## OG 2020: Question No. 304

If p, r, and s are consecutive integers in ascending order and x is the average (arithmetic mean) of the three integers, what is the value of x?

- Twice x is equal to the sum of p, r, and s.
- The sum of p, r, and s is zero.

Source | OG 2020 |

Type | Data Sufficiency |

Topic | Number Properties |

Sub-Topic | Statistics |

Difficulty | Easy |

### Solution

__Steps 1 & 2: Understand Question and Draw Inferences__

__Steps 1 & 2: Understand Question and Draw Inferences__

In this question, we are given

- The numbers p, r, and s are consecutive integers in ascending order.
- x is the average (arithmetic mean) of the three integers.

We need to determine

- The value of x.

As x is the average of p, r, and s, we can write x = (p + r + s)/3 –(A)

Therefore, to find the value of x, we need to know either the individual values of p, r, and s, or their sum.

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, twice x is equal to the sum of p, r, and s.

- 2x = p + r + s

We also know that 3x = p + r + s — (From (A)).

Therefore, we can write 2x = 3x

Or, x = 0

As we can determine the value of x, 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, the sum of p, r, and s is zero.

- p + r + s = 0

As x = (p + r + s)/3, we can say

- x = 0/3 = 0

As we can determine the value of x, statement 2 is 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 either of the statements individually, this step is not required.

Hence, the correct answer choice is option D.

**Takeaways**

In a DS question, always do thorough Question Stem Analysis. Use all pieces of information given to infer all you can.

For example, in this question, writing the value of x in terms of p, r, and s in the question stem analysis was very important. Without this, statement 1 analysis would not be so efficient.