SOLUTION IN 151 TO 160

151.  On dividing 13294 by 97, we get remainder =5

           Required number to be subtracted = 5.

152. Clearly, 5 x (sum of numbers) is divisible by 15.

             Sum of numbers must be divisible by 3

             Now, (250 + 341) = 591 is divisible by 3. So, required pair is 250, 341.

153. Required number is divisible by 72 as well as by 112, if it is divisible by their LCM, which    is 1008.

            Now, 1008 when divided by 72, gives quotient =14

            Required number = 14.

154.      Let it be n times. Then,(1111 – 99 n)  <00.

          By hit and trial, we find that n=11.

155.   On dividing 457 by 11, remainder is 6

         Required number is either 451 or 462. Nearest to 456 are 462.

156.  On dividing 99547 by 687, the 619, which is more than half of 687? So, we must add (687    – 619) = 68 to the given number.

         Required number = (99547 + 68) = 99615.

157.   Largest number of 5 digits = (99999. On dividing 99999 by 99, we get 9 as remainder

           required number = (99999 – 9) – 99990.

158.  Smallest number of 5 digits =10000.

        On dividing 10000 by 476, we get remainder = 4.

         Required number =[10000 +(476 -4)] = 10472.

159.   Required number = 999 x 366 + 103= (1000 – 1) x 366 +103 = 366000 – 366 + 103

         = 365737.

160.  4150= 55 x X + 25 55 X = 4125 X = 4125 \55 = 75.