Aptitude Questions on Numbers
Review Concepts for Numbers
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 $10x + y = 10 \times 6 + 3 = 63$.
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
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,$3^{25} = (3^4)^6 \times 3 \equiv 1^6 \times 3 = 3 \mod 5$
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