Correct Answer:
Option B —
81
To find the value of X, we can use the definitions of the Arithmetic Mean (average) and the Geometric Mean.
Step 1: Use the Arithmetic Mean
The Arithmetic Mean of two numbers is found by adding them together and dividing by 2.
The average of X and Y is 41.
This means that X plus Y divided by 2 equals 41.
Multiplying 41 by 2 tells us that the sum of X and Y must equal 82.
Step 2: Use the Geometric Mean
The Geometric Mean of two numbers is found by multiplying them together and taking the square root of the result.
The Geometric Mean of X and Y is 9.
This means the square root of (X times Y) equals 9.
Squaring 9 tells us that X times Y must equal 81.
Step 3: Analyze the Options
We are looking for two numbers that add up to 82 and multiply together to equal 81.
Let's test the options for X to see which one fits this rule:
If X is 81, then Y must be 1 (since 81 plus 1 equals 82, and 81 times 1 equals 81).
Since 81 perfectly satisfies both conditions, it is a possible value for X.
Correct Answer:
B) 81
Answer verified by Quintessence Classes faculty — Karan Nagar, Srinagar.
