Problems on Numbers · Exercise 4 of 6
65 mixed-level problems on numbers in the style of campus placement tests (TCS, Infosys, Wipro, Accenture, Cognizant, Capgemini), SSC CGL/CHSL/MTS, RRB NTPC and Group D, IBPS/SBI, UPSC CSAT and state exams.
Which number must be added to 47 to give 100?
47 + x = 100
x = 53
Answer: 53
A two-digit number plus the sum of its digits equals 52. What is the number?
10a + b + a + b = 52 → 11a + 2b = 52
a = 4 → 2b = 8 → b = 4
(a = 2 would need b = 15 – not a digit)
Number = 44
Answer: 44
What is the sum of all the three-digit numbers that can be formed by using each of the digits 1, 2 and 3 exactly once?
There are 6 such numbers.
Each digit appears twice in every place.
Sum = 2 × (1 + 2 + 3) × 111 = 2 × 6 × 111 = 1,332
Answer: 1,332
A number is first increased by 10 and the result is then decreased by 10%. The final value is 81. What was the number?
(x + 10) × 0.9 = 81
x + 10 = 90
x = 80
Answer: 80
Three times the larger of two numbers exceeds five times the smaller by 3, and the numbers add up to 17. What is the larger number?
3L = 5S + 3 and L + S = 17
3(17 − S) = 5S + 3 → 51 − 3S = 5S + 3
8S = 48 → S = 6
L = 11
Answer: 11
The product of two numbers is 120. One of them is 8. What is the other?
Other = 120 ÷ 8
= 15
Answer: 15
The product of two numbers is 1,575 and the larger divided by the smaller is 9/7. What is their sum?
Let the numbers be 9k and 7k.
63k² = 1,575 → k² = 25 → k = 5
Numbers 45 and 35 → sum 80
Answer: 80
A two-digit number whose digits add up to 9 is 18 less than the square of that digit sum. What is the number?
Square of the digit sum = 9² = 81
Number = 81 − 18 = 63
Check: 6 + 3 = 9 ✔
Answer: 63
The sum of two numbers is 45 and their difference is one-ninth of their sum. What is the larger number?
Difference = 45 ÷ 9 = 5
Larger = (45 + 5) ÷ 2 = 25
Answer: 25
When a number is tripled and then decreased by 15, the result equals the number increased by 25. What is the number?
3x − 15 = x + 25
2x = 40
x = 20
Answer: 20
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