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## OG 2020: Question No. 320

Is the average (arithmetic mean) of the numbers x, y, and z greater than z?

1. z − x < y − z
2. x < z < y

 Source OG 2020 Type Data Sufficiency Topic Algebra, Number Properties Sub-Topic Inequalities/ Statistics Difficulty Medium

### Solution

#### Steps 1 & 2: Understand Question and Draw Inferences

In this question, we are asked to determine whether the average (arithmetic mean) of the numbers x, y, and z is greater than the number z or not.

• If (x + y +z) / 3  > z

Then, x + y + z > 3z

Or, x + y > 2z

Hence, if the value of x + y is greater than 2z, then we can conclude that the average of x, y, and z is greater than z.

With this understanding, let us now analyse the individual statements.

#### Step 3: Analyse Statement 1

As per the information given in statement 1, z – x < y – z

• z – x < y – z

Or, x + y > z + z

Or, x + y > 2z

As we can derive that x + y > 2z, we can say the average of x, y, and z is greater than z.

Hence, statement 1 is sufficient to answer the question.

#### Step 4: Analyse Statement 2

As per the information given in statement 2, x < z < y.

• However, from this statement, we cannot say whether x + y > 2z or not.

Hence, statement 2 is not sufficient to answer the question.

#### Step 5: Combine Both Statements Together (If Needed)

Since we can determine the answer from statement 1 individually, this step is not required.

Hence, the correct answer choice is option A.

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