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Probability to chose numbers

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Probability to chose numbers

by yourshail123 » Sat Nov 10, 2012 10:57 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

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by pemdas » Sat Nov 10, 2012 11:10 am
yourshail123 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

#GMAT Prep Question Bank set - Difficulty=Hard question.
n(n+1)(n+2) must be divisible by 2^3
96 contains 48 twos (96/2=48), each two added by two gives 2^2 (n+2 or 2+2)). Also consider 7, 15, 23, 31 ... or 96/8=12 numbers which are factored by 8 with less 1 value. Hence the required probability is (48+12)/96=60/96=5/8

answer d)
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by yourshail123 » Sat Nov 10, 2012 11:19 am
Thank you!!
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by eaakbari » Sat Nov 10, 2012 11:38 am
yourshail123 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

#GMAT Prep Question Bank set - Difficulty=Hard question.
What is the correct answer.

IMO A

Between 1 and 96 there are 12 multiples of 8

Hence probability of choosing n to be a multiple of 8 is 12/96 = 1/12

Since the given function is n(n+1)(n+2), the probability of picking n which is a multiple of 8 is

3 x 1/12

= 1/4

Hence A.

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by GMATGuruNY » Sat Nov 10, 2012 7:59 pm
If n is an integer from 1 to 96 (inclusive), what is the probability that n*(n+1)*(n+2) is divisible by 8?

A.1/4
B.1/2
C.5/8
D.7/8
E.3/4
Case 1: n(n+1)(n+2) = even*odd*even = multiple of 8:
Since every other even integer is a multiple of 4, the product here will always include an even integer and a multiple of 4, resulting in a multiple of 8.
Thus, n can be any even integer between 1 and 96.
96/2 = 48 favorable choices for n.

Case 2: n+1 is a multiple of 8:
The product will be a multiple of 8 if n+1 is a multiple of 8.
Number of multiples of 8 between 1 and 96 = 96/8 = 12.
Thus, there are 12 favorable choices for n+1, implying that there are 12 more favorable choices for n.

Total favorable choices for n = 48+12 = 60.
Favorable choices/Total choices = 60/96 = 5/8.

The correct answer is C.
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