Simplification and Approximation Questions with Solution

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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.
  (710)2 + (5 + 14)2 = (?)3 – 28

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

Solution : 

(710)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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simplification questions for lic assistant
 

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