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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

If n > 2, then the sum, S, of the integers from 1 through n [#permalink]
07 Jun 2012, 03:53

1

This post received KUDOS

3

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

35% (medium)

Question Stats:

66% (02:11) correct
34% (00:42) wrong based on 109 sessions

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)

Re: If n > 2, then the sum, S, of the integers from 1 through n [#permalink]
07 Jun 2012, 13:26

Expert's 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.

Re: If n > 2, then the sum, S, of the integers from 1 through n [#permalink]
06 Nov 2012, 03:43

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!

Re: If n > 2, then the sum, S, of the integers from 1 through n [#permalink]
06 Nov 2012, 03:56

Expert's post

KevinBrink wrote:

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. _________________

Re: If n > 2, then the sum, S, of the integers from 1 through n [#permalink]
06 Jan 2013, 00:05

shreya717 wrote:

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

If n > 2, then the sum, [#permalink]
06 Jan 2014, 20:36

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.

Re: If n > 2, then the sum, [#permalink]
06 Jan 2014, 20:49

Expert's post

akankshasoneja wrote:

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.

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. _________________

Re: If n > 2, then the sum, [#permalink]
07 Jan 2014, 01:54

Expert's post

akankshasoneja wrote:

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.

Re: If n > 2, then the sum, S, of the integers from 1 through n [#permalink]
07 Jan 2014, 22:54

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

Re: If n > 2, then the sum, S, of the integers from 1 through n [#permalink]
16 Feb 2014, 08:43

Bunuel wrote:

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

gmatclubot

Re: If n > 2, then the sum, S, of the integers from 1 through n
[#permalink]
16 Feb 2014, 08:43

Hello everyone! Researching, networking, and understanding the “feel” for a school are all part of the essential journey to a top MBA. Wouldn’t it be great... ...

As part of our focus on MBA applications next week, which includes a live QA for readers on Thursday with admissions expert Chioma Isiadinso, we asked our bloggers to...