Which of the following is a perfect cube?
Explanation:
Check each option: 125 = 5³ (perfect cube) ✓, 100 = 10² (not a perfect cube), 144 = 12² (not a perfect cube), 200 = 8 × 25 (not a perfect cube). Answer is 125.
Find the HCF of 48, 64, and 80.
Explanation:
Prime factorization: 48 = 2⁴ × 3, 64 = 2⁶, 80 = 2⁴ × 5. HCF is the product of lowest powers of common prime factors. Only 2 is common to all. Lowest power of 2 is 2⁴ = 16. Therefore, HCF = 16.
If the sum of digits of a number is divisible by 3, then the number is divisible by 3. Which of the following is divisible by 3?
Explanation:
Check sum of digits: 121: 1+2+1 = 4 (not divisible by 3), 122: 1+2+2 = 5 (not divisible by 3), 123: 1+2+3 = 6 (divisible by 3) ✓, 124: 1+2+4 = 7 (not divisible by 3). Therefore 123 is divisible by 3.
Find the value of (2⁵ × 3⁴)/(2³ × 3²).
Explanation:
Using exponent rules: (2⁵ × 3⁴)/(2³ × 3²) = 2^(5-3) × 3^(4-2) = 2² × 3² = 4 × 9 = 36.
A shopkeeper marks goods 40% above cost price and gives a discount of 20%. What is his profit percentage?
Explanation:
SP = MP × (100-discount%)/100 = CP × 1.4 × 0.8 = 1.12CP. Profit% = 12%
A man travels 120 km in 8 hours. If he increases his speed by 25%, how much distance will he cover in 5 hours?
A
75 km
B
93.75 km
C
100 km
D
112.5 km
Correct Answer:
B. 93.75 km
Explanation:
Original speed = 120/8 = 15 km/h. New speed = 15 × 1.25 = 18.75 km/h. Distance in 5 hours = 18.75 × 5 = 93.75 km
Two pipes A and B can fill a tank in 10 hours and 15 hours respectively. If both pipes are opened together, in how many hours will the tank be filled?
A
5 hours
B
6 hours
C
7.5 hours
D
8 hours
Correct Answer:
B. 6 hours
Explanation:
Combined rate = 1/10 + 1/15 = 5/30 = 1/6. Time = 6 hours
A boat travels 60 km downstream in 4 hours and 60 km upstream in 6 hours. What is the speed of the current?
A
2.5 km/h
B
5 km/h
C
7.5 km/h
D
10 km/h
Correct Answer:
A. 2.5 km/h
Explanation:
Downstream speed = 15 km/h, Upstream speed = 10 km/h. Current = (15-10)/2 = 2.5 km/h
If 30% of a number is 120, what is 25% of that number?
Explanation:
Number = 120/0.30 = 400. 25% of 400 = 100
A train 150m long takes 12 seconds to pass a pole. What is its speed in km/h?
A
36 km/h
B
45 km/h
C
54 km/h
D
60 km/h
Correct Answer:
B. 45 km/h
Explanation:
Speed = Distance/Time = 150/12 = 12.5 m/s = 12.5 × 3.6 = 45 km/h
