prbability

Expert replies

gmatnmein2010: Master | Next Rank: 500 Posts; Posts: 185; Joined: Thu Feb 04, 2010 3:06 am; Thanked: 6 times

by gmatnmein2010 » Sat Feb 06, 2010 12:25 am

If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?
A) 1/4
B) 3/8
C) 1/2
D) 5/8
E) 3/4

Like this post

Source: Beat The GMAT — Problem Solving | Sat Feb 06, 2010 12:25 am

ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Sat Feb 06, 2010 1:07 am

gmatnmein2010 wrote:If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?
A) 1/4
B) 3/8
C) 1/2
D) 5/8
E) 3/4

If the number divided by 8 leaves a remainder of

a) 1

n is odd, so is n+2; n+1 is not divisible by 8 => n(n + 1)(n + 2) is not divisible by 8

b) 2
n is even; so is n+2; n+2 is a multiple of 4 => n(n + 1)(n + 2) is divisible by 8

c) 3
n is odd, so is n+2; n+1 is not divisible by 8 => n(n + 1)(n + 2) is not divisible by 8

d) 4
n is even; so is n+2; n is a multiple of 4 => n(n + 1)(n + 2) is divisible by 8

e) 5
n is odd, so is n+2; n+1 is not divisible by 8 => n(n + 1)(n + 2) is not divisible by 8

f) 6
n is even; so is n+2; n+2 is a multiple of 8 => n(n + 1)(n + 2) is divisible by 8

g) 7
n is odd, so is n+2; n+1 is divisible by 8 => n(n + 1)(n + 2) is divisible by 8

f) 8
n is even; so is n+2; n is a multiple of 8 => n(n + 1)(n + 2) is divisible by 8

Now since 96 is a multiple of 8 there is an equal probability of one these cases happening

Probability = 5/8

Always borrow money from a pessimist, he doesn't expect to be paid back.

Like this post

shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Sat Feb 06, 2010 1:21 am

If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?
A) 1/4
B) 3/8
C) 1/2
D) 5/8
E) 3/4

For this question we start with two conditions for n(n+1)(n+2)
1st condition: if n is odd,
so n+1 is even and n+2 is odd so n(n+1)(n+2) is divisble by 8 only if n+1 is multiple of 8,
total no. of such values = 12(8,16,.....96).
2nd conditon: if n is even,so n+1 is ODD and n+2 is EVEN
so either n is divisble by 4 or not divisible by 4.
i) if n is divisible by 4, n+2 is surely divisible by 2 as it is even. (e.g. 4,5,6)
ii) if n is divisble by 2 and not by 4, then also n+2 is surely divisble by 4 (e.g. 6,7,8)
thus for all n for 2nd condition is true ..hence total no. of such values = 96/2 = 48

so total no. of n(n+1)(n+2) divisible by 8 = 48+12=60

Hence, probability = 60/98 = 5/8. so ans is D.

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review