Number System: Aptitude Questions with Answers
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?
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 $10x + y = 10 \times 6 + 3 = 63$.
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?
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 Two numbers have a product of 120, and their greatest common divisor (HCF) is 6. Find their least common multiple (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 remainder you will get when on dividing $2^{30}$ 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 Two consecutive even numbers, when squared and added together, give a total of 244. What are these two 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
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?
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 Consider a two-digit number where the sum of its digits equals 12, and their difference is 4. Find 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, it matches precisely 50% of the same number. What is this number that balances the equation?
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 Picture 3 raised to the 25th power, an enormous number! When this is divided by 5, what remainder do you think it leaves?
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,$3^{25} = (3^4)^6 \times 3 \equiv 1^6 \times 3 = 3 \mod 5$
Q. 11 Find the LCM for: 36 and 90
A) 360
B) 180
C) 540
D) 18
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
A) 120
B) 10
C) 40
D) 20
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
A) 390
B) 3
C) 12
D) 6
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 $3^ { 11 } +3^ { 12 } +3^ { 13 } =$
A) $13(3^{11})$
B) $17(3^{11})$
C) $19(3^{11})$
D) $13(3^{10})$
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 ?
A) 5050
B) 7500
C) 10500
D) 15000
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.
A) 1.02
B) 1.03
C) 2.03
D) 3.02
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 ?
A) Six
B) Seven
C) Eight
D) Nine
Check Solution
Ans: B
Refer Topic wise Questions with Solutions for Quantitative Aptitude
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