MCQs on Simplifications & Approximations

[Set - 5]

1. Simplify $12^2 - 5^2 + 3 \times 8$

A) 141
B) 142
C) 143
D) 144

Show Answer

Correct Answer: C) 143
Explanation:
First, calculate the exponents:
$12^2 = 144$
$5^2 = 25$
Then, multiply:
$3 \times 8 = 24$
Now, perform the addition and subtraction:
$144 - 25 + 24 = 143$

2. Approximate $734.82 + 498.76 - 382.65 + 187.34$

A) 1038.26
B) 1038.27
C) 1038.28
D) 1038.29

Show Answer

Correct Answer: B) 1038.27
Explanation:
First, add and subtract in sequence:
$734.82 + 498.76 = 1233.58$
$1233.58 - 382.65 = 850.93$
$850.93 + 187.34 = 1038.27$

3. Solve $\frac{(72 + 48)}{8} \times 9 - 6^2$

A) 98
B) 99
C) 100
D) 101

Show Answer

Correct Answer: B) 99
Explanation:
First, calculate inside the parentheses:
$72 + 48 = 120$
Then, divide:
$120 \div 8 = 15$
Now, multiply:
$15 \times 9 = 135$
Then, calculate the exponent:
$6^2 = 36$
Finally, subtract:
$135 - 36 = 99$

4. Approximate $1342.56 + 642.15 - 498.73 + 791.82$

A) 2277.8
B) 2275.8
C) 2278.8
D) 2276.8

Show Answer

Correct Answer: A) 2277.8
Explanation:
First, add and subtract in sequence:
$1342.56 + 642.15 = 1984.71$
$1984.71 - 498.73 = 1485.98$
$1485.98 + 791.82 = 2277.8$

5. Simplify $9^3 - 7 \times (6 + 3) + 2^3$

A) 673
B) 674
C) 675
D) 676

Show Answer

Correct Answer: B) 674
Explanation:
First, calculate inside the parentheses:
$6 + 3 = 9$
Then, multiply:
$7 \times 9 = 63$
Then, calculate the exponents:
$9^3 = 729$
$2^3 = 8$
Now, perform the subtraction and addition:
$729 - 63 + 8 = 674$

6. Approximate $537.89 + 231.56 - 127.45 + 354.89$

A) 995.99
B) 996.98
C) 995.89
D) 996.89

Show Answer

Correct Answer: D) 996.89
Explanation:
First, add and subtract in sequence:
$537.89 + 231.56 = 769.45$
$769.45 - 127.45 = 642.00$
$642.00 + 354.89 = 996.89$

7. Solve $8^3 - 4 \times 9 + 6^2$

A) 510
B) 511
C) 512
D) 513

Show Answer

Correct Answer: C) 512
Explanation:
First, calculate the exponents:
$8^3 = 512$
$6^2 = 36$
Then, multiply:
$4 \times 9 = 36$
Now, perform the subtraction and addition:
$512 - 36 + 36 = 512$

8. Approximate $1649.75 + 742.31 - 562.14 + 389.43$

A) 2219.33
B) 2219.34
C) 2219.35
D) 2219.36

Show Answer

Correct Answer: C) 2219.35
Explanation:
First, add and subtract in sequence:
$1649.75 + 742.31 = 2392.06$
$2392.06 - 562.14 = 1829.92$
$1829.92 + 389.43 = 2219.35$

9. Simplify $13 \times (7 + 5) - 9^2$

A) 45
B) 65
C) 55
D) 75

Show Answer

Correct Answer: D) 75
Explanation:
First, calculate inside the parentheses:
$7 + 5 = 12$
Then, multiply:
$13 \times 12 = 156$
Then, calculate the exponent:
$9^2 = 81$
Now, subtract:
$156 - 81 = 75$

10. Approximate $754.89 + 324.17 - 178.45 + 459.87$

A) 1360.46
B) 1360.47
C) 1360.48
D) 1360.49

Show Answer

Correct Answer: C) 1360.48
Explanation:
First, add and subtract in sequence:
$754.89 + 324.17 = 1079.06$
$1079.06 - 178.45 = 900.61$
$900.61 + 459.87 = 1360.48$

11. Solve $\frac{(36 + 48)}{12} \times 11 - 3^2$

A) 58
B) 68
C) 78
D) 98

Show Answer

Correct Answer: B) 68
Explanation:
First, calculate inside the parentheses:
$36 + 48 = 84$
Then, divide:
$84 \div 12 = 7$
Now, multiply:
$7 \times 11 = 77$
Then, calculate the exponent:
$3^2 = 9$
Finally, subtract:
$77 - 9 = 68$

12. Approximate $1368.45 + 598.76 - 421.34 + 789.42$

A) 2335.09
B) 2335.29
C) 2335.39
D) 2335.59

Show Answer

Correct Answer: B) 2335.29
Explanation:
First, add and subtract in sequence:
$1368.45 + 598.76 = 1967.21$
$1967.21 - 421.34 = 1545.87$
$1545.87 + 789.42 = 2335.29$

13. Simplify $6^2 + 5^3 - 4^2$

A) 141
B) 144
C) 145
D) 155

Show Answer

Correct Answer: C) 145
Explanation:
First, calculate the exponents:
$6^2 = 36$
$5^3 = 125$
$4^2 = 16$
Now, perform the addition and subtraction:
$36 + 125 - 16 = 145$

14. Approximate $921.57 + 428.39 - 276.24 + 561.12$

A) 1634.84
B) 1638.84
C) 1644.84
D) 1634.74

Show Answer

Correct Answer: A) 1634.84
Explanation:
First, add and subtract in sequence:
$921.57 + 428.39 = 1349.96$
$1349.96 - 276.24 = 1073.72$
$1073.72 + 561.12 = 1634.84$

15. Solve $7 \times (8 + 4) - 3^3$

A) 56
B) 57
C) 58
D) 59

Show Answer

Correct Answer: B) 57
Explanation:
First, calculate inside the parentheses:
$8 + 4 = 12$
Then, multiply:
$7 \times 12 = 84$
Then, calculate the exponent:
$3^3 = 27$
Now, subtract:
$84 - 27 = 57$

16. Approximate $1489.56 + 743.25 - 563.41 + 324.58$

A) 1992.98
B) 1993.88
C) 1993.98
D) 1994.89

Show Answer

Correct Answer: C) 1993.98
Explanation:
First, add and subtract in sequence:
$1489.56 + 743.25 = 2232.81$
$2232.81 - 563.41 = 1669.40$
$1669.40 + 324.58 = 1993.98$

17. Simplify $11^3 - 4^2 + 9^2$

A) 1366
B) 1376
C) 1386
D) 1396

Show Answer

Correct Answer: D) 1396
Explanation:
First, calculate the exponents:
$11^3 = 1331$
$4^2 = 16$
$9^2 = 81$
Now, perform the addition and subtraction:
$1331 - 16 + 81 = 1396$

18. Approximate $347.56 + 214.98 - 109.67 + 453.89$

A) 906.76
B) 976.67
C) 976.76
D) 967.67

Show Answer

Correct Answer: A) 906.76
Explanation:
First, add and subtract in sequence:
$347.56 + 214.98 = 562.54$
$562.54 - 109.67 = 452.87$
$452.87 + 453.89 = 906.76$

19. Solve $\frac{(72 + 28)}{5} \times 6 - 7^2$

A) 70
B) 71
C) 72
D) 73

Show Answer

Correct Answer: B) 71
Explanation:
First, calculate inside the parentheses:
$72 + 28 = 100$
Then, divide:
$100 \div 5 = 20$
Now, multiply:
$20 \times 6 = 120$
Then, calculate the exponent:
$7^2 = 49$
Finally, subtract:
$120 - 49 = 71$

20. Approximate $2765.12 + 934.56 - 678.45 + 591.34$

A) 3610.57
B) 3611.57
C) 3612.57
D) 3615.77

Show Answer

Correct Answer: C) 3612.57
Explanation:
First, add and subtract in sequence:
$2765.12 + 934.56 = 3699.68$
$3699.68 - 678.45 = 3021.23$
$3021.23 + 591.34 = 3612.57$

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MCQs on Simplifications & Approximations

[Set - 5]

1. Simplify 12^2 - 5^2 + 3 \times 8

2. Approximate 734.82 + 498.76 - 382.65 + 187.34

3. Solve \frac{(72 + 48)}{8} \times 9 - 6^2

4. Approximate 1342.56 + 642.15 - 498.73 + 791.82

5. Simplify 9^3 - 7 \times (6 + 3) + 2^3

6. Approximate 537.89 + 231.56 - 127.45 + 354.89

7. Solve 8^3 - 4 \times 9 + 6^2

8. Approximate 1649.75 + 742.31 - 562.14 + 389.43

9. Simplify 13 \times (7 + 5) - 9^2

10. Approximate 754.89 + 324.17 - 178.45 + 459.87

11. Solve \frac{(36 + 48)}{12} \times 11 - 3^2

12. Approximate 1368.45 + 598.76 - 421.34 + 789.42

13. Simplify 6^2 + 5^3 - 4^2

14. Approximate 921.57 + 428.39 - 276.24 + 561.12

15. Solve 7 \times (8 + 4) - 3^3

16. Approximate 1489.56 + 743.25 - 563.41 + 324.58

17. Simplify 11^3 - 4^2 + 9^2

18. Approximate 347.56 + 214.98 - 109.67 + 453.89

19. Solve \frac{(72 + 28)}{5} \times 6 - 7^2

20. Approximate 2765.12 + 934.56 - 678.45 + 591.34

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1. Simplify $12^2 - 5^2 + 3 \times 8$

2. Approximate $734.82 + 498.76 - 382.65 + 187.34$

3. Solve $\frac{(72 + 48)}{8} \times 9 - 6^2$

4. Approximate $1342.56 + 642.15 - 498.73 + 791.82$

5. Simplify $9^3 - 7 \times (6 + 3) + 2^3$

6. Approximate $537.89 + 231.56 - 127.45 + 354.89$

7. Solve $8^3 - 4 \times 9 + 6^2$

8. Approximate $1649.75 + 742.31 - 562.14 + 389.43$

9. Simplify $13 \times (7 + 5) - 9^2$

10. Approximate $754.89 + 324.17 - 178.45 + 459.87$

11. Solve $\frac{(36 + 48)}{12} \times 11 - 3^2$

12. Approximate $1368.45 + 598.76 - 421.34 + 789.42$

13. Simplify $6^2 + 5^3 - 4^2$

14. Approximate $921.57 + 428.39 - 276.24 + 561.12$

15. Solve $7 \times (8 + 4) - 3^3$

16. Approximate $1489.56 + 743.25 - 563.41 + 324.58$

17. Simplify $11^3 - 4^2 + 9^2$

18. Approximate $347.56 + 214.98 - 109.67 + 453.89$

19. Solve $\frac{(72 + 28)}{5} \times 6 - 7^2$

20. Approximate $2765.12 + 934.56 - 678.45 + 591.34$