1.

Find the smallest number which when divided by 18,12,24 leaves remainder of 16,10 and 24 respectively

Answer»

If a NUMBER 'a' and a number 'b' are DIVISIBLE by a number 'n' then, a+b and a-b is ALSO divisible by n

=> let the number be n which divides 62, 132 and 237 leaving a REMINDER r

=> the required number then becomes H.C.F of 62-r, 132-r and 237-r

=> it could also be the H.C.F of 
(132-r)-(62-r) and (237-r)-(132-r)

i.e. 70 and 105

=> H.C.F of 70 and 105 = 35

the required number n is 35.


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