Welcome to this curated set of 51 Simplification Aptitude Questions and Answers. These solved MCQs cover key topics such as BODMAS, fractions, decimals, percentages, and exponents. Every question includes a step-by-step explanation so you never have to guess why an answer is correct. If you’re gearing up for bank exams, SSC, or any competitive test, this is a great place to start practising.
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Simplification Formulas
BODMAS, the order of operations
B = Brackets, first the small ones, then the curly ones, then the square ones
O = Of
D = Division
M = Multiplication
A = Addition
S = Subtraction
Of comes before division. So 1/2 of 20 ÷ 5 is 10 ÷ 5 = 2, not 1/2 of 4.
Division and multiplication rank equally, so solve them left to right. The same holds for addition and subtraction.
Sign rules
Plus and plus give plus
Plus and minus give minus
Minus and minus give plus
Removing a minus before a bracket flips every sign inside it
Fractions
a/b + c/d = (ad + bc) ÷ bd
a/b − c/d = (ad − bc) ÷ bd
a/b × c/d = ac ÷ bd
a/b ÷ c/d = a/b × d/c
To compare two fractions, cross multiply. For a/b and c/d, compare a × d with b × c.
Decimals
In multiplication, add the decimal places of both numbers.
In division, shift the point in both numbers by the same number of places to clear the divisor.
0.06 ÷ 0.0003 becomes 600 ÷ 3 = 200
Laws of indices
aᵐ × aⁿ = a⁽ᵐ ⁺ ⁿ⁾
aᵐ ÷ aⁿ = a⁽ᵐ ⁻ ⁿ⁾
(aᵐ)ⁿ = a⁽ᵐ ˣ ⁿ⁾
a⁰ = 1
a⁻ᵐ = 1 ÷ aᵐ
(a ÷ b)⁻ᵐ = (b ÷ a)ᵐ
Surds
√a × √b = √(a × b)
√a ÷ √b = √(a ÷ b)
√a = a^(1/2) and ³√a = a^(1/3)
Remember √a + √b is never √(a + b).
The identities that save the most time
(a + b)² = a² + 2ab + b²
(a − b)² = a² − 2ab + b²
a² − b² = (a + b) (a − b)
a³ + b³ = (a + b) (a² − ab + b²)
a³ − b³ = (a − b) (a² + ab + b²)
If x + 1/x = a, then x² + 1/x² = a² − 2
Percentage and fraction values to know by sight
1/2 = 50%, 1/3 = 33.33%, 1/4 = 25%, 1/5 = 20%, 1/6 = 16.67%, 1/7 = 14.28%, 1/8 = 12.5%, 1/9 = 11.11%, 1/10 = 10%, 1/11 = 9.09%, 1/12 = 8.33%, 1/16 = 6.25%, 1/20 = 5%
x% of y = y% of x, so 16% of 25 is the same as 25% of 16, which is 4.
The standard sums
Sum of first n natural numbers = n (n + 1) ÷ 2
Sum of first n even numbers = n (n + 1)
Sum of first n odd numbers = n²
Common Simplification Mistakes to Avoid
Solving strictly left to right
BODMAS is an order, not a queue. Brackets and “of” come first, then division and multiplication together (left to right), then addition and subtraction together.
Forgetting that “of” beats division
1/2 of 20 ÷ 5 means (1/2 of 20) ÷ 5 = 10 ÷ 5 = 2, not 1/2 of 4.
Missing a sign flip after a bracket
A minus before a bracket flips every sign inside it, so 8 − (3 − 5) = 8 − 3 + 5 = 10.
Splitting a square root over addition
√a + √b is never √(a + b). √9 + √16 = 3 + 4 = 7, not √25 = 5.
Adding decimal places in division
You add decimal places only in multiplication. In division, shift the point in both numbers equally to clear the divisor.
Treating a⁰ as 0
Any non-zero number to the power 0 is 1, not 0. So 5⁰ + 2⁻¹ = 1 + 0.5 = 1.5.
51 Simplification Aptitude Questions and Answers (Solved MCQs)
Question 1. Simplify: 48 ÷ 6 × (5 + 3) − 7
a) 49
b) 52
c) 57
d) 64
Answer:
c) 57 — Brackets first: (5+3)=8; then 48/6=8; 8×8=64; 64−7=57.
Question 2. Simplify: (3/4 of 128) + (5/8 of 96)
a) 144
b) 150
c) 156
d) 160
Answer:
c) 156 — (3/4)×128=96 and (5/8)×96=60; total = 156.
Question 3. Simplify: (0.2)⁻² + (0.5)⁻¹
a) 23
b) 25
c) 27
d) 29
Answer:
c) 27 — (0.2)⁻² = (1/5)⁻² = 25; (0.5)⁻¹ = 2; total 27.
Question 4. Simplify: (7/9 + 5/6) × (18/11)
a) 29/22
b) 29/11
c) 11/29
d) 58/11
Answer:
b) 29/11 — (7/9 + 5/6) = 29/18; then (29/18)×(18/11)=29/11.
Question 5. Simplify: 1.25 × 0.8 ÷ 0.5
a) 1
b) 1.5
c) 2
d) 2.5
Answer:
c) 2 — 1.25×0.8 = 1; 1 ÷ 0.5 = 2.
Question 6. Simplify: (15% of 240) + (12% of 150)
a) 48
b) 52
c) 54
d) 60
Answer:
c) 54 — 15% of 240 = 36; 12% of 150 = 18; sum = 54.
Question 7. Simplify: (3⁴ − 2⁵) ÷ (5² − 4²)
a) 49/9
b) 9/49
c) 5
d) 7
Answer:
a) 49/9 — (81−32)=49 and (25−16)=9.
Question 8. Simplify: 5 + {18 ÷ (3 × 2)} × 4
a) 11
b) 13
c) 15
d) 17
Answer:
d) 17 — 3×2=6; 18/6=3; 3×4=12; 5+12=17.
Question 9. Simplify: (2/3) ÷ (5/9) × (3/10)
a) 3/25
b) 6/25
c) 9/25
d) 12/25
Answer:
c) 9/25 — (2/3)×(9/5)×(3/10)=9/25.
Question 10. Simplify: (7.2 ÷ 0.18) + (3.6 ÷ 0.12)
a) 60
b) 70
c) 80
d) 90
Answer:
b) 70 — 7.2/0.18=40 and 3.6/0.12=30; total 70.
Question 11. Simplify: 1/2 + 1/3 + 1/4
a) 11/12
b) 13/12
c) 5/6
d) 7/12
Answer:
b) 13/12 — LCM 12: (6+4+3)/12 = 13/12.
Question 12. Simplify: (2/5) of (3/4 of 500)
a) 120
b) 150
c) 180
d) 200
Answer:
b) 150 — (3/4)×500=375; (2/5)×375=150.
Question 13. Simplify: 0.06 ÷ 0.0003
a) 20
b) 50
c) 100
d) 200
Answer:
d) 200 — 0.0003 × 200 = 0.06.
Question 14. Simplify: (9! ÷ 7!) ÷ (6! ÷ 4!)
a) 12/5
b) 5/12
c) 5/2
d) 2/5
Answer:
a) 12/5 — (9!/7!)=9×8; (6!/4!)=6×5; ratio = 72/30 = 12/5.
Question 15. Simplify: (1 − 1/2) ÷ (1/3) + 1/4
a) 5/4
b) 6/4
c) 7/4
d) 9/4
Answer:
c) 7/4 — (1/2)÷(1/3)=3/2; 3/2+1/4=6/4+1/4=7/4.
Question 16. Simplify: (2.5% of 8000) − (1.25% of 6400)
a) 80
b) 100
c) 120
d) 140
Answer:
c) 120 — 2.5% of 8000=200; 1.25% of 6400=80; difference 120.
Question 17. Simplify: (3/5) of 45
a) 21
b) 24
c) 27
d) 30
Answer:
c) 27 — (3/5)×45 = 27.
Question 18. Simplify: √50 − √8
a) √2
b) 2√2
c) 3√2
d) 4√2
Answer:
c) 3√2 — √50=5√2 and √8=2√2.
Question 19. Simplify: (√27 + √12) ÷ √3
a) 3
b) 4
c) 5
d) 6
Answer:
c) 5 — √27=3√3 and √12=2√3; (5√3)/√3=5.
Question 20. Simplify: (2⁵ × 4³) ÷ 8⁴
a) 1/4
b) 1/2
c) 2
d) 4
Answer:
b) 1/2 — 2⁵×(2²)³=2¹¹; (2³)⁴=2¹²; so 2¹¹/2¹²=1/2.
Question 21. Simplify: 9^(3/2)
a) 9
b) 18
c) 27
d) 81
Answer:
c) 27 — 9^(3/2) = (√9)³ = 3³.
Question 22. Simplify: (√16 + √25)²
a) 49
b) 64
c) 81
d) 100
Answer:
c) 81 — (4+5)² = 81.
Question 23. Simplify: √0.04 ÷ 0.2
a) 0.5
b) 1
c) 2
d) 5
Answer:
b) 1 — √0.04 = 0.2.
Question 24. Simplify: (3⁻² + 3⁻¹) ÷ 3⁻³
a) 6
b) 9
c) 12
d) 15
Answer:
c) 12 — (1/9+1/3)=(4/9); divide by (1/27) gives (4/9)×27=12.
Question 25. Simplify: √5 ÷ √20
a) 1/4
b) 1/2
c) √2
d) 2
Answer:
b) 1/2 — √5/√20 = √(5/20)=√(1/4)=1/2.
Question 26. Simplify: (2√3)(3√12)
a) 18
b) 24
c) 36
d) 72
Answer:
c) 36 — √12=2√3; so 3√12=6√3; product = 2√3×6√3=12×3=36.
Question 27. Simplify: (a³ b⁻²) ÷ (a⁻¹ b⁴)
a) a²/b⁶
b) a⁴/b⁶
c) a⁶/b⁴
d) a⁴/b²
Answer:
b) a⁴/b⁶ — a^(3−(−1))=a⁴ and b^(−2−4)=b⁻⁶.
Question 28. Simplify: √0.0009
a) 0.003
b) 0.03
c) 0.3
d) 3
Answer:
b) 0.03 — 0.03² = 0.0009.
Question 29. Simplify: 1 ÷ (√3 − √2)
a) √3 − √2
b) √3 + √2
c) 1/(√3 + √2)
d) √6
Answer:
b) √3 + √2 — Rationalize: multiply by (√3+√2).
Question 30. Simplify: (5⁰ + 2⁻¹) × 8
a) 8
b) 10
c) 12
d) 14
Answer:
c) 12 — 5⁰=1 and 2⁻¹=1/2; (1.5)×8=12.
Question 31. If x = 2^(1/3), simplify: x⁶ × x⁻²
a) 2
b) 4
c) 2 × 2^(1/3)
d) 4 × 2^(1/3)
Answer:
c) 2 × 2^(1/3) — x⁶×x⁻² = x⁴ = 2^(4/3) = 2×2^(1/3).
Question 32. Simplify: (7² × 7³) ÷ 7⁴
a) 1
b) 7
c) 49
d) 343
Answer:
b) 7 — 7^(2+3−4)=7¹.
Question 33. Simplify: (√48 + √75) ÷ √3
a) 6
b) 7
c) 8
d) 9
Answer:
d) 9 — √48=4√3 and √75=5√3; total 9√3; divide by √3 gives 9.
Question 34. Simplify: 999 × 1001 − 1000²
a) −1
b) 0
c) 1
d) 1000
Answer:
a) −1 — (1000−1)(1000+1)=1000²−1; subtract 1000² gives −1.
Question 35. Simplify: 48.6 ÷ 0.9 × 1.5
a) 72
b) 81
c) 90
d) 96
Answer:
b) 81 — 48.6/0.9=54; 54×1.5=81.
Question 36. Approximate to nearest integer: √51 + √19
a) 11
b) 12
c) 13
d) 14
Answer:
b) 12 — √51≈7.14 and √19≈4.36; sum ≈11.50.
Question 37. Approximate to nearest integer: 19.98 × 5.02
a) 99
b) 100
c) 101
d) 102
Answer:
b) 100 — Close to 20×5 = 100; exact is 100.2996, nearest 100.
Question 38. Simplify: 3/7 + 2/5 − 1/35
a) 3/5
b) 4/5
c) 5/7
d) 6/7
Answer:
b) 4/5 — LCM 35: 15/35 + 14/35 − 1/35 = 28/35 = 4/5.
Question 39. If 35% of x = 280, then x is:
a) 600
b) 700
c) 800
d) 900
Answer:
c) 800 — x = 280 ÷ 0.35.
Question 40. Simplify: 1.2³ ÷ 0.6²
a) 3.2
b) 4.0
c) 4.8
d) 6.0
Answer:
c) 4.8 — 1.2³=1.728 and 0.6²=0.36; 1.728/0.36=4.8.
Question 41. Simplify: (4.99)² − (5.01)²
a) −0.2
b) −0.1
c) 0.1
d) 0.2
Answer:
a) −0.2 — a²−b²=(a−b)(a+b)=(-0.02)(10)=−0.2.
Question 42. Simplify: (1 ÷ 0.125) + (1 ÷ 0.04)
a) 28
b) 30
c) 33
d) 35
Answer:
c) 33 — 1/0.125=8 and 1/0.04=25.
Question 43. Simplify: (2/3 of 450) ÷ (5/6 of 360)
a) 3/2
b) 1
c) 2/3
d) 1/2
Answer:
b) 1 — (2/3)×450=300 and (5/6)×360=300; ratio 1.
Question 44. Find: (7/8)% of 6400
a) 48
b) 56
c) 64
d) 72
Answer:
b) 56 — (7/8)% = 7/800; 6400×7/800=56.
Question 45. Approximate (to 3 decimals): 0.999³
a) 0.996
b) 0.997
c) 0.998
d) 0.999
Answer:
b) 0.997 — (1−0.001)³ ≈ 1−0.003+0.000003 = 0.997003.
Question 46. Simplify: (2¹⁰ − 2⁸) ÷ 2⁷
a) 4
b) 5
c) 6
d) 7
Answer:
c) 6 — (1024−256)/128 = 768/128 = 6.
Question 47. Simplify: 1 ÷ (0.2 × 0.05)
a) 10
b) 50
c) 100
d) 200
Answer:
c) 100 — 0.2×0.05=0.01; 1/0.01=100.
Question 48. Simplify: 75% of 320 + 12.5% of 800
a) 300
b) 320
c) 340
d) 360
Answer:
c) 340 — 75% of 320=240; 12.5% of 800=100.
Question 49. Find the average of: 1/2, 2/3, 3/4
a) 19/36
b) 23/36
c) 25/36
d) 29/36
Answer:
b) 23/36 — Sum = 1/2 + 2/3 + 3/4 = (6 + 8 + 9)/12 = 23/12; average = (23/12) ÷ 3 = 23/36.
Question 50. Simplify: (5/6)⁻¹ + (3/4)⁻¹
a) 32/15
b) 38/15
c) 40/15
d) 46/15
Answer:
b) 38/15 — (5/6)⁻¹=6/5 and (3/4)⁻¹=4/3; sum = 18/15+20/15.
Question 51. Find the exact value: 98 × 102
a) 9,996
b) 10,000
c) 10,004
d) 10,200
Answer:
a) 9,996 — (100−2)(100+2)=10000−4.
Aptitude Questions and Answers for other topics
| Number system and series | ||
|---|---|---|
| HCF and LCM | Simplification | Number Series |
| Interest and commercial maths | ||
| Percentage | Profit and Loss | Compound Interest |
| Partnership | ||
| Ratio, average and mixture | ||
| Ratio and Proportion | Alligation or Mixture | Problems on Ages |
| Speed, time and distance | ||
| Time and Distance | Problems on Trains | Boats and Streams |
| Work and rate | ||
| Time and Work | Pipes and Cistern | |
| Mensuration | ||
| Volume and Surface Area | Height and Distance | |
| Permutation and probability | ||
| Permutation and Combination | Probability | |
| Calendar and clock | ||
| Calendar | Clock | |
