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16.
(25)7.5 + (5)2.5 ÷ (125)1.5 = 5?
  • A.
    8.5
  • C.
    16
  • E.
    None of these
  • B.
    13
  • D.
    17.5
  • Answer & Explanation
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Answer : [B]
Explanation :
 
Let (25)7.5 + (5)2.5 ÷ (125)1.5 = 5x. Then,
(52)7.5 x (5)2.5
(53)1.5
 = 5x      
 
 
 
5(2 x 7.5) x 52.5
5(3 x 1.5)
 = 5x    
 
 
 
515 x 52.5
54.5
 = 5x    
 
 
  5x = 5(15 + 25 - 4.5) = 513  
 
 
  x = 13  
 
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17.
If m and n are whole numbers such that mn = 121, then the value of (m - 1)n + 1 is:
  • A.
    1
  • C.
    121
  • B.
    10
  • D.
    1000
  • Answer & Explanation
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Answer : [D]
Explanation :
 
We know that 112 = 121. Putting m = 11 and n = 2, we get :
 
(m - 1)n + 1 = (11 - 1)(2 + 1) = 103 = 1000.
 
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18.
If
9n x 35 x (27)3
3 x (81)4
 = 27, then the value of n is:      
  • A.
    0
  • C.
    3
  • B.
    2
  • D.
    4
  • Answer & Explanation
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Answer : [C]
Explanation :
 
9n x 35 x (27)3
3 x (81)4
 = 27
 
(32)n x 35 x (33)3
3 x (34)4
 = 33    
 
   
 
32n x 35 x (33 x 3)
3 x 3(4 x 4)
 = 33    
 
 
 
32n + 5 + 9
3 x 316
 = 33    
 
 
 
32n + 14
317
 = 33    
 
 
 
3(2n + 14 - 17) = 33      
 
 
 
32n - 3 = 33      
 
 
 
2n - 3 = 3      
 
 
 
2n = 6      
 
 
 
n = 3      
 
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19.
The value of [(10)150 ÷ (10)146] is:
  • A.
    1000
  • C.
    100000
  • B.
    10000
  • D.
    106
  • Answer & Explanation
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Answer : [B]
Explanation :
 
(10)150 ÷ (10)146 =
(10)150
(10)146
 = (10)(150 - 146) = 104 = 10000      
 
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20.
If  
a
b
  x-1 =  
b
a
  x-3 , then the value of x is:            
  • A.
    1  
    2  
  • C.
    2
  • B.
    1
  • D.
    7  
    2  
  • Answer & Explanation
  • Report
Answer : [C]
Explanation :
 
 
a
b
  x - 1 =  
b
a
  x - 3
 
 
a
b
  x - 1 =  
a
b
  - (x - 3) =  
a
b
  (3 - x)        
 
 
 
x - 1 = 3 - x      
 
 
 
2x = 4      
 
 
 
x = 2      
 
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