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61.
A six-digit number is formed by repeating a three-digit number; for example, 256256 or 678678 etc. Any number of this form is always exactly divisible by :
  • A.
    7 only
  • C.
    13 only
  • B.
    11 only
  • D.
    1001
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Answer : [D]
Explanation :
 
256256 = 256 x 1001; 678678 = 678 x 1001, etc.
 
So, any number of this form is divisible by 1001
 
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62.
When a number is divided by 31, the remainder is 29. When the same number is divided by 16, What will be the remainder?
  • A.
    11
  • C.
    15
  • B.
    13
  • D.
    Data inadequate
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Answer : [D]
Explanation :
 
Number = (31 x Q) + 29. Given data is inadequate.
 
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63.
The number of digits of the smallest number, which when multiplied by 7 gives the result consisting entirely of nines, is:
  • A.
    3
  • C.
    6
  • B.
    5
  • D.
    8
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Answer : [C]
Explanation :
 
By hit and trial, we find that a number exactly divisible by 7 and consisting entirely of nines is 999999. Number of digits in it = 6.
 
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64.
7845 -? = 8461 – 3569
  • A.
    2593
  • C.
    3569
  • B.
    2773
  • D.
    None of these
  • Answer & Explanation
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Answer : [D]
Explanation :
 
     Let 7845 - x = 8461 - 3569
 
  Then, 7845 - x = 4892
 
                    x = (7845 - 4892) = 2953
 
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65.
The unit's digit in the product (3127)173 is:
  • A.
    1
  • C.
    7
  • B.
    3
  • D.
    9
  • Answer & Explanation
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Answer : [C]
Explanation :
 
Unit digit in (3127)173 - Unit digit in (7)173. Now, 74 gives unit digit 1
 
   (7)173 = (74)43 x 71. Thus, (7)173 gives unit digit 7.      
 
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