These questions are based on the information given below.
Four friends P, Q, R and S got the top four ranks in a competitive examination, but P did not get the first, Q did not get the second, R did not get the third and S did not get the fourth rank. Who secured which rank?
I. Neither P nor S were among the first 2.
II. Neither Q nor R was third or fourth.

Options

A. if the question can be answered by using statement I alone but not by using II alone.
B. if the question can be answered by using statement II alone but not by using I alone.
C. if the question can be answered by using any one of the two statements alone.
D. if the question can be answered by using both the statement together but not by either statement alone.

Answer

To solve the problem, we need to determine the ranks of four friends P, Q, R, and S based on the given conditions. Let's break down the information step by step.

### Step 1: Analyze the Initial Information
We have the following information:
- P did not get the first rank.
- Q did not get the second rank.
- R did not get the third rank.
- S did not get the fourth rank.

From this, we can summarize:
- P ≠ 1st
- Q ≠ 2nd
- R ≠ 3rd
- S ≠ 4th

### Step 2: Evaluate Statement I
Statement I states: "Neither P nor S were among the first 2."

This implies:
- P ≠ 1st and P ≠ 2nd
- S ≠ 1st and S ≠ 2nd

Since P and S cannot occupy the first two ranks, the only candidates left for the first two ranks are Q and R.

### Step 3: Determine Possible Ranks from Statement I
Since P and S cannot be in the first two ranks:
- Q must be 1st or 2nd.
- R must be 1st or 2nd.

However, since R cannot be 3rd (from the initial information), if Q is 1st, then R must be 2nd.

Thus, we can conclude:
- If Q is 1st, then R is 2nd.
- This leaves P and S for 3rd and 4th. Since S cannot be 4th, S must be 3rd and P must be 4th.

So from Statement I, we have:
1st: Q
2nd: R
3rd: S
4th: P

### Step 4: Evaluate Statement II
Statement II states: "Neither Q nor R was third or fourth."

This implies:
- Q ≠ 3rd and Q ≠ 4th
- R ≠ 3rd and R ≠ 4th

Since Q and R cannot occupy the last two ranks, they must occupy the first two ranks.

### Step 5: Determine Possible Ranks from Statement II
Since Q and R must be in the first two ranks, and P cannot be 1st, we can conclude:
- If Q is 1st, then R must be 2nd.
- This leaves P and S for 3rd and 4th. Since S cannot be 4th, S must be 3rd and P must be 4th.

So from Statement II, we also have:
1st: Q
2nd: R
3rd: S
4th: P

### Conclusion
Both statements independently lead us to the same conclusion about the ranks:
1st: Q
2nd: R
3rd: S
4th: P

Thus, both statements are sufficient to answer the question.

### Final Answer
The answer is that both statements alone are sufficient to determine the ranks of P, Q, R, and S.