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: http://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
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Brent Hanneson – Creator of gmatprepnow.com
Before you spend another second preparing for the GMAT, check out my article series, Are you doing it wrong?.
You’ll learn what the GMAT actually tests, and why memorizing a ton of formulas actually makes you less effective.
22 May 2016, 12:29
25%
(medium)
68%
(00:58)
correct 
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