SSC Simplification Questions Practice Set with Tricks

About This Practice Set

Simplification questions look easy, and that is exactly why so many students lose marks in them. A small slip in the order of operations, a misplaced decimal point or a wasted minute on long multiplication can cost you a question you actually knew how to solve.

This set has 50 simplification questions in five short sets. Each question comes with the answer and a small trick, so you also learn the faster way to reach it. Try to spend no more than 30 seconds on each question, and use the tricks to save time on the ones that look long.

How to use it: Solve one set at a time, check your answers, and read the tricks even for the questions you got right. There is often a quicker route than the one you used.

Rules and Tricks to Remember

• BODMAS: Brackets, Orders (powers and roots), Division and Multiplication (left to right), then Addition and Subtraction (left to right).
• Difference of squares: a² − b² = (a + b)(a − b).
• Square of a sum or difference: (a ± b)² = a² ± 2ab + b².
• Multiplying by 25, 125, 5: 25 = 100/4, 125 = 1000/8 and 5 = 10/2. Divide first, then add zeros.
• Numbers near 100 or 1000: write them as (100 ± x) and use the identities above.
• Decimals: Ignore the decimal point while multiplying, then put back the total number of decimal places.

Set A: BODMAS Warm-Up (Q1–Q10)

Q1. 18 + 6 × 4 − 12 ÷ 3 = ?
Answer: 38
Trick: Do multiplication and division first: 6 × 4 = 24 and 12 ÷ 3 = 4. Then 18 + 24 − 4 = 38.

Q2. 45 − [12 + (30 − 18) ÷ 3] = ?
Answer: 29
Trick: Solve the bracket first: (30 − 18) = 12, 12 ÷ 3 = 4, 12 + 4 = 16. Then 45 − 16 = 29.

Q3. 8 × 12 ÷ 4 + 15 − 7 = ?
Answer: 32
Trick: Go left to right for × and ÷: 96 ÷ 4 = 24. Then 24 + 15 − 7 = 32.

Q4. (25 + 15) × 3 − 60 ÷ 5 = ?
Answer: 108
Trick: 40 × 3 = 120 and 60 ÷ 5 = 12, so 120 − 12 = 108.

Q5. 100 − 4 × (5 + 3²) = ?
Answer: 44
Trick: 3² = 9, (5 + 9) = 14, 4 × 14 = 56, and 100 − 56 = 44.

Q6. 72 ÷ 8 × 3 + 4 × 5 = ?
Answer: 47
Trick: 72 ÷ 8 = 9, 9 × 3 = 27, 4 × 5 = 20. Total 47.

Q7. 36 ÷ (4 + 2) × 5 − 8 = ?
Answer: 22
Trick: 36 ÷ 6 = 6, 6 × 5 = 30, 30 − 8 = 22.

Q8. 15 × 4 − 3 × (8 − 2) + 10 = ?
Answer: 52
Trick: 60 − 18 + 10 = 52.

Q9. 240 ÷ 6 ÷ 4 + 12 × 2 = ?
Answer: 34
Trick: 240 ÷ 6 = 40, 40 ÷ 4 = 10, 12 × 2 = 24. Total 34.

Q10. [(7 + 5) × 3 − 6] ÷ 5 = ?
Answer: 6
Trick: 12 × 3 = 36, 36 − 6 = 30, 30 ÷ 5 = 6.

Set B: Decimals and Fractions (Q11–Q20)

Q11. 0.5 × 0.4 + 0.3 × 0.2 = ?
Answer: 0.26
Trick: 0.20 + 0.06 = 0.26. Count decimal places: 1 + 1 = 2 places in each product.

Q12. 12.5 + 7.25 − 4.75 = ?
Answer: 15
Trick: Group 7.25 − 4.75 = 2.5 first. Then 12.5 + 2.5 = 15.

Q13. 3.6 ÷ 0.12 = ?
Answer: 30
Trick: Multiply both numbers by 100: 360 ÷ 12 = 30.

Q14. 0.25 × 48 + 0.75 × 16 = ?
Answer: 24
Trick: 0.25 is 1/4, so 48/4 = 12. 0.75 is 3/4, so 3 × 4 = 12. Sum = 24.

Q15. 1/2 + 1/3 + 1/6 = ?
Answer: 1
Trick: Take LCM 6: 3/6 + 2/6 + 1/6 = 6/6 = 1.

Q16. 3/4 of 80 + 2/5 of 50 = ?
Answer: 80
Trick: 3/4 of 80 = 60 and 2/5 of 50 = 20. Sum = 80.

Q17. (5/6 − 1/3) × 12 = ?
Answer: 6
Trick: 5/6 − 2/6 = 3/6 = 1/2, and 1/2 × 12 = 6.

Q18. 2 1/2 + 3 1/4 − 1 3/4 = ?
Answer: 4
Trick: Convert to decimals: 2.5 + 3.25 − 1.75 = 4.

Q19. 7/8 ÷ 7/16 = ?
Answer: 2
Trick: Flip and multiply: 7/8 × 16/7 = 2.

Q20. 0.6 × 0.6 ÷ 0.09 = ?
Answer: 4
Trick: 0.36 ÷ 0.09 = 36 ÷ 9 = 4.

Set C: Squares, Cubes and Roots (Q21–Q30)

Q21. √144 + √169 − √81 = ?
Answer: 16
Trick: 12 + 13 − 9 = 16.

Q22. 15² − 14² = ?
Answer: 29
Trick: Use a² − b² = (a + b)(a − b) = 29 × 1 = 29.

Q23. ∛27 + ∛64 + ∛125 = ?
Answer: 12
Trick: 3 + 4 + 5 = 12.

Q24. √0.0144 = ?
Answer: 0.12
Trick: √144 = 12, and 0.0144 has 4 decimal places, so the root has 2. Answer 0.12.

Q25. 25² ÷ 5² = ?
Answer: 25
Trick: (25/5)² = 5² = 25.

Q26. √(12² + 16²) = ?
Answer: 20
Trick: 144 + 256 = 400, and √400 = 20 (a 3-4-5 triangle scaled by 4).

Q27. 999 × 999 = ?
Answer: 998,001
Trick: (1000 − 1)² = 1,000,000 − 2,000 + 1 = 998,001.

Q28. 105 × 95 = ?
Answer: 9,975
Trick: (100 + 5)(100 − 5) = 10,000 − 25 = 9,975.

Q29. 68² − 32² = ?
Answer: 3,600
Trick: (68 + 32)(68 − 32) = 100 × 36 = 3,600.

Q30. √1764 = ?
Answer: 42
Trick: The last digit 4 means the root ends in 2 or 8. 40² = 1,600 and 50² = 2,500, so try 42: 42² = 1,764.

Set D: Speed Tricks and Identities (Q31–Q40)

Q31. 47² + 2 × 47 × 3 + 3² = ?
Answer: 2,500
Trick: This is (a + b)², so (47 + 3)² = 50² = 2,500.

Q32. 8.5² − 1.5² = ?
Answer: 70
Trick: (8.5 + 1.5)(8.5 − 1.5) = 10 × 7 = 70.

Q33. 1.25 × 1.25 − 0.25 × 0.25 = ?
Answer: 1.5
Trick: (1.25 + 0.25)(1.25 − 0.25) = 1.5 × 1 = 1.5.

Q34. 397 × 403 = ?
Answer: 159,991
Trick: (400 − 3)(400 + 3) = 160,000 − 9 = 159,991.

Q35. 25 × 48 = ?
Answer: 1,200
Trick: 25 × 4 = 100, so 25 × 48 = 100 × 12 = 1,200.

Q36. 125 × 88 = ?
Answer: 11,000
Trick: 125 = 1000/8, so 88/8 × 1000 = 11 × 1000 = 11,000.

Q37. 19 × 21 = ?
Answer: 399
Trick: (20 − 1)(20 + 1) = 400 − 1 = 399.

Q38. 99 × 101 = ?
Answer: 9,999
Trick: (100 − 1)(100 + 1) = 10,000 − 1 = 9,999.

Q39. 4.5 × 0.8 × 25 = ?
Answer: 90
Trick: Combine 0.8 × 25 = 20 and then 4.5 × 20 = 90.

Q40. 1/4 of 1/5 of 480 = ?
Answer: 24
Trick: 480 ÷ 5 = 96 and 96 ÷ 4 = 24.

Set E: Mixed Questions (Q41–Q50)

Q41. 36% of 250 + 24% of 150 = ?
Answer: 126
Trick: 36% of 250 = 90 and 24% of 150 = 36. Sum = 126.

Q42. 15% of 200 − 12% of 150 + 5% of 80 = ?
Answer: 16
Trick: 30 − 18 + 4 = 16.

Q43. 0.8² + 0.6² = ?
Answer: 1
Trick: 0.64 + 0.36 = 1.00.

Q44. 5/8 × 64 + 3/4 × 24 = ?
Answer: 58
Trick: 5/8 of 64 = 40 and 3/4 of 24 = 18. Sum = 58.

Q45. 2.4² − 1.4² = ?
Answer: 3.8
Trick: (2.4 + 1.4)(2.4 − 1.4) = 3.8 × 1 = 3.8.

Q46. 2 + 1 ÷ (1 + 1/3) = ?
Answer: 2.75
Trick: 1 + 1/3 = 4/3, and 1 ÷ 4/3 = 3/4. So 2 + 0.75 = 2.75.

Q47. (15² + 10²) ÷ 25 = ?
Answer: 13
Trick: 225 + 100 = 325, and 325 ÷ 25 = 13.

Q48. 7 × 8 + 9 × 6 ÷ 3 − 4 = ?
Answer: 70
Trick: 56 + 54 ÷ 3 − 4 = 56 + 18 − 4 = 70.

Q49. 64 ÷ 4 × 2 − 3 × 5 + 10 = ?
Answer: 27
Trick: 64 ÷ 4 × 2 = 32, then 32 − 15 + 10 = 27.

Q50. [(18 + 12) × 5 − 30] ÷ 4 = ?
Answer: 30
Trick: 30 × 5 = 150, 150 − 30 = 120, 120 ÷ 4 = 30.

Where Students Usually Go Wrong

• Doing operations strictly left to right. In 18 + 6 × 4, the multiplication comes first, so the answer is 42, not 96.
• Dropping a negative sign when opening a bracket that has a minus in front of it.
• Losing decimal places in long multiplication. Count them at the end and check that the answer looks sensible.
• Using the long method by habit. If two numbers are close to each other, or close to a round number, look for an identity before you start multiplying.

How to Get Faster

Speed in simplification comes from knowing squares up to 30, cubes up to 15 and the common fraction-to-decimal values by heart. Spend ten minutes a day on those tables, and take a set like this one once every two days. In two weeks you will notice that most questions stop feeling like calculations and start feeling like patterns.