GATE | GATE CS 2010 | Question 27

What is the probability that divisor of 1099 is a multiple of 1096?
(A) 1/625
(B) 4/625
(C) 12/625
(D) 16/625


Answer: (A)

Explanation: Following are multiples of 1096 which are also divisor of 1099

1096, 2×1096, 4×1096, 5×1096, 8×1096, 10×1096, 20×1096, 25×1096, 40×1096, 50×1096, 10×1096, 125×1096, 200×1096, 250×1096, 500×1096, 1000×1096

The total number of divisors of 1099 = 10000  (See http://www.math.cmu.edu/~mlavrov/arml/13-14/number-theory-09-29-13.pdf)



So the probability = 16/10000=1/625

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