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

 It is currently 21 Aug 2019, 05:12

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

n is an integer from 1 to 50, what is the probability that n(n+1) is n

Author Message
TAGS:

Hide Tags

Intern
Joined: 10 Jul 2016
Posts: 44
n is an integer from 1 to 50, what is the probability that n(n+1) is n  [#permalink]

Show Tags

24 Jan 2017, 00:54
9
00:00

Difficulty:

85% (hard)

Question Stats:

51% (01:55) correct 49% (02:34) wrong based on 147 sessions

HideShow timer Statistics

n is an integer from 1 to 50, what is the probability that n(n+1) is not divisible by 4?

A. 12/25
B. 13/25
C. 14/25
D. 15/25
E. 16/25
Math Expert
Joined: 02 Aug 2009
Posts: 7755
Re: n is an integer from 1 to 50, what is the probability that n(n+1) is n  [#permalink]

Show Tags

24 Jan 2017, 05:33
2
3
siddharthsinha123 wrote:
n is an integer from 1 to 50, what is the probability that n(n+1) is not divisible by 4?

A. 12/25
B. 13/25
C. 14/25
D. 15/25
E. 16/25

For n(n+1) to be multiple of 4, either n or n+1 should be multiple of 4, as ONLY one of n or n+1 will be even and other will be ODD..

Till 50 , multiple of 4 are 50/4=12.25 so 12 multiples are there..
These 12 can be both n and n+1, so total 2*12=24..

Since n can take values from 1 to 50..
So n(n+1) will take 50 values..

Therefore ways when none of n and n+1 will be multiple of 4 is 50-24=26..
Prob of picking these =26/50=13/25

B
_________________
General Discussion
Math Expert
Joined: 02 Sep 2009
Posts: 57193
Re: n is an integer from 1 to 50, what is the probability that n(n+1) is n  [#permalink]

Show Tags

24 Jan 2017, 01:10
1
2
Senior SC Moderator
Joined: 14 Nov 2016
Posts: 1323
Location: Malaysia
n is an integer from 1 to 50, what is the probability that n(n+1) is n  [#permalink]

Show Tags

24 Jan 2017, 04:59
2
2
siddharthsinha123 wrote:
n is an integer from 1 to 50, what is the probability that n(n+1) is not divisible by 4?

A. 12/25
B. 13/25
C. 14/25
D. 15/25
E. 16/25

Multiples of x in the range = [ (Last multiple of x in the range - First multiple of x in the range ) / x ]+ 1

$$n = 4, 8, 12, 16, ..., 48$$

Multiples of x in the range = [ (48 - 4) / 4 ]+ 1 = 12

$$(n+1)$$ to be a multiples of 4, n must be 3, 7, 11, 15, ...., 47

$$n(n+1)$$ to be a multiple of 3, n can take 12 + 12 = 24 value

P = (favourable outcome) / (total number of outcomes)

P = 24 / 50

Probability that n(n+1) is not divisible by 4 = 1 - (24/50) = 13/25
_________________
"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 7412
Location: United States (CA)
Re: n is an integer from 1 to 50, what is the probability that n(n+1) is n  [#permalink]

Show Tags

27 Jan 2017, 10:31
siddharthsinha123 wrote:
n is an integer from 1 to 50, what is the probability that n(n+1) is not divisible by 4?

A. 12/25
B. 13/25
C. 14/25
D. 15/25
E. 16/25

We can use the following equation:

1 = P(n(n+1) is divisible by 4) + P(n(n+1) is NOT divisible by 4)

Thus:

P(n(n+1) is NOT divisible by 4) = 1 - P(n(n+1) is divisible by 4)

Let’s determine the probability that n(n+1) is divisible by 4. If n(n+1) is divisible by 4, then either n is divisible by 4 or n +1 is divisible by 4. Calculating the number of values of n divisible by 4 is the same as calculating the number of multiples of 4 between 1 and 50 inclusive. To calculate this, we can use this formula:

(largest multiple of 4 - smallest multiple of 4)/4 + 1

(48 - 4)/4 + 1

44/4 + 1 = 11 + 1 = 12

Thus, there are 12 multiples of 4 between 1 and 50 inclusive. That is, n can be any one of these 12 multiples of 4 so that n(n + 1) will be divisible by 4.

Similarly, if (n + 1) is a multiple of 4, n(n + 1) also will be divisible by 4. Since we know that there are 12 values of n that are multiples of 4, there must be another 12 values of n such that (n + 1) is a multiple of 4. Let’s expand on this idea:

When n = 3, n + 1 = 4, and thus n(n+1) is a multiple of 4.

When n = 23, n + 1 = 24, and thus n(n+1) is a multiple of 4.

When n = 47, n + 1 = 48, and thus n(n+1) is a multiple of 4.

We can see that there are 12 values of n that are multiples of 4, and 12 more values of n for (n + 1) to be a multiple of 4. Since there are 50 total integers from 1 to 50, inclusive, the probability of selecting a value of n so that n(n+1) is a multiple of 4 is:

24/50 = 12/25

Thus, the probability that n(n+1) IS NOT a multiple of 4 is 1 - 12/25 = 13/25.

_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Non-Human User
Joined: 09 Sep 2013
Posts: 12051
Re: n is an integer from 1 to 50, what is the probability that n(n+1) is n  [#permalink]

Show Tags

04 Aug 2019, 12:16
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.
_________________
Re: n is an integer from 1 to 50, what is the probability that n(n+1) is n   [#permalink] 04 Aug 2019, 12:16
Display posts from previous: Sort by