Is 15 the average (arithmetic mean) of x, y, and 15?

Question

(1) x + y= 30

(2) x - y = 4

amanvermagmat · Answer

Average of x, y and 15 is = (x+y+15)/3.  If  this is equal to 15, then we will have:
x+y+15 = 45 OR x+y = 30
So if we can determine whether x+y is 30 or not (with surety) then we will be able to answer.

Statement 1 
This gives x+y = 30.  Sufficient . This gives us YES as an answer to the question asked.

Statement 2 
x-y = 4. This does not help us in determining whether sum of x & y is 30 or not. So  not sufficient .

Hence  A answer

GMATinsight · Answer

Question : Is (x+y+15)/3 = 15?

Question  : Is (x+y) = 30?

Statements 1: x + y= 30

Sufficient

Statements 2: x - y= 4

NOT SUFFICIENT

Answer: option A

MathRevolution · Answer

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question.

We can modify the question as follows.

The question asks if  (x+y+15)/3 = 15 .

(x+y+15)/3 = 15  ?
 ⇔ x + y + 15 = 45  ?
 ⇔ x + y = 30  ?

The equivalent question " x + y = 30  ?" is same as the condition 1).

The condition 1) is sufficient.

Condition 2)
 x = 17, y = 13  : Yes
 x = 5, y = 1  : No
Since we don't have a unique answer, the condition 2) is not sufficient.

Therefore, A is the answer.

Is 15 the average (arithmetic mean) of x, y, and 15?

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GMAT Data Sufficiency (DS) Questions

Is 15 the average (arithmetic mean) of x, y, and 15?

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