Simplification and Approximation Questions with Solution

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By Smartkeeda
23 Sep 2019
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Hi Aspirants,
 
On this page practice Simplification and Approximation Questions for NRA CET, Bank PO and Insurance Exams like IBPS PO, IBPS Clerk, LIC Assistant, SBI PO, SBI Clerk and EPFO etc.

As quantitative aptitude section seems difficult for banking and insurance aspirants still there are some topics where you can gain marks with some practice like Simplification, Approximation and Number Series and Quadratic Equation.

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approximation questions
 
Directions: What approximate value will come in place of question mark (?).

1. 2744.03 – 840 + 11.07 = ? ÷ 8.02

A. 4
B. – 8
C. – 5
D. 15
E. 20

Solution :

2744.03 – 840 + 11.07 = ? ÷ 8.02

Approximate value:

2744 – 841 + 11.07 = ? ÷ 8

14 – 29 +11 = ? ÷ 2

25 – 29 = ? ÷ 2

–4 × 2 = ?

? = – 8

Hence, option B is correct.

2.  1164 × 128 ÷ 8.008 + 969.007 = ?

A. 18800
B. 19000
C. 19600
D. 19200
E. 18600

Solution : By taking the approximate value for the expression, we have

1164 × 128 ÷ 8.008 + 969.007 = ?
 
1164 × 128 ×  1  + 969.007 = ?
8.008
 
? ≈ 1164 × 128 ×  1  + 969
8

? = 1164 × 16 + 969

? = 18624 + 969 = 19593 ≈ 19600

Hence, option C is correct.

3.  2222.1 × 11 + 3333.1 × 11.01 + 4444 × 11 + 5555 × 11 – 6666.1 × 11 = ?

A. 10864
B. 86884
C. 97768
D. 77768
E. 88768

Solution : 2222.1 × 11 + 3333.1 × 11.01 + 4444 × 11 + 5555 × 11 – 6666.1 × 11 = ?
 
? ≈ 2222 × 11 + 3333 × 11 + 4444 × 11 + 5555 × 11 – 6666 × 11 
 
= 11[2222 + 3333 + 4444 + 5555 – 6666] 
 
= 11[2222 + 3333 + 4444 + 5555 – 6666] 
 
= 11 × 8888 = 97768
 
Hence, option C is correct.

4. (37.12)2 + (43.88)2 = (?2 – √2600) × √1297

A. 6
B. 8
C. 10
D. 12
E. 14

Solution : (37.12)2 + (43.88)2 = (?2 – √2600) × √1297

⇒ (37)2 + (44)2  ≈ (?2 – √2601) × √1296
 
?2 – 51 =  372 + 442  =  1369 + 1936  =  3305  = 91.8
36 36 36

⇒ ?2 = 91.8 + 51 = 142.80 ≈ 144

⇒ ? = √144 = 12

Hence, option D is correct.

5. 
? = 1528 √16.09 + 25% of 512.04 – 75.12 of  4
5

A. 6180
B. 6557
C. 5892
D. 6050
E. 6815

Solution :
 
1528√16.09 + 25% of 512.04 – 75.12 of  4
5

? ≈ 1528√16 + 25% of 512 – 75 × 0.8

? = 6112 + 128 – 60 = 6180

Hence, option A is correct. 

6.   (√624.75 – √168.80) × (√255.61 + √729.057) = ?

A. 496
B. 454
C. 502
D. 528
E. 516

Solution : (√624.75 – √168.80) × (√255.61 + √729.057)   = ?
 
(√625 – √169) × (√256 + √729)   = ?

(25 – 13) × (16 + 27)  = ?

12 × 43 = ?

? = 516

Hence, option E is correct.

7. (26.912)2 × 6.001 ÷ 6.12 + (7.03)3 + 40.02 = ? – 210.75

A. 1685
B. 1158
C. 1323
D. 1925
E. 1485

Solution : 

(26.912)2 × 6.001 ÷ 6.12 + (7.03)3 + 40.02 = ? – 210.75
 
Or, (27)2 × 6 ×  1  + (7)3 + 40 ≈ ? – 211
6

or, ? ≈ 729 + 343 + 40 + 211 = 1323

Hence, option C is correct.

8. (354.08 + ?)/ 31.98 + 124.89 % of 64.03 – (361.06)1/2 = (1000000.11)1/3

A. 980
B. 688
C. 872
D. 426
E. 894

Solution :
 
(354.08 + ?)  + 124.89 % of 64.03 – (361.06)1/2 = (1000000.11)1/3
31.98
 
354 + ?  +  125  × 64 – (361)1/2 ≈ (1000000)1/3
32 100
 
354 + ?  = 100 + 19 – 80
32


(354 + ?) = 39 × 32

? = 1248 – 354 = 894

Hence, option E is correct.

9. (25.03)2 + ( 16.93)2 – (13.06)2 = ? + 72 ÷ 9

A. 730 
B. 737
C. 749
D. 762
E. 771

Solution :

(25.03)2 + ( 16.93)2 – (13.06)2 = ? + 72 ÷ 9

≈ 625 + 289 – 169 – 8 = ?

? = 914 – 177

? = 737

Hence, option B is correct.

10.  256.013 + 360.99 ÷ 16.001 × 415.968 = ?2 – 8280.88

A. 20
B. 22
C. 25
D. 29
E. 38

Solution :256.013 + 360.99 ÷ 16.001 × 415.968 = ?2 – 8280.88

256 + 361 ÷ 16 × 416 = (?)28281

256 + 19 × 26 = (?)2 – 91

256 + 494 + 91 = (?)2

(?)2 = 841

? = 841 = 29

Hence, option D is correct.

Want to practice more Approximation Questions in the form of quizzes? Here are the links:

Quiz 1 Quiz 2 Quiz 3
Quiz 4 Quiz 5 Quiz 6
Quiz 7 Quiz 8 Quiz 9
Quiz 10 Quiz 11 Quiz 12

simplification questions
 
Directions: What value will come in place of question mark (?).

1.
  (7 – 10)2 + (5 + 14)2 = (?)3 – 28

A. √2
B.  4
C. √6
D.  3
E.  None of these

Solution : 

(7 – 10)2 + (5 + 14)2 = (?)3 – 28

(?)3 = 7 + 10 – 270 + 5 + 14 + 270 + 28

(?)3 = 36 + 28 = 64

∴   ? = 64 = 4

Hence, option B is correct.

2.  5.832 + 35% of 6500 – ?% of 1250 = 222.8

A. 164.32
B. 18.23
C. 174.32
D. 194.23
E. None of these

Solution :

5.832 + 35% of 6500 – ?% of 1250 = 222.8

or, 1.8 + 2275 – ? × 12.5 = 222.8

or, ? × 12.5 = 2276.8 – 222.8
 
or, ? =  2054  = 164.32
12.5

Hence, option A is correct.

3. 
 
39 13  – 47 18  + 23 11  – 2 1  = ?
17 34 17 34
 
A. 13 5
34
 
B. 11 29
34
 
C. 29 13
34
 
D. 13 29
34
 
E. 13 27
34

Solution :
 
39 13  – 47 18  + 23 11  – 2 1  = ?
17 34 17 34
 
? = (39 – 47 + 23 – 2) ( 13  –  18  +  11  –  1 )
17 34 17 34
 
? = (62 – 49) +  ( 26 – 18 + 22 – 1 )
34
 
? = 13 29
34

Hence, option D is correct.

4.
(3.7)–3 × (13.69)–2 ×  1  ÷ (13.69)–5 = (3.7)?
50.653

A. 0
B. 1
C. 2
D. 3 
E. None of these

Solution :
 
(3.7)–3 × (13.69)–2 ×  1  ÷ (13.69)–5 = (3.7)?
50.653

or, (3.7)? = (3.7)–3 × (3.7)–2×2 × (3.7)–3 × (3.7)10

= (3.7)–3–4–3+10 = (3.7)0

∴ ? = 0

Hence, option A is correct.

5.  
4 2  + 2 6  – 6 2  = ?
10 3 8
 
A . 2 111
110
 
B. 2 120
110
 
C. 1 120
114
 
D. 1 114
120

E.None of these

Solution :
 
4 2  + 2 6  – 6 2  = ?
10 3 8
 
? = (4 + 2 – 6) +  2  +  6  –  2
10 3 8
 
? = 0 +  (24 + 240 – 30)
120
 
? = 0 +  234
120
 
? = 1 114
120

Hence, option D is correct.

6. 
 
19 ÷  [ 1 –  1  + 2  2 ]  = ?
2 3

A. 
1
6

B.  6

C. 
1
2

D. 
1
19

E. None of these

Solution :
 
19 ÷  [ 1 –  1  + 2  2 ]  = ?
2 3
 
? = 19 ÷  [ 1 –  1  + 2  2 ]
2 3
 
? = 19 ÷  [ 3 –  1  +  2 ]
2 3
 
? = 19 ÷  [ 3 –  3  +  4 ]
6 6
 
? = 19 ÷  [ 3 +  1 ]
6
 
? = 19 ÷  [ 19 ]
6
 
? = 19 ×  [ 6 ]
19

? = 6

Hence, option B is correct.

7. 
7428 ×  3  ×  2  × ? = 619
4 9

A. 0.5
B. 1.5
C. 0.2
D. 2.4
E. None of these

Solution :
 
7428 ×  3  ×  2  × ? = 619
4 9
 
7428 ×  1  ×  1  × ? = 619
2 3
 
3714 ×  1  × ? = 619
3

1238 × ? = 619
 
? =  619  = 0.5
1238

Hence, option A is correct.

8. 
[ 3  +  1 { 3  –  1 ( 7  –  3 ) } ]  = ?
2 2 4 2 8 4

A.
59
15

B.
59
32

C.
59
37

D.
58
11

E. None of these

Solution :
 
[ 3  +  1 { 3  –  1 ( 7  –  3 ) } ]  = ?
2 2 4 2 8 4
 
? =  [ 3  +  1 { 3  –  1 ( 7  –  6 ) } ]
2 2 4 2 8 8
 
? =  [ 3  +  1 { 3  –  1 ( 1 ) } ]
2 2 4 2 8
 
? =  [ 3  +  1 { 3  –  1 } ]
2 2 4 16
 
? =  [ 3  +  1 { 12  –  1 } ]
2 2 16 16
 
? =  [ 3  +  1 { 11 } ]
2 2 16
 
? =  [ 3  +  11 ]
2 32
 
? =  [ 48  +  11 ]
32 32
 
? =  [ 59 ]
32

Hence, option B is correct.

9. 6318 ÷ 17576 = ? × 9

A. 643
B. 729
C. 743
D. 629
E. None of these

Solution :  6318 ÷ 17576 = ? × 9
 
? =  (
6318 ÷ 17576
) 2
9  
 
? =  ( 6318 ÷ 26 ) 2
9  
 
? =  ( 243 ) 2
9  

? = (27)2

? = 729

Hence, option B is correct.

10. 
2?  = (82 × 52) ÷  ( 2002 )

A. 6 
B. 4
C. 5 
D. 8
E. None of these

Solution 
 
2?  = (82 × 52) ÷  ( 2002 )
 
64 × 25  =  8  =  8  × 
2
 = 
42
( 2002 )
2 2 2
 
2?  =  25

∴  ? = 5

Hence, option C is correct.

Want to practice more Simplification Questions in the form of quizzes? Here are the links:
 
Quiz 1 Quiz 2 Quiz 3
Quiz 4 Quiz 5 Quiz 6
Quiz 7 Quiz 8 Quiz 9
Quiz 10 Quiz 11 Quiz 12

simplification and approximation

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