CUET UG 2025 — General Test Quantitative Reasoning

Two-digit numbers range from 10 to 99.

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The first two-digit number divisible by 3:

10 ÷ 3 is not a whole number

11 ÷ 3 is not a whole number

12 ÷ 3 = 4

The first two-digit number divisible by 3 is 12.

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The last two-digit number divisible by 3:

99 ÷ 3 = 33

The last two-digit number divisible by 3 is 99.

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The two-digit numbers divisible by 3 form the sequence: 12, 15, 18, 21, 24, ... 96, 99

Each number is 3 more than the previous one (common difference = 3).

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For a sequence with constant difference:

Number of terms $= \dfrac{\text{Last} - \text{First}}{\text{Common difference}} + 1$=Common differenceLast−First​+1

$$n = \dfrac{99 - 12}{3} + 1$$n=399−12​+1

$$n = \dfrac{87}{3} + 1$$n=387​+1

$$n = 29 + 1$$n=29+1

$$n = 30$$n=30

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Therefore, there are 30 two-digit numbers divisible by 3.

The answer is Option 1: 30