Quantitative Aptitude

Simplification and Roots: Practice Questions with Answers

14 practice questions on Simplification and Roots, with answers; most also have an explanation or a worked solution. Try each one before you open its answer.

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1. Q.1

   Simplify: 100 − [20 + {10 − (6 − 2)}]

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   Answer: 74

   Solution:

   1. Innermost brackets first: (6 − 2) = 4.
   2. Next layer: {10 − 4} = 6.
   3. Next layer: [20 + 6] = 26.
   4. Finally: 100 − 26 = 74.

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2. Q.2

   Simplify: 30 − bar(10 ÷ 2 + 3) × 2, where bar(...) denotes a vinculum — the expression under it is treated as a single term and simplified first, using its own internal BODMAS.

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   Answer: 14

   Solution:

   1. Inside the vinculum, ordinary BODMAS still applies: 10 ÷ 2 = 5, then 5 + 3 = 8. So bar(10 ÷ 2 + 3) = 8, treated as one number.
   2. The rest of the expression now reads: 30 − 8 × 2.
   3. Multiplication before subtraction: 8 × 2 = 16, then 30 − 16 = 14.

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3. Q.3

   Simplify: (3/4) of 60 + 25% of 80 − 15

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   Answer: 50

   Solution:

   1. "Of" terms first: (3/4) of 60 = 45, and 25% of 80 = 20.
   2. Addition and subtraction, left to right: 45 + 20 − 15 = 50.

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4. Q.4

   Simplify: 5 of 8 ÷ 4 + 6 × 2

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   Answer: 22

   Solution:

   1. "Of" first: 5 of 8 = 40.
   2. Division and multiplication next: 40 ÷ 4 = 10, and 6 × 2 = 12.
   3. Addition last: 10 + 12 = 22.

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5. Q.5

   Simplify: 2/5 of 100 − (3/4 of 20 − 5)

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   Answer: 30

   Solution:

   1. Innermost bracket first: 3/4 of 20 = 15, so the bracket becomes (15 − 5) = 10.
   2. Now the "of" outside the bracket: 2/5 of 100 = 40.
   3. Finally: 40 − 10 = 30.

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6. Q.6

   Simplify: 1.2 × 5/6 + 1.8

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   Answer: 2.8

   Solution:

   1. Convert the decimal to a fraction so everything is in one form: 1.2 = 6/5.
   2. (6/5) × (5/6) = 1 (the 5s and 6s cancel exactly — this is why converting first avoids rounding).
   3. 1 + 1.8 = 2.8.

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7. Q.7

   Simplify: 15 + 6 ÷ 3 × 2 − 4

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   Answer: 15

   Solution:

   1. Division and multiplication first, left to right: 6 ÷ 3 = 2, then 2 × 2 = 4.
   2. Now addition and subtraction, left to right: 15 + 4 − 4 = 15.

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8. Q.8

   Simplify: 2/5 of 100 − (3/4 of 20 − 5)

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   Answer: 30. Bracket first: 3/4 of 20 = 15, so (15−5)=10; then 2/5 of 100 = 40; 40−10.

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9. Q.9

   Simplify: 1.2 × 5/6 + 1.8

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   Answer: 2.8. 1.2 = 6/5; (6/5)×(5/6) = 1; 1+1.8.

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10. Q.10

    Simplify: 50 − [15 + {20 − (8 + 4)}]

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    Answer: 27. Innermost: 8+4=12; {20−12}=8; [15+8]=23; 50−23.

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11. Q.11

    Simplify: 36 ÷ 6 × 2 + 5 − 3 of 2

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    Answer: 11. "Of" first: 3 of 2 = 6; then 36÷6=6, 6×2=12; 12+5−6.

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12. Q.12

    Simplify: 2 of 15 ÷ 5 − 3 × 2

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    Answer: 0. "Of" first: 2 of 15 = 30; then 30÷5=6 and 3×2=6; 6−6.

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13. Q.13

    Simplify: 30 − bar(10 ÷ 2 + 3) × 2, with bar(...) a vinculum.

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    Answer: 14. Inside the bar: 10÷2+3 = 8; then 30 − 8×2 = 30−16.

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14. Q.14

    Simplify: 20 − 4 × 3 + 6 ÷ 2

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    Answer: 11. Multiplication/division first: 4×3=12, 6÷2=3; then 20−12+3.

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