1
What is the LCM of 12 and 18?
Correct answer: B. 36
Prime factors: 12 = 2² × 3 and 18 = 2 × 3². LCM takes the highest powers: 2² × 3² = 36.
easy
Basic Arithmetic and Algebra MCQs
Solved Basic Arithmetic and Algebra MCQs: LCM/HCF, fractions, squares and roots, simple equations, simple interest, time and work, and speed.
26 MCQsUpdated 27 October 2026
This set covers the arithmetic and algebra that every competitive test begins with: LCM and HCF, squares, cubes and roots, simple equations, fractions, interest, work and speed, and quick number facts.
Every answer includes the working, so you can check the method as well as the result. Time yourself: most of these questions should take under a minute once the method is familiar.
- 2
What is the HCF of 48 and 72?
Correct answer: C. 24
48 = 2⁴ × 3 and 72 = 2³ × 3². HCF takes the lowest powers: 2³ × 3 = 24.
easy - 3
The product of two numbers is 216 and their HCF is 6. What is their LCM?
Correct answer: D. 36
For any two numbers, HCF × LCM = product. LCM = 216 ÷ 6 = 36.
medium - 4
What is the square root of 1,764?
Correct answer: C. 42
42 × 42 = 1,764, so √1,764 = 42.
medium - 5
What is the value of 15²?
Correct answer: A. 225
15² means 15 × 15 = 225. A quick shortcut for squaring numbers ending in 5: multiply the first digit by the next number (1 × 2 = 2), then write 25 after it, giving 225.
Read detailseasy - 6
What is the cube of 6?
Correct answer: B. 216
6³ = 6 × 6 × 6 = 216.
easy - 7
Solve for x: 3x + 7 = 31
Correct answer: D. 8
Subtract 7: 3x = 24. Divide by 3: x = 8.
easy - 8
Solve for x: 5x − 4 = 2x + 11
Correct answer: A. 5
Move terms: 5x − 2x = 11 + 4, so 3x = 15 and x = 5.
easy - 9
If x/4 + 3 = 8, what is x?
Correct answer: A. 20
Subtract 3: x/4 = 5. Multiply by 4: x = 20.
easy - 10
The sum of two numbers is 20 and their difference is 4. What is the larger number?
Correct answer: A. 12
Adding the equations x + y = 20 and x − y = 4 gives 2x = 24, so x = 12 (the other number is 8).
easy - 11
Simplify: 3/4 + 2/3
Correct answer: A. 17/12
Common denominator 12: 9/12 + 8/12 = 17/12 (that is 1 5/12).
easy - 12
What is 2/5 of 3/4?
Correct answer: A. 3/10
Multiply: (2 × 3) ÷ (5 × 4) = 6/20 = 3/10.
easy - 13
Which fraction is the largest: 3/5, 5/8, 2/3, 7/12?
Correct answer: C. 2/3
As decimals: 3/5 = 0.6, 5/8 = 0.625, 2/3 ≈ 0.667, 7/12 ≈ 0.583. The largest is 2/3.
medium - 14
What is the simple interest on Rs. 5,000 at 8% per year for 3 years?
Correct answer: B. Rs. 1,200
SI = P × R × T ÷ 100 = 5,000 × 8 × 3 ÷ 100 = Rs. 1,200.
easy - 15
Rs. 6,000 earns Rs. 900 simple interest in 3 years. What is the annual rate?
Correct answer: A. 5%
R = SI × 100 ÷ (P × T) = 900 × 100 ÷ (6,000 × 3) = 5%.
medium - 16
A can finish a job in 10 days and B can finish it in 15 days. How long will they take working together?
Correct answer: A. 6 days
Work per day = 1/10 + 1/15 = 5/30 = 1/6, so together they take 6 days.
medium - 17
12 workers can build a wall in 20 days. How many days will 15 workers take?
Correct answer: D. 16 days
Total work = 12 × 20 = 240 worker-days. With 15 workers: 240 ÷ 15 = 16 days.
medium - 18
A tap fills a tank in 4 hours and a drain empties it in 6 hours. If both are open, how long will the tank take to fill?
Correct answer: B. 12 hours
Net filling per hour = 1/4 − 1/6 = 1/12, so the tank fills in 12 hours.
hard - 19
A speed of 72 km/h is equal to:
Correct answer: C. 20 m/s
Multiply by 5/18: 72 × 5/18 = 20 m/s.
medium - 20
A bus travels 150 km at 50 km/h. How long does the journey take?
Correct answer: C. 3 hours
Time = distance ÷ speed = 150 ÷ 50 = 3 hours.
easy