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.
Twice a number is 45 more than half of it. What is the number?
2x − x/2 = 45
3x/2 = 45
x = 30
Answer: 30
The sum of two numbers is 9 and the difference of their squares is 27. What is the larger number?
a² − b² = (a + b)(a − b) = 27
9(a − b) = 27 → a − b = 3
Larger = (9 + 3) ÷ 2 = 6
Answer: 6
A and B together have ₹ 110. Two-fifths of A's money equals one-third of B's money. How much does B have?
2A/5 = B/3 → 6A = 5B → A : B = 5 : 6
B = 110 × 6/11 = 60
Answer: ₹ 60
20% of a number plus 30 equals 50% of the number. What is the number?
0.2x + 30 = 0.5x
30 = 0.3x
x = 100
Answer: 100
The product of three consecutive even numbers is 4,032. What is the middle number?
∛4,032 ≈ 15.9, so try 14 × 16 × 18 = 4,032 ✔
Middle = 16
Answer: 16
A number divided by 9 gives 12. What does the number give when divided by 4?
Number = 9 × 12 = 108
108 ÷ 4 = 27
Answer: 27
For how many two-digit numbers is the sum of the number and the number formed by reversing its digits a perfect square?
Number + reverse = 11(a + b)
For 11(a + b) to be a perfect square, a + b must be 11 (a + b ≤ 18)
Two-digit numbers with digit sum 11: 29, 38, 47, 56, 65, 74, 83, 92
Count = 8
Answer: 8
If 7 is subtracted from 5 times a number, the result is 3 more than 3 times the number. What is the number?
5x − 7 = 3x + 3
2x = 10
x = 5
Answer: 5
One number is 80% of another, and their sum is 252. What is the smaller number?
Let the larger be x; smaller = 0.8x
1.8x = 252 → x = 140
Smaller = 112
Answer: 112
Five consecutive natural numbers add up to 100. What is the product of the smallest and the largest?
Middle = 100 ÷ 5 = 20
Numbers: 18, 19, 20, 21, 22
Product = 18 × 22 = 396
Answer: 396
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