Bunuel wrote:
What is the average of x, y, and z?
(1) 2x + y + 4z = 23
(2) 3x + 4y + z = 22
Target question: What is the average of x, y, and z?NOTE:
the average of x, y and z = (x + y + z)/3 Statement 1: 2x + y + 4z = 23 This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of x, y and z that satisfy statement 1. Here are two:
Case a: x = 0, y = 23 and z = 0. In this case,
the average of x, y and z = (0 + 23 + 0)/3 = 23/3Case b: x = 11, y = 1 and z = 0. In this case,
the average of x, y and z = (11 + 1 + 0)/3 = 12/3 = 4Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, read my article: https://www.gmatprepnow.com/articles/dat ... lug-values Statement 2: 3x + 4y + z = 22 There are several values of x, y and z that satisfy statement 1. Here are two:
Case a: x = 0, y = 0 and z = 22. In this case,
the average of x, y and z = (0 + 0 + 22)/3 = 22/3Case b: x = 0, y = 5 and z = 2. In this case,
the average of x, y and z = (0 + 5 + 2)/3 = 7/3Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that 2x + y + 4z = 23
Statement 2 tells us that 3x + 4y + z = 22
ADD the two equations to get: 5x + 5y + 5z = 45
Divide both sides by 5 to get:
x + y + z = 9Since the average of x, y and z = (x + y + z)/3, we can see that the average of x, y and z =
9/3 = 3
So,
the average = 3Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C