Quantitative Reasoning

Number System

Easy

How many two-digit numbers are divisible by 3?

✅ Correct Option: 1

Two-digit numbers range from 10 to 99.

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.

The last two-digit number divisible by 3:

99 ÷ 3 = 33

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

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).

For a sequence with constant difference:

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

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

$n = \dfrac{87}{3} + 1$

$n = 29 + 1$

$n = 30$

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

The answer is Option 1: 30

2025: 14 May Shift 2

Consider the following statements

(A) To obtain prime numbers less than 121, we have to reject all the multiples of 2, 3, 5 and 7.

(B) Every composite number less than 121 is divisible by a prime number less than 11.

(D) 7710312401 is divisible by 11.

Which of the statement(s) given above is/are correct?

Choose the correct answer from the options given below:

2026: 12 May Shift 2

Select the missing number from given options.

12	7	95
14	8	132
16	9	?

2022: 24 Aug Shift 1

Find the missing number in place of ? from the following given options.

2023: 24 May Shift 3

Given below are two statements:

Statement (I): All natural numbers are rational numbers.

Statement (II): 1 is the smallest prime number.

In the light of the above statements, choose the most appropriate answer from the options given below:

2022: 20 Aug Shift 1

Find the smallest among the following ?

$\sqrt[4]{6}, \sqrt{2}, \sqrt[3]{4}$ and $\sqrt{3}$

2022: 26 Aug Shift 1

Find the value of $\sqrt[3]{117649}$ =

How many two-digit numbers are divisible by 3?

Solution

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