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Probability

by hey_thr67 » Fri Jun 29, 2012 2:29 am
If x is a randomly chosen integer between 1 and 20, inclusive, and y is a randomly chosen integer between 21 and 40, inclusive, what is the probability that xy is a multiple of 4?
(A) 1/4
(B) 1/3
(C) 3/8
(D) 7/16
(E) 1/2
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by Anurag@Gurome » Fri Jun 29, 2012 2:42 am
hey_thr67 wrote:If x is a randomly chosen integer between 1 and 20, inclusive, and y is a randomly chosen integer between 21 and 40, inclusive, what is the probability that xy is a multiple of 4?
Each group has 20 consecutive integers.
Hence, in each group there will be 20/2 = 10 even and 10 odd integers.
And, in each group there will be 20/4 = 5 multiples of 4.

There are three cases xy will NOT to be a multiple of 4:
  • 1. both x and y are odd --> 10*10 = 100 pairs
    2. x is odd and y is even but not multiple of 4 --> 10*5 = 50 pairs
    3. y is odd and x is even but not multiple of 4 --> 10*5 = 50 pairs

    Hence, a total of (100 + 50 + 50) = 200 pairs
Total number of possible values of xy = 20*20 = 400

Hence, required probability = 1 - (200/400) = 1 - 1/2 = 1/2

The correct answer is E.
Anurag Mairal, Ph.D., MBA
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