Q36 / 57 · JEE Advanced 2021 (Paper 2) · Mathematics

A number is chosen at random from the set $\{1, 2, 3, \dots, 2000\}$ . Let $p$ be the probability that the chosen number is a multiple of 3 or $7$ . Then the value of $500 p$ is ____.

Correct answer: 214

Solution

Multiple of $3 = 3, 6, 9 \dots . 1998$ are $666$

Multiple of $7 = 7, 14 \dots . 1995$ are $285$

Multiple of $21 = 21, 42 \dots 1995$ are $95$

$p = \frac{666 + 285 - 95}{2000} = \frac{856}{2000} = \frac{214}{500} = p$

$500 p = 214$

Hence, the correct answer is 214.