A number X is randomly selected from the set of all non-prime integers

Question

A number X is randomly selected from the set of all non-prime integers from 1 to 20 and a number a number Y is randomly selected from the set of all prime numbers from 1 to 20. What is the sum of the probability that product of X and Y is divisible by 7 and the probability that the product of X and Y is divisible by 2?

A. 19/96
B. 25/96
C. 7/12
D. 47/48
E. 1

A. 19/96
B. 25/96
C. 7/12
D. 47/48
E. 1

chetan2u · Answer

There are 8 primes and 12 non primes in first 20 positive integers.

Case I: Probability of product XY to be a multiple of 7.
When X is 14, Y could be any of the 8…….8 ways
When Y is 7, X could be any of the 12…….12 ways
One is common in the above cases when X is 14 and Y is 7, so subtract 1. 
Total ways = 12*8 = 96
P=  \frac{8+12-1}{96}=\frac{19}{96}

Case II: Probability of product XY to be a multiple of 2.
When X is any of evens less 2, Y could be any of the 8…….9*8 ways
When Y is 2, X could be any of the 12…….12 ways
9 are common in the above cases when X is any even till 20 and Y is 2, so subtract 9. 
Total ways = 12*8 = 96
P=  \frac{72+12-9}{96}=\frac{75}{96}

SUM of Ps =  \frac{19}{96}+\frac{75}{96}=\frac{94}{96}=\frac{47}{48}

D

Azeem123 · Answer

I did with the same method but i took total number of cases as 20c2. Can you explain what am I missing here?

Bunuel · Answer

You’re treating it as if you are choosing 2 numbers out of 20, but that’s not what the problem says. Using 20C2 would allow pairs like (4,6) or (2,3), which are both from the same group, and these are not allowed. You are choosing X from the non-primes (12 options) and Y from the primes (8 options). So the total number of outcomes is 12 * 8 = 96, not 20C2.

glagad · Answer

I wonder how is "1" treated in such scenarios. The traditional definition says 1 is neither prime nor composite.

I dont know whether this is a concept tested in GMAT. But definitely spent a few seconds thinking through it while solving this question.

Thoughts?  Bunuel   chetan2u

Bunuel · Answer

1 is neither prime nor composite. But how is this confusing for this question? 1 falls into the non-prime category for this question.

glagad · Answer

Sorry, my bad. I mis-equated non-prime as composite.

A number X is randomly selected from the set of all non-prime integers

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GMAT Problem Solving (PS) Questions

A number X is randomly selected from the set of all non-prime integers

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