Now,
if n is even,
then, n = 2k, S = k(2k+1)....(a)

if n is odd,
then, n = 2k+1, S = (2k+1)(k+1)...(b)

Depending on value of k (integer), S can be odd/even
But for n>2, it will always be a product of two numbers....(from (a) & (b))

Thus, answer is (D)

Regards,
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 13 Dec 2024
Posts: 97,874
Own Kudos:
685,671
Given Kudos: 88,269
Products:
GMAT Club Tests Forum Quiz
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 97,874
Kudos: 685,671
If n > 2, then the sum, S, of the integers from 1 through n can be cal 07 Jun 2012, 14:26
Kudos
Add Kudos
Bookmarks
Bookmark this Post
If n > 2, then the sum, S, of the integers from 1 through n can be calculated by the following formula: S = n(n + 1)/2. Which one of the following statements about S must be true?
A. S is always odd.
B. S is always even.
C. S must be a prime number
D. S must not be a prime number
E. S must be a perfect square

Notice that we are asked "which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.

A. S is always odd --> not necessarily true if n=3 then 1+2+3=6=even.
B. S is always even --> not necessarily true if n=5 then 1+2+3+4+5=15=odd.
C. S must be a prime number --> not true if n=3 then 1+2+3=6=not prime.
E. S must be a perfect square --> not necessarily true if n=3 then 1+2+3=6=not a perfect square.

Only choice D is left.

Answer: D.
avatar
KevinBrink
avatar
Joined: 02 Nov 2012
Last visit: 21 Mar 2013
Posts: 24
Own Kudos:
10
Given Kudos: 11
Posts: 24
Kudos: 10
If n > 2, then the sum, S, of the integers from 1 through n can be cal 06 Nov 2012, 04:43
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Correct me if I am not right, but since n > 2, S is always even since odd * even = even and 2 is the only even prime number S can never be a prime number!
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 13 Dec 2024
Posts: 97,874
Own Kudos:
685,671
Given Kudos: 88,269
Products:
GMAT Club Tests Forum Quiz
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 97,874
Kudos: 685,671
If n > 2, then the sum, S, of the integers from 1 through n can be cal 06 Nov 2012, 04:56
Kudos
Add Kudos
Bookmarks
Bookmark this Post
KevinBrink
Correct me if I am not right, but since n > 2, S is always even since odd * even = even and 2 is the only even prime number S can never be a prime number!

No, that's not correct. If S is always even, then B must also be correct. But if n=5 then 1+2+3+4+5=15=odd.
avatar
geneticsgene
avatar
Joined: 12 Jan 2012
Last visit: 24 Jan 2021
Posts: 17
Own Kudos:
26
Given Kudos: 10
GMAT 1: 720 Q49 V39
GMAT 1: 720 Q49 V39
Posts: 17
Kudos: 26
If n > 2, then the sum, S, of the integers from 1 through n can be cal 06 Jan 2013, 01:05
Kudos
Add Kudos
Bookmarks
Bookmark this Post
shreya717
If n > 2, then the sum, S, of the integers from 1 through n can be calculated by the following formula: S = n(n + 1)/2. Which one of the following statements about S must be true?

A. S is always odd.
B. S is always even.
C. S must be a prime number
D. S must not be a prime number
E. S must be a perfect square


Can you please explain between B & D. Both need to be correct in order for the question to be valid right ?

(S needs to be even to be divisible by 2 & S shouldn't be a prime number)

Thanks,
Shreya

S = [n(n+1)]/2 for n>2 S should be divisible by either n or n+1 (for n = odd S is divisible by n and for n=even S is divisible by n+1) so it cannot be a prime no.
Answer: D
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 13 Dec 2024
Posts: 15,546
Own Kudos:
70,244
Given Kudos: 449
Location: Pune, India
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 15,546
Kudos: 70,244
If n > 2, then the sum, S, of the integers from 1 through n can be cal 06 Jan 2014, 21:49
Kudos
Add Kudos
Bookmarks
Bookmark this Post
akankshasoneja
If n > 2, then the sum, S, of the integers from 1 through n can be calculated by the following
formula: S = n(n + 1)/2. Which one of the following statements about S must be true?
(A) S is always odd.
(B) S is always even.
(C) S must be a prime number.
(D) S must not be a prime number.
(E) S must be a perfect square.

Show SpoilerMy doubt
Though i agree that the OA is right but even option B should be correct.

Put n = 5

S = 5*6/2 = 15
S is not always even. It may be even, it may be odd. If the even integer (out of n and n+1) is not a multiple of 4, then S will be odd.
avatar
joe26219
avatar
Joined: 10 Oct 2013
Last visit: 25 Jul 2016
Posts: 31
Own Kudos:
21
Given Kudos: 44
Concentration: Marketing, Entrepreneurship
Schools: Kellogg '18 (D) Ross '18 (M) Darden '18 (D) Duke '18 (WL) Tepper '18 (A$)
GMAT 1: 730 Q50 V38
Schools: Kellogg '18 (D) Ross '18 (M) Darden '18 (D) Duke '18 (WL) Tepper '18 (A$)
GMAT 1: 730 Q50 V38
Posts: 31
Kudos: 21
If n > 2, then the sum, S, of the integers from 1 through n can be cal 07 Jan 2014, 23:54
Kudos
Add Kudos
Bookmarks
Bookmark this Post
S= n (n+1) /2 ,
Either n or n+1 , is even & also n > 2,
Thus after dividing by 2, S can be shown to be a product of two distinct numbers (not including 1) ----> S can never be prime . So D it is :-D
User avatar
jlgdr
User avatar
Joined: 06 Sep 2013
Last visit: 24 Jul 2015
Posts: 1,328
Own Kudos:
2,571
Given Kudos: 355
Concentration: Finance
Schools: Wharton '17 (A) HBS '17 (WA$)
Schools: Wharton '17 (A) HBS '17 (WA$)
Posts: 1,328
Kudos: 2,571
If n > 2, then the sum, S, of the integers from 1 through n can be cal 16 Feb 2014, 09:43
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If n > 2, then the sum, S, of the integers from 1 through n can be calculated by the following formula: S = n(n + 1)/2. Which one of the following statements about S must be true?
A. S is always odd.
B. S is always even.
C. S must be a prime number
D. S must not be a prime number
E. S must be a perfect square

Notice that we are asked "which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.

A. S is always odd --> not necessarily true if n=3 then 1+2+3=6=even.
B. S is always even --> not necessarily true if n=5 then 1+2+3+4+5=15=odd.
C. S must be a prime number --> not true if n=3 then 1+2+3=6=not prime.
E. S must be a perfect square --> not necessarily true if n=3 then 1+2+3=6=not a perfect square.

Only choice D is left.

Answer: D.

Does anyone know why can't the sum be a prime number?

So I began trying to understand this. First since all prime numbers greater than 3 are of the form 6k+1 or 6k-1
Now then let's take 1+6k, that means that 2+3+4......+n cannot be a multiple of 6, but i'm trying to figure out why this can't be true?

Thanks
Cheers
J

Bumpinggg
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 35,817
Own Kudos:
929
Posts: 35,817
Kudos: 929
If n > 2, then the sum, S, of the integers from 1 through n can be cal 21 Jul 2022, 09:19
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderator:
Bunuel
Math Expert
97874 posts