Number System Question 3 - CAT 2020

Step-by-Step Explanation

Let's analyze the given compound inequality chain step-by-step:

0.2 < (m)/(20),(n)/(m),(n)/(11) < 0.5

• Step 1: Focus on the fraction with a fixed denominator

0.2 < (n)/(11) < 0.5 ⇒ 2.2 < n < 5.5

The problem states that n is an even natural number. The only even integer between 2.2 and 5.5 is n = 4.

• Step 2: Find the range for m

0.2 < (m)/(20) < 0.5 ⇒ 4 < m < 10

This means m can be 5, 6, 7, 8, or 9.

• Step 3: Narrow down m using the middle fraction

Substitute n = 4 into the middle inequality:

0.2 < (4)/(m) < 0.5

• From (4)/(m) < 0.5, we get m > 8.
• From (4)/(m) > 0.2, we get m < 20.

Since m must be between 4 and 10, and also strictly greater than 8, the only valid integer is m = 9.

• Step 4: Compute the final value

m - 2n = 9 - 2(4) = 9 - 8 = 1

Correct Option: B

💡 FundaMakers Tip:

Always solve the variable bounded by constants first n/11. Finding one exact value (n = 4) early on simplifies the rest of the question, letting you test the remaining options for m quickly.