Simplifications: Solved 620 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. Can you find the value for the following expression:
(1675÷5) + (5328÷12) * (8430÷15) = (?)^2 − 235
(1675÷5) + (5328÷12) * (8430÷15) = (?)^2 − 235
SHOW ANSWER
Correct Ans:500.09
Explanation:
Given expression is:
(1675÷5) + (5328÷12) * (8430÷15) = (?)^2 − 235
=> 335 + 444 * 562 = (?)^2 − 235
=> 335 + 249528 = (?)^2 − 235
=> 249863 = (?)^2 − 235
=> 249863 + 235 = (?)^2
=> 250098 = (?)^2
=> (?) = sqrt(250098)
=> (?) = 500.09
(1675÷5) + (5328÷12) * (8430÷15) = (?)^2 − 235
=> 335 + 444 * 562 = (?)^2 − 235
=> 335 + 249528 = (?)^2 − 235
=> 249863 = (?)^2 − 235
=> 249863 + 235 = (?)^2
=> 250098 = (?)^2
=> (?) = sqrt(250098)
=> (?) = 500.09
2. Can you find the value for the following expression:
(29)^2 * 91 ÷ 7 + (8)^3 + 61 =(?) ^ 3 + 858
(29)^2 * 91 ÷ 7 + (8)^3 + 61 =(?) ^ 3 + 858
SHOW ANSWER
Correct Ans:22
Explanation:
Given expression is:
(29)^2 * 91 ÷ 7 + (8)^3 + 61 =(?)^3 + 858
=> 841 x (13) + 512 + 61 = (?)^3 + 858
=> 10933 + 512 + 61 = (?)^3 + 858
=> 11506 = (?)^3 + 858
=> 11506 - 858 = (?)^3
=> 10648 = (?)^3
=> (?) = cube root(10648)
=> (?) = 22
(29)^2 * 91 ÷ 7 + (8)^3 + 61 =(?)^3 + 858
=> 841 x (13) + 512 + 61 = (?)^3 + 858
=> 10933 + 512 + 61 = (?)^3 + 858
=> 11506 = (?)^3 + 858
=> 11506 - 858 = (?)^3
=> 10648 = (?)^3
=> (?) = cube root(10648)
=> (?) = 22
3. Can you find the value of "?" in the following expression:
[50 - {20 + 60% of (26/13 + 24/12 + 21) - 2} + 8] = 625/?
[50 - {20 + 60% of (26/13 + 24/12 + 21) - 2} + 8] = 625/?
SHOW ANSWER
Correct Ans:25
Explanation:
Given expression is:
[50 - {20 + 60% of (26/13 + 24/12 + 21) - 2} + 8] = 625/?
=> [50 - {20 + 60% of (2 + 2 + 21) - 2} + 8] = 625/x
=> [50 - {20 + 60% of (25) - 2} + 8] = 625/x
=> [50 - {20 + (60/100 * 25) - 2} + 8] = 625/x
=> [50 - {20 + 15 - 2} + 8] = 625/x
=> [50 - {33} + 8] = 625/x
=> [50 - 33 + 8] = 625/x
=> 25 = 625/x
=> x = 625 / 25
=> x = 25.
[50 - {20 + 60% of (26/13 + 24/12 + 21) - 2} + 8] = 625/?
=> [50 - {20 + 60% of (2 + 2 + 21) - 2} + 8] = 625/x
=> [50 - {20 + 60% of (25) - 2} + 8] = 625/x
=> [50 - {20 + (60/100 * 25) - 2} + 8] = 625/x
=> [50 - {20 + 15 - 2} + 8] = 625/x
=> [50 - {33} + 8] = 625/x
=> [50 - 33 + 8] = 625/x
=> 25 = 625/x
=> x = 625 / 25
=> x = 25.
4. Can you simplify the following expression:
5(17/37) x 4(51/52) x 11(1/7) + 2(3/4)
5(17/37) x 4(51/52) x 11(1/7) + 2(3/4)
SHOW ANSWER
Correct Ans:305.75
Explanation:
Given expression is:
5(17/37) x 4(51/52) x 11(1/7) + 2(3/4)
= {(37 * 5 + 17) / 37} x {(52 * 4 + 51) / 52} x {(7 * 11 + 1) / 7} + {(4 * 2 + 3) / 4}
= {202 / 37} x {259 / 52} x {78 / 7} + {11 / 4}
On simplifying, 259 / 37 = 7
= 202 x 7 / 52 x 78 / 7 + 11/4
= 202 x 78 / 52 + 11/4
= 101 x 78 / 26 + 11/4
= 101 x 3 + 11/4
= 303 + 11/4
= (1212 + 11) / 4
= 1223 / 4
= 305.75
Therefore, 5(17/37) x 4(51/52) x 11(1/7) + 2(3/4) = 305.75
5(17/37) x 4(51/52) x 11(1/7) + 2(3/4)
= {(37 * 5 + 17) / 37} x {(52 * 4 + 51) / 52} x {(7 * 11 + 1) / 7} + {(4 * 2 + 3) / 4}
= {202 / 37} x {259 / 52} x {78 / 7} + {11 / 4}
On simplifying, 259 / 37 = 7
= 202 x 7 / 52 x 78 / 7 + 11/4
= 202 x 78 / 52 + 11/4
= 101 x 78 / 26 + 11/4
= 101 x 3 + 11/4
= 303 + 11/4
= (1212 + 11) / 4
= 1223 / 4
= 305.75
Therefore, 5(17/37) x 4(51/52) x 11(1/7) + 2(3/4) = 305.75
5. Can you find the value of the expression:
(512 * 5 ^ 2 * 3) / (45 *32 )
(512 * 5 ^ 2 * 3) / (45 *32 )
SHOW ANSWER
Correct Ans:26 (2/3)
Explanation:
Given
To find out the value of the expression
=> ( 512 * 5 ^ 2 *3 ) / (45 *32)
= ( 512 * 25 * 3 ) / ( 45 * 32 )
= ( 16 * 5 ) / ( 3 )
= 80 / 3
= 26 ( 2 / 3)
To find out the value of the expression
=> ( 512 * 5 ^ 2 *3 ) / (45 *32)
= ( 512 * 25 * 3 ) / ( 45 * 32 )
= ( 16 * 5 ) / ( 3 )
= 80 / 3
= 26 ( 2 / 3)
6. Solve the given expression
(8195 / 745) + ? * 12 = 7847
(8195 / 745) + ? * 12 = 7847
SHOW ANSWER
Correct Ans:653
Explanation:
To find out the value of the expression
=> (8195 / 745) + ? * 12 = 7847
=> 11 + X * 12 = 7847
=> 11 + 12 X =7847
=> 12 X = 7847 - 11
=> 12 X = 7836
=> X = 7836 / 12
=> X = 653
=> (8195 / 745) + ? * 12 = 7847
=> 11 + X * 12 = 7847
=> 11 + 12 X =7847
=> 12 X = 7847 - 11
=> 12 X = 7836
=> X = 7836 / 12
=> X = 653
7. Can you find the value for the expression:
(9 / 18) * (162 / 207) ÷ (554 / 294) + (79 / 100) = ?
(9 / 18) * (162 / 207) ÷ (554 / 294) + (79 / 100) = ?
SHOW ANSWER
Correct Ans:1
Explanation:
Given expression is:
(9 / 18) * (162 / 207) ÷ (554 / 294) + (79 / 100) = ?
= (9 / 18) * (162 / 207) X (294 / 554) + (79 / 100)
= (1 / 2) * (18 / 23) X (147 / 277) + 0.79
= (9 / 23) X (147 / 277) + 0.79
= {(9 * 147) / (23 * 277)} + 0.79
= (1323 / 6371) + 0.79
= 0.21 + 0.79
= 1
Hence the answer is : (9 / 18) * (162 / 207) ÷ (554 / 294) + (79 / 100) = 1
(9 / 18) * (162 / 207) ÷ (554 / 294) + (79 / 100) = ?
= (9 / 18) * (162 / 207) X (294 / 554) + (79 / 100)
= (1 / 2) * (18 / 23) X (147 / 277) + 0.79
= (9 / 23) X (147 / 277) + 0.79
= {(9 * 147) / (23 * 277)} + 0.79
= (1323 / 6371) + 0.79
= 0.21 + 0.79
= 1
Hence the answer is : (9 / 18) * (162 / 207) ÷ (554 / 294) + (79 / 100) = 1
8. Can you find the value for the expression:
(6859)^(1/3) * (50625)^(1/4) + 5^2 = ? * 5
(6859)^(1/3) * (50625)^(1/4) + 5^2 = ? * 5
SHOW ANSWER
Correct Ans:62
Explanation:
Given expression is:
(6859)^(1/3) * (50625)^(1/4) + 5^2 = ? * 5
Since cuberoot of (6859) [i.e., (6859)^(1/3)] = 19
and (50625)^(1/4) = [(225)^2]^(1/4)
= [225]^(1/2)
= 15
Therefore, (6859)^(1/3) * (50625)^(1/4) + 5^2 = ? * 5
=> 19 * 15 + 5^2 = ? * 5
=> 285 + 25 = ? * 5
=> 310 = ? * 5
=> 310 / 5 = ?
=> 62 = ?
Hence the answer is : "62"
(6859)^(1/3) * (50625)^(1/4) + 5^2 = ? * 5
Since cuberoot of (6859) [i.e., (6859)^(1/3)] = 19
and (50625)^(1/4) = [(225)^2]^(1/4)
= [225]^(1/2)
= 15
Therefore, (6859)^(1/3) * (50625)^(1/4) + 5^2 = ? * 5
=> 19 * 15 + 5^2 = ? * 5
=> 285 + 25 = ? * 5
=> 310 = ? * 5
=> 310 / 5 = ?
=> 62 = ?
Hence the answer is : "62"
9. Can you find the value for the expression:
2Sqrt(2) * 3Sqrt(3) * 5Sqrt(2) * 9Sqrt(3) = ?
2Sqrt(2) * 3Sqrt(3) * 5Sqrt(2) * 9Sqrt(3) = ?
SHOW ANSWER
Correct Ans:1620
Explanation:
Given expression is:
2Sqrt(2) * 3Sqrt(3) * 5Sqrt(2) * 9Sqrt(3) = ?
=> 2 * 3 * 5 * 9 [Sqrt(2)]^2 * Sqrt(3)^2 = ?
= 270 * [2] * [3]
= 270 * 6
= 1620
2Sqrt(2) * 3Sqrt(3) * 5Sqrt(2) * 9Sqrt(3) = ?
=> 2 * 3 * 5 * 9 [Sqrt(2)]^2 * Sqrt(3)^2 = ?
= 270 * [2] * [3]
= 270 * 6
= 1620
10. Can you find the value for the expression:
[(64)^1/2 ]^4.2 × (8)^4.2 × (7)^8.4 × (56)^4.3 = (56)^?
[(64)^1/2 ]^4.2 × (8)^4.2 × (7)^8.4 × (56)^4.3 = (56)^?
SHOW ANSWER
Correct Ans:12.7
Explanation:
Given expression is:
[(64)^1/2 ]^4.2 × (8)^4.2 × (7)^8.4 × (56)^4.3 = (56)^?
=> [(8^2)^1/2 ]^4.2 × (8)^4.2 × (7)^8.4 × (56)^4.3 = (56)^?
=> [(8)]^4.2 × (8)^4.2 × (7)^8.4 × (56)^4.3 = (56)^?
=> (8)^{4.2 + 4.2} × (7)^8.4 × (56)^4.3 = (56)^?
=> (8)^8.4 × (7)^8.4 × (56)^4.3 = (56)^?
=> (8 * 7)^8.4 × (56)^4.3 = (56)^?
=> (56)^8.4 × (56)^4.3 = (56)^?
=> (56)^{8.4 + 4.3} = (56)^?
=> (56)^{12.7} = (56)^?
Thus the answer is : "12.7"
[(64)^1/2 ]^4.2 × (8)^4.2 × (7)^8.4 × (56)^4.3 = (56)^?
=> [(8^2)^1/2 ]^4.2 × (8)^4.2 × (7)^8.4 × (56)^4.3 = (56)^?
=> [(8)]^4.2 × (8)^4.2 × (7)^8.4 × (56)^4.3 = (56)^?
=> (8)^{4.2 + 4.2} × (7)^8.4 × (56)^4.3 = (56)^?
=> (8)^8.4 × (7)^8.4 × (56)^4.3 = (56)^?
=> (8 * 7)^8.4 × (56)^4.3 = (56)^?
=> (56)^8.4 × (56)^4.3 = (56)^?
=> (56)^{8.4 + 4.3} = (56)^?
=> (56)^{12.7} = (56)^?
Thus the answer is : "12.7"
11. Can you find the value for the expression:
6 (1/3) + 4 (1/5) + 1 (3/7) – 2 (1/7) + 4 (2/5) × 3 (1/3) = ?
6 (1/3) + 4 (1/5) + 1 (3/7) – 2 (1/7) + 4 (2/5) × 3 (1/3) = ?
SHOW ANSWER
Correct Ans:24 (17/35)
Explanation:
Given expression is:
6 (1/3) + 4 (1/5) + 1 (3/7) - 2 (1/7) + 4 (2/5) × 3 (1/3) = ?
= (19 / 3) + (21 / 5) + (10 / 7) - (15 / 7) + (22 / 5) * (10 / 3)
= (19 / 3) + (21 / 5) + [(10 - 15) / 7] + (44 / 3)
= (19 / 3) + (21 / 5) - (5 / 7) + (44 / 3)
= (19 + 44) / 3 + (21 / 5) - (5 / 7)
= (63 / 3) + (21 / 5) - (5 / 7)
= 21 + (21 / 5) - (5 / 7)
On taking L.C.M we get,
= (735 + 147 - 25) / 35
= 857 / 35
= 24 (17/ 35)
6 (1/3) + 4 (1/5) + 1 (3/7) - 2 (1/7) + 4 (2/5) × 3 (1/3) = ?
= (19 / 3) + (21 / 5) + (10 / 7) - (15 / 7) + (22 / 5) * (10 / 3)
= (19 / 3) + (21 / 5) + [(10 - 15) / 7] + (44 / 3)
= (19 / 3) + (21 / 5) - (5 / 7) + (44 / 3)
= (19 + 44) / 3 + (21 / 5) - (5 / 7)
= (63 / 3) + (21 / 5) - (5 / 7)
= 21 + (21 / 5) - (5 / 7)
On taking L.C.M we get,
= (735 + 147 - 25) / 35
= 857 / 35
= 24 (17/ 35)
12. Can you find the value for the expression:
(∛12167) × (∛274625) × (∛250047) = ?
(∛12167) × (∛274625) × (∛250047) = ?
SHOW ANSWER
Correct Ans:94185
Explanation:
Given expression is:
(∛12167) × (∛274625) × (∛250047)=?
= (∛12167) × (∛274625) × (∛250047)
= 23 × 65 × 63
= 94185
(∛12167) × (∛274625) × (∛250047)=?
= (∛12167) × (∛274625) × (∛250047)
= 23 × 65 × 63
= 94185
13. Can you find the value for the expression:
15×(1/4) + 32×(1/3) + 12×(3/4) × 7 × (1/17) = ? + 13×(1/4)
15×(1/4) + 32×(1/3) + 12×(3/4) × 7 × (1/17) = ? + 13×(1/4)
SHOW ANSWER
Correct Ans:124 x (1/3)
Explanation:
Given expression is:
15×(1/4) + 32×(1/3) + 12×(3/4) × 7×(1/17) = ? + 13×(1/4)
=> (61 / 4) + (97 / 3) + (51 / 4) * (120 / 17) = ? + (53 / 4)
=> (61 / 4) + (97 / 3) + 90 = ? + (53 / 4)
=> (61 / 4) + (97 / 3) + 90 - (53 / 4) = ?
=> [(61 - 53) / 4] + (97 / 3) + 90 = ?
=> [8 / 4] + (97 / 3) + 90 = ?
=> 2 + (97 / 3) + 90 = ?
On taking L.C.M for left hand side, we get
=> (6 + 97 + 270) / 3 = ?
=> (373 / 3) = ?
=> 124 (1 / 3) = ?
Hence the answer is : "124 (1 / 3)"
15×(1/4) + 32×(1/3) + 12×(3/4) × 7×(1/17) = ? + 13×(1/4)
=> (61 / 4) + (97 / 3) + (51 / 4) * (120 / 17) = ? + (53 / 4)
=> (61 / 4) + (97 / 3) + 90 = ? + (53 / 4)
=> (61 / 4) + (97 / 3) + 90 - (53 / 4) = ?
=> [(61 - 53) / 4] + (97 / 3) + 90 = ?
=> [8 / 4] + (97 / 3) + 90 = ?
=> 2 + (97 / 3) + 90 = ?
On taking L.C.M for left hand side, we get
=> (6 + 97 + 270) / 3 = ?
=> (373 / 3) = ?
=> 124 (1 / 3) = ?
Hence the answer is : "124 (1 / 3)"
14. Can you find the value for the expression:
143^2 + 188^2 + 201^2 - 142^2 - 186^2 - 199^2 = ?
143^2 + 188^2 + 201^2 - 142^2 - 186^2 - 199^2 = ?
SHOW ANSWER
Correct Ans:1833
Explanation:
Given expression is:
143^2 + 188^2 + 201^2 - 142^2 - 186^2 - 199^2 = ?
= (143^2 – 142^2) + (188^2 – 186^2) + ( 201^2 – 199^2)
Using Formula: a^2 – b^2 = (a+b)(a-b), we have:
(143 + 142)(143 – 142) + (188 + 186)(188 – 186) + (201 + 199)(201 – 199)
= [285 x 1] + [374 x 2] + [400 x 2]
= 285 + 748 + 800
= 1833
143^2 + 188^2 + 201^2 - 142^2 - 186^2 - 199^2 = ?
= (143^2 – 142^2) + (188^2 – 186^2) + ( 201^2 – 199^2)
Using Formula: a^2 – b^2 = (a+b)(a-b), we have:
(143 + 142)(143 – 142) + (188 + 186)(188 – 186) + (201 + 199)(201 – 199)
= [285 x 1] + [374 x 2] + [400 x 2]
= 285 + 748 + 800
= 1833
15. Can you find the value for the expression:
(35)^2 / [(125)^ (1/3)] + (25)^2 / 125
(35)^2 / [(125)^ (1/3)] + (25)^2 / 125
SHOW ANSWER
Correct Ans:250
Explanation:
Given expression is
(35)^2 / [(125)^ (1/3)] + (25)^2 / 125
= (1225 / 5) + (625 / 125)
= 245 + 5
= 250
(35)^2 / [(125)^ (1/3)] + (25)^2 / 125
= (1225 / 5) + (625 / 125)
= 245 + 5
= 250
16. Can you find the value for 'X' in the below expression:
[ {(144^ 2) / 48} * X] / 22 = 216
[ {(144^ 2) / 48} * X] / 22 = 216
SHOW ANSWER
Correct Ans:11
Explanation:
Given expression is
[ {(144^ 2) / 48} * X] / 22 = 216
=> [(20736 / 48) * X] / 22 = 216
=> [432 * X] / 22 = 216
=> 432 * X = 216 * 22
=> 432 * X = 4752
= X = 4752 / 432
=> X = 11
[ {(144^ 2) / 48} * X] / 22 = 216
=> [(20736 / 48) * X] / 22 = 216
=> [432 * X] / 22 = 216
=> 432 * X = 216 * 22
=> 432 * X = 4752
= X = 4752 / 432
=> X = 11
17. Can you find the value for the expression:
(9 / 13) of 221 + 1 (4 / 9) of 378 = 241 + ?
(9 / 13) of 221 + 1 (4 / 9) of 378 = 241 + ?
SHOW ANSWER
Correct Ans:458
Explanation:
Given expression is
( 9 / 13) of 221 + 1 ( 4 / 9 ) of 378 = 241 + ?
=> ( 9 / 13 ) * 221 + ( 13 / 9 ) * 378 - 241 = ?
= ( 9 * 17) + ( 13 * 42 ) - 241
= 153 + 546 - 241
= 699 - 241
= 458
( 9 / 13) of 221 + 1 ( 4 / 9 ) of 378 = 241 + ?
=> ( 9 / 13 ) * 221 + ( 13 / 9 ) * 378 - 241 = ?
= ( 9 * 17) + ( 13 * 42 ) - 241
= 153 + 546 - 241
= 699 - 241
= 458
18. Can you find the value for the expression:
5 + 55 + 555+ 5555 + 55555
5 + 55 + 555+ 5555 + 55555
SHOW ANSWER
Correct Ans:61725
Explanation:
Given expression is
5 + 55 + 555+ 5555 + 55555
By adding each and every number together we get,
= 60 + 555 + 5555 + 55555
= 615 + 5555 + 55555
= 6170 + 55555
= 61725
5 + 55 + 555+ 5555 + 55555
By adding each and every number together we get,
= 60 + 555 + 5555 + 55555
= 615 + 5555 + 55555
= 6170 + 55555
= 61725
19. Evaluate the expression: 12 / 4 + 12 / 3 + 20 - 24 / 4 + 1
SHOW ANSWER
Correct Ans:22
Explanation:
20. Èvaluate the expression: 2 + 6 - 18 / 4 + 21 - 10 / 4 - 2
SHOW ANSWER
Correct Ans:20
Explanation:
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