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

 It is currently 25 Jun 2019, 23:22

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

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

For how many integers n, such that 2≤n≤80, [m][fraction](n-1)*n*(n+1)/

Author Message
TAGS:

Hide Tags

Director
Joined: 19 Oct 2018
Posts: 560
Location: India
For how many integers n, such that 2≤n≤80, [m][fraction](n-1)*n*(n+1)/  [#permalink]

Show Tags

26 May 2019, 17:47
3
00:00

Difficulty:

55% (hard)

Question Stats:

31% (01:36) correct 69% (02:25) wrong based on 16 sessions

HideShow timer Statistics

For how many integers n, such that 2≤n≤80, $$\frac{(n-1)*n*(n+1)}{8}$$ is an integer.

A. 9
B. 29
C. 40
D. 49
E. 59
ISB School Moderator
Joined: 08 Dec 2013
Posts: 457
Location: India
Concentration: Nonprofit, Sustainability
GMAT 1: 630 Q47 V30
WE: Operations (Non-Profit and Government)
Re: For how many integers n, such that 2≤n≤80, [m][fraction](n-1)*n*(n+1)/  [#permalink]

Show Tags

26 May 2019, 18:09
nick1816 wrote:
For how many integers n, such that 2≤n≤80, $$\frac{(n-1)*n*(n+1)}{8}$$ is an integer.

A. 9
B. 29
C. 40
D. 49
E. 59

I started putting random numbers to find a pattern so that I can extrapolate.

I observed that for every (n-1)*n*(n+1) where n is a multiple of 8 the function f(n) is perfectly divisible by 8.
Also, n that is odd, f(n) is also perfectly divisible by 8.

So, there are 10 multiples of 8 between [2,80].
And there are 39 odd numbers between [2,80].
So possible values of n (Integers) 49, IMO D
_________________
Kindly drop a '+1 Kudos' if you find this post helpful.

GMAT Math Book

-I never wanted what I gave up
I never gave up what I wanted-
Senior Manager
Joined: 20 Jul 2017
Posts: 341
For how many integers n, such that 2≤n≤80, [m][fraction](n-1)*n*(n+1)/  [#permalink]

Show Tags

26 May 2019, 19:48
nick1816 wrote:
For how many integers n, such that 2≤n≤80, $$\frac{(n-1)*n*(n+1)}{8}$$ is an integer.

A. 9
B. 29
C. 40
D. 49
E. 59

(n-1)*n*(n+1) is a product of 3 consecutive integers.

So, it can be of 2 types
1. even*odd*even
2. Odd*even*odd

Case1: even*odd*even
If one even number is a multiple of 2, the next even number will definitely be a multiple of 4.
Eg: 2*3*4, 10*11*12 etc..

So, number if possible values of n are
3, 5, . . . . 79.

To find number of terms of Arithmetic Progression, use Last term
79 = 3 + (n-1)2
n = 39.

Case2: Odd*even*odd
In this case, the even number SHOULD be a multiple of 8 as the other 2 numbers are odd.
So, favourable values are just the number of multiples of 8 from 2≤n≤80 which are 10 values.

So, total values of n = 39 + 10 = 49

IMO D.

Posted from my mobile device
Manager
Joined: 20 Mar 2018
Posts: 99
Location: Ghana
Concentration: Finance, Real Estate
For how many integers n, such that 2≤n≤80, [m][fraction](n-1)*n*(n+1)/  [#permalink]

Show Tags

26 May 2019, 22:52
(n-1)n(n+1)/8=Integer , where 2<=n=<80

(n^2-1)n/8=Integer ,True only when
(1) n=odd. e.g. (7^2-1)(7)/8=Integer
(2) (n^2-1)n is a multiple of 8 e.g. (8^2-1)8/8 =Integer

Odd numbers =(80-2)/2 =39
Multiples of 8 = (80-8)/8 +1 =10
Therefore total number of integers is 49

Posted from my mobile device
For how many integers n, such that 2≤n≤80, [m][fraction](n-1)*n*(n+1)/   [#permalink] 26 May 2019, 22:52
Display posts from previous: Sort by