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Question 116
Let x be the least number of 4 digits that when divided by 2, 3, 4, 5, 6 and 7 leaves a remainder of 1 in each case. If x lies between 2000 and 2500, then what is the sum of the digits of x?
Solution
L.C.M. (2,3,4,5,6,7) = 420
Now, number of the form that when divided by 2, 3, 4, 5, 6 and 7 leaves a remainder of 1 in each case will be = $$x=420k+1$$ where $$k$$ is a constant.
Now, if $$x$$ lies between 2000 and 2500, then $$k=5$$
=> $$x=420\times5+1=2101$$
$$\therefore$$ Sum of digits = 4
=> Ans - (D)
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