Quantitative Reasoning

Number System

Easy

What is the remainder when the number $(44)^2$ is divided by 9?

✅ Correct Option: 1

To find the remainder when $(44)^2$ is divided by 9, find what remainder 44 gives when divided by 9.

Dividing 44 by 9:

$9 \times 4 = 36$

$44 - 36 = 8$

So 44 leaves remainder 8 when divided by 9.

When finding remainders, 44 can be replaced with 8 (its remainder) to get the same final answer.

Square this remainder:

$8^2 = 64$

Find the remainder when 64 is divided by 9.

Dividing 64 by 9:

$9 \times 7 = 63$

$64 - 63 = 1$

So 64 leaves remainder 1 when divided by 9.

The remainder of a square equals the square of the remainder.

Remainder of $(44)^2 \div 9$ = Remainder of $(8)^2 \div 9$ = Remainder of $64 \div 9 = 1$

Therefore, the remainder is 1.

2022: 20 Aug Shift 1

What is the smallest number of five digits formed by using the digits 2, 4, 0, 3, 5 ?

2023: 1 June Shift 1

Which of the following is correct for divisibility?

(1) A number is divisible by 6 if it is divisible by 3 or 2.

(2) A number is divisible by 5 if its unit digit is 0 or 5.

(3) A number is divisible by 3 if its unit digit is divisible by 3.

(4) A number is divisible by 4 if the number formed by its last two digits is divisible by 4.

Choose the correct answer from the options given below:

2025: 20 May Shift 2

How many two-digit numbers are divisible by 3?

2022: 17 Aug Shift 1

The value of $\frac{(8.9)^2 - (2.1)^2}{8.9 - 2.1}$

2026: 29 May Shift 2

Find the sum of the first n positive integers.

2026: 20 May Shift 1

Match List-I with List-II

Choose the correct answer from the options given below:

What is the remainder when the number (44)2(44)^2(44)2 is divided by 9?