Aptitude Questions on Numbers for Placements
Welcome to our practice page dedicated to helping you ace Numbers questions for placement aptitude tests! This page is packed with carefully crafted questions designed to build your skills in solving a range of questions. Practice, review solutions, and keep challenging yourself. With consistent practice, you’ll develop a solid foundation to handle any Numbers problem that comes your way!
Q. 1 If the sum of the digits of a two-digit number is 9 and the difference between the digits is 3, what is the number?
A) 63
B) 36
C) 54
D) 45
Check Solution
Ans: A) 63
Let the number be 10x+y , where x is the tens digit and y is the units digit.
Given:
- x+y=9
- x−y=3
Add the equations: $2x = 12 \Rightarrow x = 6$
Substitute x=6 into x+y=9 : y=3
The number is $10x + y = 10 \times 6 + 3 = 63$.
Q. 2 Find a number such that when 15 is subtracted from 7 times the number, the result is equal to 10 more than twice the number.
A) 5
B) 6
C) 7
D) 8
Check Solution
Ans: A) 5
Let the number be x.
Given: 7x−15=2x+10
Rearrange to solve for x : $5x = 25 \Rightarrow x = 5$
Q. 3 The product of two numbers is 120, and their HCF is 6. What is their LCM?
A) 20
B) 30
C) 40
D) 50
Check Solution
Ans: A) 20
We know: Product of two numbers=$ \text{HCF} \times \text{LCM}$
Thus,$120 = 6 \times \text{LCM} \Rightarrow \text{LCM} = 20$
Q. 4 What is the remainder when $2^{30}$ is divided by 5?
A) 1
B) 2
C) 3
D) 4
Check Solution
Ans: D) 4
By Fermat’s Little Theorem, $2^4 \equiv 1 \mod 5$
Thus, $2^{30} = (2^4)^7 \times 2^2 \equiv 1^7 \times 4 = 4 \mod 5$
Q. 5 The sum of the squares of two consecutive even numbers is 244. What are the numbers?
A) 10, 12
B) 12, 14
C) 14, 16
D) 16, 18
Check Solution
Ans: A) 10, 12
Let the two consecutive even numbers be x and x+2
Given: $x^2 + (x + 2)^2 = 244$
Expanding and simplifying: $2x^2 + 4x + 4 = 244 \Rightarrow x^2 + 2x – 120 = 0$
Solving the quadratic, we get x=10
The numbers are 10 and 12
Q. 6 If 40% of a number is added to 25, the result is the same as 60% of the number. What is the number?
A) 50
B) 60
C) 75
D) 125
Check Solution
Ans: D) 125
Let the number be x
Given: 0.4x+25=0.6x
Rearrange to solve for x : $25 = 0.2x \Rightarrow x = 125$
Q. 7 If the sum of the digits of a two-digit number is 12 and the difference between the digits is 4, what is the number?
A) 48
B) 39
C) 84
D) 57
Check Solution
Ans: C) 84
Let the two-digit number be 10x+y , where x is the tens digit and y is the units digit.
Given:
- x+y=12
- x−y=4
Adding these equations:$2x = 16 \Rightarrow x = 8$
Substitute x=8 into x+y=12 : y=4
The number is $10 \times 8 + 4 = 84$
Q. 8 If 30% of a number is added to 40, the result is the same as 50% of the number. What is the number?
A) 60
B) 80
C) 100
D) 200
Check Solution
Ans: D) 200
Let the number be x
Given : $0.3x+40=0.5x$
Rearrange to solve for x : $40 = 0.2x \Rightarrow x = 200$
Q. 9 The product of two numbers is 180, and their HCF is 6. What is their LCM?
A) 30
B) 36
C) 60
D) 45
Check Solution
Ans: A) 30
We know : Product of two numbers=$ \text{HCF} \times \text{LCM}$
Thus,$180 = 6 \times \text{LCM} \Rightarrow \text{LCM} = 30$
Q. 10 What is the remainder when $3^{25}$ is divided by 5?
A) 1
B) 2
C) 3
D) 4
Check Solution
Ans: C) 3
By Fermat’s Little Theorem, $3^4 \equiv 1 \mod 5$.
Thus,$3^{25} = (3^4)^6 \times 3 \equiv 1^6 \times 3 = 3 \mod 5$
Practice Questions for next topic: https://www.learntheta.com/aptitude-questions-algebra/
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