Latest GMAT Aptitude Question SOLUTION: Set S is the set of all prime integers between 0 and 20. If three numbers are chosen randomly from set S and each number can be chosen only once, what is the positive difference be

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(#M40023918) GMAT Numerical Ability question Keep an EYE

Set S is the set of all prime integers between 0 and 20. If three numbers are chosen randomly from set S and each number can be chosen only once, what is the positive difference between the probability that the product of these three numbers is a number less than 31 and the probability that the sum of these three numbers is odd?
(A) 1/336
(B) 1/2
(C) 17/28
(D) 3/4
(E) 301/336

Asked In GMAT rajesh (10 years ago)

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rohan chawla  (10 years ago)

answer is c i.e 17/28

there are 8 prime numbers in s that are 2,3,5,7,11,13,17,19
now the three numbers whose product is less than 31 are 2,3,5
so the number of ways of taking these numbers in a group of 3 is 1
total number of ways of taking 3 numbers from 8 numbers is 8c3 = 56
so probability that a product of three numbers is less than 31 is 1/56
let it be p1
p1= 1/56

now for sum to be odd we have to take all three numbers as odd that is we should not take 2
this can be found by finding the ways in which 2 appears and subtracting it from total number of ways
now if 2 occurs then remaining two numbers can be selected in 7c2 ways = 21 ways
so number of ways in which 2 not occurs is 8c3-7c2 = 56-21 = 35
so probability that sum is odd is 35/56
let it be p2
p2= 35/56
difference between these two probabilities is 35/56-1/56 = 34/56 = 17/28
so the answer is 17/28

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