## OG 2020: Question No. 320

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

- z − x < y − z
- 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__

__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__

__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__

__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)__

__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.

**Did you know a 700+ GMAT Score can increase your chances to get into your dream business school? We can help you achieve that. Why don’t you try out our FREE Trial? We are the most-reviewed online GMAT Preparation company in GMATClub with more than 1950 reviews.**