What is the average (arithmetic mean) of \(x\) and \(y?\)

[Gmat_mission]

What is the average (arithmetic mean) of \(x\) and \(y?\)

(1) The average of \(x\) and \(2y\) is 10.
(2) The average of \(2x\) and \(7y\) is 32.

[spoiler]OA=C[/spoiler]

Source: Official Guide

[Srishtim23]

To find the arithmetic mean of x and y we need values of x and y
St1: gives us one equation with 2 variables.
Not sufficient
St2 Same as st1

Taking both statements together: We have two equations and two variables. enough to find the value of x and Y
Hence sufficient

OA: C

[Scott@TargetTestPrep]

What is the average (arithmetic mean) of \(x\) and \(y?\)

(1) The average of \(x\) and \(2y\) is 10.
(2) The average of \(2x\) and \(7y\) is 32.

[spoiler]OA=C[/spoiler]

Source: Official Guide

Solution:

Question Stem Analysis:

We need to determine the average of x and y, i.e., the value of (x + y)/2. Notice that if we can determine the values of x and y, then we can determine the value of (x + y)/2.

Statement One Alone:

We are given that (x + 2y)/2 = 10. However, since we can’t determine either the value of x or of y, we can’t determine the value of (x + y)/2. Statement one alone is not sufficient.

Statement Two Alone:

We are given that (2x + 7y)/2 = 32. However, since we can’t determine either the value of x or of y, we can’t determine the value of (x + y)/2. Statement two alone is not sufficient.

Statements One and Two Together:

From the two statements, we have two linear equations in two variables. Note that neither equation is dependent on the other, which means that one equation is not a linear multiple of the other. Thus, we can solve for the values of x and y, and hence we can determine the value of (x + y)/2. Both statements are sufficient.

Answer: C

[Scott@TargetTestPrep]

What is the average (arithmetic mean) of \(x\) and \(y?\)

(1) The average of \(x\) and \(2y\) is 10.
(2) The average of \(2x\) and \(7y\) is 32.

[spoiler]OA=C[/spoiler]

Source: Official Guide

Solution:

Question Stem Analysis:

We need to determine the average of x and y, i.e., the value of (x + y)/2. Notice that if we can determine the values of x and y, then we can determine the value of (x + y)/2.

Statement One Alone:

We are given that (x + 2y)/2 = 10. However, since we can’t determine either the value of x or of y, we can’t determine the value of (x + y)/2. Statement one alone is not sufficient.

Statement Two Alone:

We are given that (2x + 7y)/2 = 32. However, since we can’t determine either the value of x or of y, we can’t determine the value of (x + y)/2. Statement two alone is not sufficient.

Statements One and Two Together:

From the two statements, we have two linear equations in two variables. Note that neither equation is dependent on the other, which means that one equation is not a linear multiple of the other. Thus, we can solve for the values of x and y, and hence we can determine the value of (x + y)/2. Both statements are sufficient.

Answer: C