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NDA 2023 Maths · Mathematics · Probability · medium

A two-digit number is chosen at random. The probability that it is a multiple of 7 is

Single correct option

A two-digit number is chosen at random. The probability that it is a multiple of 77 is
  1. A. 745\dfrac{7}{45}
  2. B. 17\dfrac17
  3. C. 215\dfrac{2}{15}
  4. D. 1390\dfrac{13}{90}
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Answer: (D) 1390\dfrac{13}{90}

There are 9090 two-digit numbers (1010 to 9999). The multiples of 77 among them are 14,21,…,9814,21,\ldots,98, which is 98−147+1=13\dfrac{98-14}{7}+1=13 numbers. The probability is 1390\dfrac{13}{90}. The value 745=1490\dfrac{7}{45}=\dfrac{14}{90} counts one extra multiple (such as 77 or an end point error).
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Original question written in the NDA 2023 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake