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MCQ on Approximation for all Competitive exams

## 1) $$\displaystyle 7231\div 21\times 1.7=?$$

(a) 585

(b) 650

(c) 555

(d) 525

(e) 505

Solution: (a)
$$\displaystyle ?=\frac{{7231}}{{21}}\times 1.7\approx 585$$

## 2) $$\displaystyle \frac{1}{8}of\frac{2}{3}of\frac{3}{5}of1715=?$$

(a) 80

(b) 85

(c) 90

(d) 95

(e) 75

Solution: (b)
$$\displaystyle \frac{1}{8}\times \frac{2}{3}\times \frac{3}{5}\times 1715=85.75\approx 85$$

## 3) $$\displaystyle \sqrt[3]{{5332}}=?$$

(a) 8

(b) 38

(c) 58

(d) 68

(e) 18

Solution: (e)
$$\displaystyle ?=\sqrt[3]{{5332}}\approx 18$$
$$\displaystyle (18\times 18\times 18=5832)$$
Alternately without pen and paper,
If we carefully observe the options, 8 is too small number to reach 5332 if multipled three times. If we take 40 (nearest number to 38). 40 multiplied two times gives 1600 and of its again multiply with 40 we can expect a very huge number. So it is not the answer, so are the rest two (c) and (d) options which are greater than 38. So, the answer is (e). With regular practice this answer can be ascertained in less than 20 seconds.

## 4) $$\displaystyle \sqrt[3]{{4663}}+349=?\div 21.003$$

(a) 7600

(b) 7650

(c) 7860

(d) 7560

(e) 7680

Solution: (e)
$$\displaystyle ?\div 21.003=\sqrt[3]{{4663}}+349$$
$$\displaystyle ?\div 21=17+349=366$$
$$\displaystyle ?=366\times 21=7686\approx 7680$$

## 5) 39.897% of 4331 + 58.779% of 5003 = ?

(a) 4300

(b) 4500

(c) 4700

(d) 4900

(e) 5100

Solution: (c)
$$\displaystyle 4331\times \frac{{39.897}}{{100}}+5003\times \frac{{58.779}}{{100}}$$
$$\displaystyle 4330\times \frac{{40}}{{100}}+5000\times \frac{{59}}{{100}}$$
=1732+2950 = 4682 approx 4700

## 6) $$\displaystyle 9525\div 80\div 8=?$$

(a) 23

(b) 15

(c) 7

(d) 19

(e) 10

Solution: (b)
$$\displaystyle \frac{{9525}}{{80\times 8}}=\frac{{1905}}{{128}}=14.88\approx 15$$
Do not waste time in dividing, directly calculate in mind. Ten times of 128 is 1280 so we need another 600 to get 1900. Which is nothing but approximately half of 1280. That means five times of 128. So, approximately 10 times plus 5 times equal to 15 is your answer.

## 7) $$\displaystyle {{9.5}^{2}}=?$$

(a) 75

(b) 90

(c) 125

(d) 110

(e) 80

Solution: (b)
$$\displaystyle {{9.5}^{2}}=90.25\approx 90$$
or, alternately
9.5 nearest numbers are 9 or 10. Squares of the number are 81 and 100. So answer should lie inbetween these number so 90 is the answer

## 8) $$\displaystyle 5454\div 54\div 5=?$$

(a) 15

(b) 25

(c) 30

(d) 20

(e) 10

Solution: (d)
$$\displaystyle \frac{{5454}}{{54\times 5}}=\frac{{101}}{5}=20.1\approx 20$$
Alternately without pen and paper,
5454 is approximately 100 times more and when 100 is divided by 5 we get 20

## 9) $$\displaystyle 840.0003\div 23.999=?$$

(a) 47

(b) 8

(c) 35

(d) 18

(e) 23

Solution: (c)
$$\displaystyle ?=840.0003\div 23.999=840\div 24\approx 35$$
Alternately without pen and paper,
24 is near to 25. So, from options if we check 25 when multiplied by 50 (taking nearest number to 47) gives a number larger than 1000 and when 25 is multiplied by 30 or 40 (taking nearest numbers to 35) the resultant will be near to 840. So answer is 35.

## 10) 1504 × 5.865 – 24.091 = ? $$\displaystyle 1504\times 5.865-24.091=?$$

(a) 7200

(b) 9500

(c) 6950

(d) 5480

(e) 8800

Solution: (e)
$$\displaystyle 1504\times 5.865-24.091=?$$
$$\displaystyle ?=8796.869\approx 8800$$
Alternately without pen and paper,
1500 multiplied by 6 is 9000. By elimination and approximation we can see that the answer is (e)