Approximation and Simplification

 An approximation is anything that is similar, but not exactly equal, to something else. A number can be approximated by rounding. A calculation can be approximated by rounding the values within it before performing the operations.

Approximation is one of the most important topics among Bank and Insurance Exams like RRB Scale 1 Pre, SBI Clek Pre, IBPS PO Pre, and NIACL Etc. If you are good at maths basics then you can easily gain 4 to 5 marks in just 3 to 5 minutes.
 

Here we will discuss some important questions on approximation.

Directions: What approximate value should come in place of Question mark (?) in the following question??

Question 1:

2831.994 ÷ 23.998 + 11.99² ÷ 5.991 = ?²

A. 144

B. 12

C. 195

D. 14

E. 17

Solution:

Question 2: 

A. – 36

B. – 72

C. 12

D. – 12

E. 36

Solution:

Question 3:  10.805 × 2.5 × 9.99² = ?

A. 2500

B. 2300

C. 2700

D. 3100

E. 3500

Solution:

10.805 × 2.5 × 9.99² = ?
10.8 ×5/2× 10² ≈ ?
5.4 × 5 × 100 = ?
? = 2700 Hence, option C is correct.

Question 4: 

 8.99 × 8.99 × 8.99 ÷ 2.99 = 3^?

A. 7

B. 9

C. 3

D. 2

E. 5

Solution:

8.99 × 8.99 × 8.99 ÷ 2.99 = 3^?
9 × 9 ×9/3≈ 3^?
9 × 9 × 3 = 3⁵ = 3^? Hence, option E is correct.

Question 5:

14.982² ÷ 5.001² × 4.990 × 5^–1 = ?

A. 45

B. 75

C. 225

D. 9

E. 25

Solution:

14.982² ÷ 5.001² × 4.990 × 5^–1 = ?
15²/5²× 1/5 = ?
? = 3² = 9 Hence, option D is correct.

Question 6:

 √15626 × √8650 – (54.06)² = ? + (72.039)²

A. 3000

B. 3525

C. 3900

D. 4250

E. 3225

Solution:

√15626 × √8650 – (54.06)² = ? + (72.039)²

Or, ? ≈ √15625 × √8649 – (54)² – (72)²

≈ 125 × 93 – 2916 – 5184

= 11625 – 8100 = 3525

Hence, option B is correct.

Question 7:

(1522.76 + 2889.57 – 1025.14) ÷ 4.05 × 2 = ? + 134.099

A. 1400

B. 1450

C. 1560

D. 1640

E. 1680

Solution:

(1522.76 + 2889.57 – 1025.14) ÷ 4.05 × 2 = ? + 134.099
≈ (1523 + 2890 – 1025)/4 × 2 = ? + 134
=(4413 – 1025)/2= ? + 134
=3388/2 = ? + 134
= 1694 = ? + 134
? = 1694 – 134 = 1560
Hence, option C is correct.

Question:8

37% of 924 + √290 ÷ 25 × 450 = ?² – √6725

A. 18

B. 21

C. 27

D. 35

E. 29

Solution:

37% of 924 + √290 ÷ 25 × 450 = ?² – √6725
341.88 + √290 ÷ 25 × 450 = ?² – √6725
342 + √289 ÷ 25 × 450 ≈ ?² – √6724
342 + 17 × 18 = ?² – 82

342 + 306 + 82 = ?²
?² = 730 ≈ 729
? = 27
Hence, option C is correct.

Question 9:

A. 40

B. 20

C. 10

D. 45

E. 36

Solution:

Question:10

(√7920 × √3482) – (68.06)² = (?)² – 48.92

A. 56

B. 36

C. 26

D. 16

E. 34 

Solution:

? = 26

Hence, option C is correct.