Number System: Aptitude Questions with Answers – Free Practice!

Review Concepts for Number System

Q. 1 Imagine a two-digit number where the sum of its digits equals 9. Furthermore, the difference between these digits is 3. What is the number?

Check Solution

Ans: A) 63

Let the number be 10x+y , where x is the tens digit and y is the units digit.

Given:

1. x+y=9
2. x−y=3

Add the equations: $2x = 12 \Rightarrow x = 6$

Substitute x=6 into x+y=9 : y=3

The number is $10x + y = 10 \times 6 + 3 = 63$.

An essential problem-solving checklist worth reading to solve such questions.

Q. 2 Think of a number such that when 15 is subtracted from seven times the number, the result equals 10 more than twice the number. What could this magical number be?

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 Two numbers have a product of 120, and their greatest common divisor (HCF) is 6. Find their least common multiple (LCM)?

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 remainder you will get when on dividing $2^{30}$ by 5?

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 Two consecutive even numbers, when squared and added together, give a total of 244. What are these two numbers?

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

A quick guide to avoid common mistakes in such questions.

Q. 6 If 40% of a number is added to 25, the result matches exactly 60% of the same number. What is this number?

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 Consider a two-digit number where the sum of its digits equals 12, and their difference is 4. Find the number:

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:

1. x+y=12
2. 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, it matches precisely 50% of the same number. What is this number that balances the equation?

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?

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 Picture 3 raised to the 25th power, an enormous number! When this is divided by 5, what remainder do you think it leaves?

Check Solution

Ans: C) 3

By Fermat’s Little Theorem, $3^4 \equiv 1 \mod 5$.

Thus,$3^{25} = (3^4)^6 \times 3 \equiv 1^6 \times 3 = 3 \mod 5$

Q. 11 Find the LCM for: 36 and 90

Check Solution

Ans: B

Factorize 36 as 2 * 18, and 90 as 5 * 18. So LCM becomes = 2 * 5 * 18

Q. 12 Find the HCF for: 40 and 60

Check Solution

Ans: D

40 can be written as = 2 * 20 while 60 can be written as 3 * 20. So HCF must be 20

Q. 13 Find the HCF for: 78 and 30

Check Solution

Ans: D

78 can be written as = 13 * 6 while 30 can be written as 5 * 6. So HCF must be 6

Q. 14 $3^ { 11 } +3^ { 12 } +3^ { 13 } =$

Check Solution

Ans: A

Q. 15 The sum of the first 50 positive even integers is 2,550 . What is the sum of the odd integers from 101 to 200 , inclusive ?

Check Solution

Ans: B

Q. 16 The ages of Alice and her mother have a ratio of 1:2, and the ages of Alice and her father have a ratio of 1:3 when Alice was born. Currently, Alice is 10 years old. Determine the ratio between the ages of Alice’s mother and father now.

Check Solution

Ans: C

Refer to common word problem scenarios

Q. 17 If n=3 * 4 * p where p is a prime number greater than 3 , how many different positive non-prime divisors does n have , excluding 1 and n ?

Check Solution

Ans: B

Refer Topic wise Questions with Solutions for Quantitative Aptitude

Refer Questions for Algebra

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