GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 20 Nov 2018, 09:49

LIVE NOW!

How to Quickly Solve GMAT Questions - Chat with ExamPAL. Join HERE!


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.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • All GMAT Club Tests are Free and open on November 22nd in celebration of Thanksgiving Day!

     November 22, 2018

     November 22, 2018

     10:00 PM PST

     11:00 PM PST

    Mark your calendars - All GMAT Club Tests are free and open November 22nd to celebrate Thanksgiving Day! Access will be available from 0:01 AM to 11:59 PM, Pacific Time (USA)
  • Free lesson on number properties

     November 23, 2018

     November 23, 2018

     10:00 PM PST

     11:00 PM PST

    Practice the one most important Quant section - Integer properties, and rapidly improve your skills.

If n > 2, then the sum, S, of the integers from 1 through n

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
avatar
Joined: 01 Aug 2011
Posts: 18
If n > 2, then the sum, S, of the integers from 1 through n  [#permalink]

Show Tags

New post 07 Jun 2012, 03:53
1
4
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

71% (01:11) correct 29% (00:56) wrong based on 189 sessions

HideShow timer Statistics

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
Manager
Manager
avatar
Joined: 19 Mar 2012
Posts: 154
Location: United States
Concentration: Finance, General Management
GMAT 1: 750 Q50 V42
GPA: 3.69
WE: Analyst (Mutual Funds and Brokerage)
Re: If n > 2, then the sum, S, of the integers  [#permalink]

Show Tags

New post 07 Jun 2012, 04:41
1
1
S does not necessarily have to be even. For example, when n=5, you have:

S = [(5)(5+1)]/2 = 15, an odd number
Current Student
User avatar
B
Joined: 28 Mar 2012
Posts: 316
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
GMAT ToolKit User
Re: If n > 2, then the sum, S, of the integers  [#permalink]

Show Tags

New post 07 Jun 2012, 04:49
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,
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50711
Re: If n > 2, then the sum, S, of the integers from 1 through n  [#permalink]

Show Tags

New post 07 Jun 2012, 13:26
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.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 02 Nov 2012
Posts: 31
Re: If n > 2, then the sum, S, of the integers from 1 through n  [#permalink]

Show Tags

New post 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!
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50711
Re: If n > 2, then the sum, S, of the integers from 1 through n  [#permalink]

Show Tags

New post 06 Nov 2012, 03:56
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.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Current Student
avatar
Joined: 12 Jan 2012
Posts: 23
GMAT 1: 720 Q49 V39
Re: If n > 2, then the sum, S, of the integers from 1 through n  [#permalink]

Show Tags

New post 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
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8574
Location: Pune, India
Re: If n > 2, then the sum,  [#permalink]

Show Tags

New post 06 Jan 2014, 20:49
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.

Spoiler: :: My 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.
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Current Student
avatar
Joined: 10 Oct 2013
Posts: 33
Concentration: Marketing, Entrepreneurship
GMAT 1: 730 Q50 V38
Re: If n > 2, then the sum, S, of the integers from 1 through n  [#permalink]

Show Tags

New post 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 :-D
SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1744
Concentration: Finance
GMAT ToolKit User
Re: If n > 2, then the sum, S, of the integers from 1 through n  [#permalink]

Show Tags

New post 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
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8863
Premium Member
Re: If n > 2, then the sum, S, of the integers from 1 through n  [#permalink]

Show Tags

New post 30 Oct 2018, 01:13
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: If n > 2, then the sum, S, of the integers from 1 through n &nbs [#permalink] 30 Oct 2018, 01:13
Display posts from previous: Sort by

If n > 2, then the sum, S, of the integers from 1 through n

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.