Question 59

Let x be the least number which when divided by 12, 15, 18, 20 and 27, the remainder in each case is 2, but x is divisible by 23. If x is divided by the sum of its digits then the quotient is:

Solution

L.C.M. (12,15,18,20,27) = 540

Least number which when divided by 12, 15, 18, 20 and 27, the remainder in each case is 2 = $$x=540n+2$$, where $$n$$ is any natural number.

Also, $$x$$ is divisible by 23, thus by hit and trial, we get $$n=4$$ and $$x=2162$$

Now, when $$2162$$ is divided by $$(2+1+6+2)=11$$, quotient = $$2162=11\times196+6$$

$$\therefore$$ Quotient = 196

=> Ans - (A)

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