GATE | Sudo GATE 2020 Mock III (24 January 2019) | Question 51

N is a three digit number that is multiple of 7, then the probability that it will be a multiple of 5 is ____________ .
(A) 13 / 64
(B) 25 / 64
(C) 13 / 128
(D) None of these.

Answer: (A)
Explanation: N is a three digit multiple of 7.
N could be 105, 112, 119, 126…..994.
Or, 15 * 7, 16 * 7…..142 * 7.
Or there are 142–14 = 128 numbers.

Within these we need to locate the multiples of 5.
Or, we need to isolate multiples of 35.
Or, we need to see how many numbers there are in the list 105, 140, 175…..980.
35 * 3, 35 * 4…35 * 28…
Or, there are 26 such numbers.
Probability 26 / 128 = 13 / 64
The question is “what is the probability that it will be a multiple of 5 ?”

Hence the answer is “13 / 64”.

Option (A) is correct.
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