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The question is from Permutation and Combination. A question which combines number theory and probability. We need to find out the probabilty of a multiple of 7 being a multiple of 5. This section hosts a number of questions which are on par with CAT questions in difficulty on CAT Permutation and Combination, and CAT Probability.

Question 19: N is a 3-digit number that is a multiple of 7; what is the probability that it will be a multiple of 5?

  1. \\frac{1}{5}\\)
  2. \\frac{11}{54}\\)
  3. \\frac{13}{64}\\)
  4. \\frac{13}{66}\\)

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Explanatory Answer

Method of solving this CAT Question from Permutation and Combination: A combination of Probability and Number Theory gives a perfect question.

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 \\frac{26}{128}\\) = \\frac{13}{64}\\)

The question is "what is the probability that it will be a multiple of 5?"

Hence the answer is "\\frac{13}{64}\\)"

Choice C is the correct answer.


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