Simplifications: Solved 1054 Simplifications Questions and answers section with explanation for various online exam preparation, various interviews, Logical Reasoning Category online test. Category Questions section with detailed description, explanation will help you to master the topic.
Simplifications Questions
1. What should come in place of question mark (?) in the following question?
164.2 * 2562.1 * 142 * 1963.2 = ?
164.2 * 2562.1 * 142 * 1963.2 = ?
SHOW ANSWER
Correct Ans:(224)8.4
Explanation:
164.2 * 2562.1 * 142 * 1963.2 = ?
Let x be the value to be found,
x = 164.2 * 162*2.1 * 142 * 142*3.2
x = 164.2+4.2 * 142*2+6.4
x = 168.4 * 148.4
x = (16*14)8.4
x = 2248.4
Let x be the value to be found,
x = 164.2 * 162*2.1 * 142 * 142*3.2
x = 164.2+4.2 * 142*2+6.4
x = 168.4 * 148.4
x = (16*14)8.4
x = 2248.4
2. What should come in place of question mark (?) in the following question?
(531441)1/4 / 9 * (√4096)/8 + (√6561)/9 - 16 = ?
(531441)1/4 / 9 * (√4096)/8 + (√6561)/9 - 16 = ?
SHOW ANSWER
Correct Ans:65
Explanation:
(531441)1/4 / 9 * (√4096)/8 + (√6561)/9 - 16 = ?
Let x be the value to be found,
x= 81 / 9* 64/8 + 81/9 -16
=9*8 + 9 -16
x=65
Let x be the value to be found,
x= 81 / 9* 64/8 + 81/9 -16
=9*8 + 9 -16
x=65
3. What should come in place of question mark (?) in the following question?
√294 + √726 + √1176 + √486 – √600 = ?
√294 + √726 + √1176 + √486 – √600 = ?
SHOW ANSWER
Correct Ans:31√6
Explanation:
√294 + √726 + √1176 + √486 – √600 = ?
Assuming the value to be found as X,then
X = √6 × 49 + √6 × 121 + √6 × 196 + √6 × 81 – √6 × 100
X = 7√6 + 11√6 +14√6 + 9√6 – 10√6
Taking √6 as common,
X = √6 (7 + 11 + 14 + 9 – 10)
X = 31√6
Assuming the value to be found as X,then
X = √6 × 49 + √6 × 121 + √6 × 196 + √6 × 81 – √6 × 100
X = 7√6 + 11√6 +14√6 + 9√6 – 10√6
Taking √6 as common,
X = √6 (7 + 11 + 14 + 9 – 10)
X = 31√6
4. What should come in place of question mark (?) in the following question?
27 13/30 + 23 14/25 + 28 12/15 - 17 21/45 + 0.85 - 0.37 = ?
27 13/30 + 23 14/25 + 28 12/15 - 17 21/45 + 0.85 - 0.37 = ?
SHOW ANSWER
Correct Ans:62 121/150
Explanation:
? = 27 13/30 + 23 14/25 + 28 12/15 - 17 21/45 + 0.85 - 0.37
x = (27+23+28-17)+( 13/30 + 14/25 + 12/15 - 21/45) + 0.48
x = 61 +( 195+252+360-210 / 450) + 48/100
x = 61 + 597/450 + 48/100
x = 61 + 1626/900
x = 56526/900 (or) (61+1) (726/900)
x = 62 121/150
x = (27+23+28-17)+( 13/30 + 14/25 + 12/15 - 21/45) + 0.48
x = 61 +( 195+252+360-210 / 450) + 48/100
x = 61 + 597/450 + 48/100
x = 61 + 1626/900
x = 56526/900 (or) (61+1) (726/900)
x = 62 121/150
5. What should come in place of question mark (?) in the following question?
(474552)1/3 - (6084)1/2 + 68 - 7.8 = ?
(474552)1/3 - (6084)1/2 + 68 - 7.8 = ?
SHOW ANSWER
Correct Ans:60.2
Explanation:
?=(474552)1/3 - (6084)1/2 + 68 - 7.8 = ?
(783)1/3 - (782)1/2 + 68 - 7.8
78 - 78 + 68 - 7.8 = 60.2
Hence, option B is correct.
(783)1/3 - (782)1/2 + 68 - 7.8
78 - 78 + 68 - 7.8 = 60.2
Hence, option B is correct.
6. What will come in place of question mark?
1344 ÷ 14 ÷ 4 × 34 - 35% of 540 - 45% of 1320 = ?
1344 ÷ 14 ÷ 4 × 34 - 35% of 540 - 45% of 1320 = ?
SHOW ANSWER
Correct Ans:33
Explanation:
Given Expression is:
1344 ÷ 14 ÷ 4 x 34 - 35% of 540 - 45% of 1320 = ?
---> 96 ÷ 4 x 34 - (35/100) * 540 - (45/100) * 1320
---> 24 x 34 - 189 - 594
---> 816 - 783
---> 33
1344 ÷ 14 ÷ 4 x 34 - 35% of 540 - 45% of 1320 = ?
---> 96 ÷ 4 x 34 - (35/100) * 540 - (45/100) * 1320
---> 24 x 34 - 189 - 594
---> 816 - 783
---> 33
7. What will come in place of question mark?
26 x 19 + 23 - 52% of 1350 = ?
26 x 19 + 23
SHOW ANSWER
Correct Ans:321
Explanation:
Given Expression is:
26 x 19 + 23 - 52% of 1350
---> 494 + 529 - (52/100) * 1350
---> 1023 - 702
---> 321
26 x 19 + 23
---> 494 + 529 - (52/100) * 1350
---> 1023 - 702
---> 321
8. What will come in place of question mark (?) in the following question:
(11.275 + 101.237 + 13.5) / 64 – (17.657 + 18.976) / 22 = ?2 + 8.379 / 4
(11.275 + 101.237 + 13.5) / 64 – (17.657 + 18.976) / 22 = ?2 + 8.379 / 4
SHOW ANSWER
Correct Ans:4.5
Explanation:
(11.275 + 101.237 + 13.5) / 64 – (17.657 + 18.976) / 22 = ?2 + 8.379 / 4
(126.012) / 4 – (36.633) / 4 = ?2 + 8.379 / 4
(126.012) ÷ 4 – (36.633) / 4 – (8.379) / 4 = ?2
(126.012 - 45.012) / 4 = ?2
?2 = 81 / 4
? = 9/2 = 4.5
(126.012) / 4 – (36.633) / 4 = ?2 + 8.379 / 4
(126.012) ÷ 4 – (36.633) / 4 – (8.379) / 4 = ?2
(126.012 - 45.012) / 4 = ?2
?2 = 81 / 4
? = 9/2 = 4.5
9. What will come in place of question mark (?) in the following question:
?2 – 18.75 – 11.25 = 9.09% of 396 + 295
?2 – 18.75 – 11.25 = 9.09% of 396 + 295
SHOW ANSWER
Correct Ans:19
Explanation:
?2– 18.75 – 11.25 = 9.09% of 396 + 295
?2 – 30 = 396 ÷ 11 + 295
?2 = 36 + 295 + 30
?2 = 361
? = 19
?2 – 30 = 396 ÷ 11 + 295
?2 = 36 + 295 + 30
?2 = 361
? = 19
10. Simplify the following:
√13225 + 3√205379 + 52% of 700 = 408 + X
√13225 + 3√205379 + 52% of 700 = 408 + X
SHOW ANSWER
Correct Ans:130
Explanation:
√13225 + 3√205379 + 52% of 700 = 408 + X
115 + 59 + (52/100) x 700 - 408 = X
115 + 59 + 364 - 408 = X
X = 130
115 + 59 + (52/100) x 700 - 408 = X
115 + 59 + 364 - 408 = X
X = 130
11. Simplify the following:
32450 / 11 + (4/9) of 11520 + 48% of 7500 = ?2 - 430
32450 / 11 + (4/9) of 11520 + 48% of 7500 = ?2 - 430
SHOW ANSWER
Correct Ans:110
Explanation:
(32450/11) + (4/9) x 11520 + (48/100) x 7500 = X2 x -430
2950 + 5120 + 3600 + 430 = X2
X2 = 12100
X = 110
2950 + 5120 + 3600 + 430 = X2
X2 = 12100
X = 110
12. What will come in place of question mark (?) in the following simplification problem?
(1/11) x 1639 + (3/7) x 5362 + 400% of 1 = ? + 2241
(1/11) x 1639 + (3/7) x 5362 + 400% of 1 = ? + 2241
SHOW ANSWER
Correct Ans:210
Explanation:
Given expression is: (1/11) x 1639 + (3/7) x 5362 + 400% of 1 = ? + 2241
---> 149 + 3 x 766 + (400/100) x 1 - 2241 = ?
---> 149 + 2298 + 4 - 2241 = ?
---> 2451 - 2241 = ?
---> ? = 210
---> 149 + 3 x 766 + (400/100) x 1 - 2241 = ?
---> 149 + 2298 + 4 - 2241 = ?
---> 2451 - 2241 = ?
---> ? = 210
13. ∜62,50,000 - ∛3375 = √?
SHOW ANSWER
Correct Ans:1,225
Explanation:
Given expression is: ∜62,50,000 - ∛3375 = √?
---> ∜(50)4 - 15 = √?
----> 50 - 15 = √?
---> 35 = √?
----> ? = (35)2
----> ? = 1,225
---> ∜(50)4 - 15 = √?
----> 50 - 15 = √?
---> 35 = √?
----> ? = (35)2
----> ? = 1,225
14. √[52 x 14 - 6 x 7 + (4)?] = 18
SHOW ANSWER
Correct Ans:2
Explanation:
√[52 x 14 - 6 x 7 + (4)?] = 18
---> [25 x 14 - 6 x 7 + (4)?] = 182
---> 350 - 42 + (4)? = 324
---> 308 + (4)? = 324
---> (4)? = 324 - 308
---> (4)? = 16
---> (4)? = 42
Equating powers, we get
---> ? = 2
Hence, the answer is 2.
---> [25 x 14 - 6 x 7 + (4)?] = 182
---> 350 - 42 + (4)? = 324
---> 308 + (4)? = 324
---> (4)? = 324 - 308
---> (4)? = 16
---> (4)? = 42
Equating powers, we get
---> ? = 2
Hence, the answer is 2.
15. [(?)11/7/50] = [20/(?)10/7]
SHOW ANSWER
Correct Ans:10
Explanation:
[(x)11/7/50] = [20/(x)10/7]
[(x)11/7 * (x)10/7] = 20*50
(x)(11/7 + 10/7) = 1000
(x)21/7 = 1000
(x)3 = 103
x = 10
[(x)11/7 * (x)10/7] = 20*50
(x)(11/7 + 10/7) = 1000
(x)21/7 = 1000
(x)3 = 103
x = 10
16. 1/[2 + (1/(4 +(1/(5 - 1/3))))] = ?
SHOW ANSWER
Correct Ans:59/132
Explanation:
1/[2 + (1/(4 +(1/(5 - 1/3))))] = x
1/[2 + (1/(4 +(1/(14/3))))] = x
1/[2 + (1/(4 +3/14))] = x
1/[2 + (1/(59/14))] = x
1/[2 + 14/59] = x
1/[132/59] = x
x = 59/132
1/[2 + (1/(4 +(1/(14/3))))] = x
1/[2 + (1/(4 +3/14))] = x
1/[2 + (1/(59/14))] = x
1/[2 + 14/59] = x
1/[132/59] = x
x = 59/132
17. 23 * 2 (45-15)+168 / 4 / 2 - (11)2 = ?
SHOW ANSWER
Correct Ans:1280
Explanation:
Follow BODMAS Rule,
x = 23 x2 (45- 15)+168 / 4 / 2 - (11)2
x= 23 x 2 (30) + 168/(4x2) - (11)2
x= 23 * 60 + 21 -121
x= 1380 + 21 -121
x= 1280
x = 23 x2 (45- 15)+168 / 4 / 2 - (11)2
x= 23 x 2 (30) + 168/(4x2) - (11)2
x= 23 * 60 + 21 -121
x= 1380 + 21 -121
x= 1280
18. (7 * 7)3 / (49 * 7)3 * (2401)2 = 7?
SHOW ANSWER
Correct Ans:5
Explanation:
(7 * 7)3 / (49 * 7)3 * (2401)2 = 7x
76 / 79 * 78 = 7x
7(6 - 9 + 8) = 7x
75 = 7x
x = 5
76 / 79 * 78 = 7x
7(6 - 9 + 8) = 7x
75 = 7x
x = 5
19. 185% of 600 + 25% of 240 = ?% of 1000
SHOW ANSWER
Correct Ans:117
Explanation:
185% of 600 + 25% of 240 = x% of 1000
(185*6) + (1/4)*240 = (x/100) * 1000
1110 + 60 = 10x
x = 1170/10
x = 117
(185*6) + (1/4)*240 = (x/100) * 1000
1110 + 60 = 10x
x = 1170/10
x = 117
20. (78125)1.3 * (15625)1.25 ÷ (125)2 = 5?
SHOW ANSWER
Correct Ans:10.6
Explanation:
(78125)1.3 * (15625)1.25 ÷ (125)2 = 5x
(5)7*1.3 * (5)6*1.25 ÷ (5)3*2 = 5x
5(9.1+7.5-6) = 5x
x = 10.6
(5)7*1.3 * (5)6*1.25 ÷ (5)3*2 = 5x
5(9.1+7.5-6) = 5x
x = 10.6
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