Answer the questions based on given passage :

**Passage – **

Seven piano students T, U, V, W, X, Y, and Z are to give a recital, and their instructor is deciding the order in which they will perform. Each student will play exactly one piece, a piano solo. In deciding the order of performance, the instructor must observe the following restrictions:

- X cannot play first or second.
- W cannot play until X has played.
- Neither T nor Y can play seventh.
- Either Y or Z must play immediately after W plays.
- V must play either immediately after or immediately before U plays.

Q1. If V plays first, which one of the following must be true?

### Answer

**3**

Explanation –

Since V plays first.

1 2 3 4 5 6 7

V

From 5th restriction.

1 2 3 4 5 6 7

V U

5 vacant positions are remaining.

Now, we will follow the options given for the answer.

According to 1st option that is T plays 6th, T should be at 6th position.

Now, I will check that can T be at any other position other than 6. Let T be at 3rd position.

1 2 3 4 5 6 7

V U T

Now, I am putting X at 4th and W at 5th because W cannot play untill X plays. W will be followed by either Y or Z. Since Y cannot play at 7th, so the Y will be at 6th and Z will be at 7th.

1 2 3 4 5 6 7

V U T X W Y Z

Since there is an another sequence in which T can be at other position other than 6th. So 1st option is incorrect.

Similarly, 2nd option that is X plays 3rd is also incorrect. We can see that X can be at 4th position even after following restrictions.

Now, we will check for 3rd option that is Z plays 7th.

In our above sequence Z plays at 7th. Lets check whether that is correct or incorrect.

For checking that we will try to find another student who can play at 7th.

Since the position of V and U is confirmed at 1st and 2nd respectively as per question. Through 3rd restriction T and Y cannot be 7th. X cannot be at 7th because after X, W can play only after X. Similarly, W cannot be at 7th because after W, either Y or Z will come.

So, our sequence is correct and option 3rd that is Z plays at 7th is correct.

But we have to corss check for other two options also.

4th option says that T plays immediately after Y.

In our sequence, T can play before Y. So, 4th option is incorrect.

Last option is saying that W plays immediately after X.

If we change the positions of W and Y, then this option is also incorrect.

1 2 3 4 5 6 7

V U T X Y W Z

Hence, 3rd option is correct.

Q2. If U plays third, what is the last position in which Y can play?

### Answer

**4**

Explanation –

Since U plays 3rd.

1 2 3 4 5 6 7

U

Now, we will go for options.Since, question is for last position for Y. So, we will start from 7th position for Y.

5th option is incorrect as it says Y can play at 7th as 3rd restrictriction says T and Y cannot plays at 7th..

4th option says that Y can play at 6th.

After placing Y at 6th, we have 5 positios remaining as empty.

1 2 3 4 5 6 7

U Y

From last question, we know that only Z can play at 7th.

1 2 3 4 5 6 7

U Y Z

According to 4th restriction Y / Z will play after W. So, W will play at 5th position.

1 2 3 4 5 6 7

U W Y Z

Now, for V, we have two positions either 2nd or 4th as 5th restriction says V must play either immediately after or immediately before U plays.

We are placing V at 4th position.

1 2 3 4 5 6 7

U V W Y Z

X will be at 2nd position as 1st restriction says that X cnnot play 1st. And T will be at 1st position.

1 2 3 4 5 6 7

T X U V W Y Z

So, the last position for Y is 6th.