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11.
7 is added to a certain number; the sum is multiplied by 5; the product is divided by 9 and 3 is subtracted from the quotient. The remainder left is 12. The number is:
  • A.
    20
  • C.
    40
  • B.
    30
  • D.
    60
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Answer : [A]
Explanation :
 
Let the number be x. Then,
 
 
 
5(x + 7)
9
 - 3 = 12  
 
 
  5 (x + 7) - 27 = 108  
 
 
  5x + 35 = 135  
 
 
  5x = 100  
 
 
  x = 20  
 
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12.
A class starts at 10 a.m. and lasts till 1.27 p.m. Four periods are held during this interval. After every period, 5 minutes are given free to the students. The exact duration of each period is:
  • A.
    42 minutes
  • C.
    51 minutes
  • B.
    48 minutes
  • D.
    53 minutes
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Answer : [B]
Explanation :
 
Time between 10 a.m. and 13.27 hours = 3 hrs. 27 min. = 207 min.
 
For three periods in between free time = 15 min.
 
Remaining time = (207 15) min. = 192 min.
 
 
  Duration of each of the 4 periods =
192
4
   min. = 48 min.    
 
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13.
The fluid contained in a bucket can fill four large bottles or seven small bottles. A full large bottle is used to fill an empty small bottle. What fraction of the fluid is left over in the large bottle when the small one is full?
  • A.
    2  
    7  
  • C.
    4  
    7  
  • B.
    3  
    7  
  • D.
    5  
    7  
  • Answer & Explanation
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Answer : [B]
Explanation :
 
Let the capacity of the bucket be x litres. Then,
 
Capacity of 1 large bottle =
x
4
; Capacity of 1 small bottle =
x
7
 
 
Fluid left in large bottle =  
x
4
-
x
7
  =
3x
28
   
 
 
  Required fraction =  
3x/28
x/4
  =  
3x
28
-
4
x
  =
3
7
   
 
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14.
 
785 x 785 x 785 + 435 x 435 x 435
785 x 785 + 435 x 435 - 785 x 435
    Simplifies to :  
  • A.
    350
  • C.
    1220
  • B.
    785
  • D.
    1320
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Answer : [C]
Explanation :
 
Given exp. =  
a3 + b3
a2 + b2 - ab
   = (a + b), where a = 785, b = 435      
 
  = (785 + 435) = 1220.  
 
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15.
Vidushi and Sanya distribute Rs. 100 each in charity. Vidushi distributes money to 5 more people than Sanya and Sanya gives each Re. 1 more than Vidushi. How many people are recipients of the charity?
  • A.
    45
  • C.
    90
  • B.
    60
  • D.
    None of these
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Answer : [A]
Explanation :
 
Suppose, Sanya and Vidushi donate money to x and (x + 5) people respectively.
 
Then,
100
x
-
100
x + 5
 = 1
 
 
  100 (x + 5) - 100x = x(x + 5)  
 
 
  x2 + 5x - 500 = 0  
 
 
  (x - 20) (x + 25) = 0  
 
 
  x = 20  
 
 
  Total number of recipients of charity = x + (x + 5) = 2x + 5 = 45    
 
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