IPMAT Indore 2023 (MCQ) - If a three-digit number is chosen at random, what is the probability that it is divisible neither by 3 nor by 4? | PYQs + Solutions

IPMAT Indore 2023

Number System

Divisibility Rules

Medium

If a three-digit number is chosen at random, what is the probability that it is divisible neither by 3 nor by 4?

\frac{1}{4}

\frac{1}{2}

\frac{2}{3}

\frac{1}{3}

Correct Option: 2

Total 3 digit numbers

= 999-100+1 = 900

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Formula used:

[\text{highest}-\text{lowest}+1]

Every 3rd number is divisible by 3.

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\text{Probability(number not divisible by 3)} = \frac23

Every 4th number is divisible by 4.

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\text{Probability(number not divisible by 4)} = \frac34

Hence,

\dfrac23 \times \dfrac34 = \boxed{\frac12}