Arithmatical - Numbers

DIRECTIONS : Problems based on Numbers.
46. The sum of the smallest six digit number and the greatest five digit number is
  A.  201110
  B.  199999
  C.  211110
  D.  1099999
Solution
Requires sum=(100000 + 99999)
=199999.
47. In a division sum, the divisor is 10 times the quotient and 5 times the remainder. If the remainder is 46, the divident is
  A.  4236
  B.  4306
  C.  4336
  D.  5336
Solution
Divisor= (5×46)
= 230.
Also. 10×Q= 230
‹=› Q=23.
And, R= 46.
Dividend= (230×23+46)
= 5336.

48. A positive integer, which when added to 1000, gives a sum which is greater than when it is multiplied by 1000. This positive integer is
  A.  1
  B.  3
  C.  5
  D.  7
Solution
(1000 + N) > (1000N)
Clearly, N=1.
49. The difference between two numbers is 1365. When the larger number is divided by the smaller one, the quotient is 6 and the remainder is 15. The smaller number is
  A.  240
  B.  270
  C.  295
  D.  360
Solution
Let the smaller number be x.
Then, larger number = (1365 + x))
Therefore 1365 + x ‹=›(6x+15
‹=› 5x = 1350
‹=› x= 270.
50. If x is a whole number, then x²(x² - 1) is always divisible by
  A.  multiple of 12
  B.  24
  C.  12 - x
  D.  12
Solution
Putting x = 12,we get 2²(2² - 1)= 12.
So, x²(x² - 1) is always divisible by 12.
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