cat 2020 Question 12

Question

Let m and n be natural numbers such that n is even and 0.2 < $\frac{m}{20}$ , $\frac{n}{m}$ , $\frac{n}{11}$ < 0.5. Then m - 2n equals

Accepted Answer

=> $0.2 \lt \frac{n}{11} \lt 0.5$

=> $2.2 \lt n \lt 5.5$

Since n is an even natural number, the value of n = 4

0.2<$\frac{m}{20}$<0.5 => 4 < m < 10. Possible values of m = 5,6,7,8,9

Since 0.2<$\frac{n}{m}$<0.5, the only possible value of m is 9

Hence m-2n = 9-8 = 1

Question 12.