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
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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