Video Explanation

Text Explanation

One easy approach to understand this problem is to plug in numbers for x, y, and k. Another approach, that is quicker, is to realize that there are many values for x, y, and k that will give an average of 7 or 13. Since we don’t have specific values for any of the variables, they could be anything! 

For statement (1), an average of 7 means the sum of x, y, and k is 7 × 3 = 21. The values could be x = 7, y = 7, k = 7. That totals 21. Or, it could be x = 1, y = 2, and k = 18. That also totals 21. Each give an average of 7, but each value of x, y, and k are different. Because of that, Statement (1) is insufficient. 

For statement (2), the same logic applies. For x, y, and 3k to have an average of 13, the sum must be 3 × 13 = 39. We could have x = 2, y = 1, and 3k = 36, or we could have x = 9, y = 9, and 3k = 21. Each combination would give us an average of 13. As such, Statement (2) is also insufficient. 

Now, let’s put the two of them together to see if that’s sufficient. 

We have x + y + k = 21 and x + y + 3k = 39. Our goal is to determine the mean of x + y, so we want to get rid of k. We can do that by multipling the first equation by 3: 

3 × (x + y + k) = 3 × 21, so 3x + 3y + 3k = 63. 

From this new equation, we  subtract the equation from statement (2): 

    3x + 3y + 3k   =   63

 - ( x +   y + 3k ) = - 39

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     2x + 2y           = 24

Divide both sides by 2, and we have x + y = 12. So, the mean of x and y is 6 and we have an answer! 

Thus, our answer is (C).