MAT 2004 Question Paper

Question 133

What is the third term in a sequence of numbers that leave remainders of 1, 2 and 3 when divided by 2, 3 and 4 respectively?

Solution

L.C.M. (2,3,4) = 12

Number of the form that leave remainders of 1, 2 and 3 when divided by 2, 3 and 4 respectively = $$12x-1$$
$$\because (2-1)=(3-2)=(4-3)=1$$, where $$x$$ is a natural number

Thus, the third number = $$12(3)-1=35$$

=> Ans - (D)


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