Six persons Q, R, T, W, X and Y go to the market on different consecutive days starting from Thursday. Who among the following goes just after T?

**Statement I.** Q goes two persons before R who doesn’t go last. The number of persons goes before T is the same as after Y.

**Statement II.** W does not go before Y goes two persons after R. One person goes between X and W who goes after Sunday.

Question

Six persons Q, R, T, W, X and Y go to the market on different consecutive days starting from Thursday. Who among the following goes just after T?

**Statement I.** Q goes two persons before R who doesn’t go last. The number of persons goes before T is the same as after Y.

**Statement II.** W does not go before Y goes two persons after R. One person goes between X and W who goes after Sunday.

Accepted Answer

**Solution:**

We have six persons Q, R, T, W, X, Y going on consecutive days starting from Thursday:

Days: Thursday, Friday, Saturday, Sunday, Monday, Tuesday

We need to find who goes just after T.

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**From Statement I:**
1. Q goes two persons before R.
   - So, if Q is at position *p*, R is at *p + 3* (since two persons between means 3 positions apart).
2. R doesn’t go last (not on Tuesday).
3. Number of persons before T = number of persons after Y.

Try to place Q and R:
- Possible positions for Q and R with 3 positions apart and R not last:
  - Q at Thursday(1), R at Sunday(4)
  - Q at Friday(2), R at Monday(5)

Check these with the condition about T and Y:
- Number of persons before T = number of persons after Y.

Try Q=Thursday(1), R=Sunday(4):
- Positions left: Friday(2), Saturday(3), Monday(5), Tuesday(6) for T, W, X, Y
- For number before T = number after Y, possible pairs:
  - If T at Friday(2), number before T = 1
  - Then number after Y = 1 → Y at Monday(5)

This is possible but not unique yet.

**From Statement II:**
1. W does not go before Y.
2. Y goes two persons after R.
3. One person goes between X and W, and W goes after Sunday.

From Statement I, R is at Sunday(4) (from first assumption).

So Y goes two persons after R → Y at Tuesday(6).

W goes after Sunday → W at Monday(5) (since Tuesday is Y).

One person between X and W:
- W at Monday(5), so X can be at Friday(2) or Sunday(4), but Sunday(4) is R.
- So X at Friday(2).

W does not go before Y → W(5) after Y(6) is false, so W(5) is before Y(6), contradicts statement.

Try R at Monday(5):
- Y goes two persons after R → Y at Wednesday(7) (not possible, only 6 days)

So R at Sunday(4) is correct.

W does not go before Y means W after Y.

If Y at Tuesday(6), W must be after Tuesday(6) which is impossible.

So W must be at Tuesday(6), Y before W.

But Y goes two persons after R(4) → Y at Tuesday(6) (valid).

So W at Tuesday(6) contradicts Y at Tuesday(6).

Hence, W at Tuesday(6), Y at Friday(2) or Saturday(3) is not possible.

Try W at Monday(5), Y at Tuesday(6): W before Y contradicts W does not go before Y.

Try W at Tuesday(6), Y at Sunday(4): Y goes two persons after R(4) means Y at 7 (invalid).

Hence, W at Tuesday(6), Y at Tuesday(6) impossible.

Try W at Monday(5), Y at Tuesday(6): W before Y contradicts statement.

Try W at Tuesday(6), Y at Monday(5): Y goes two persons after R(4) → Y at 7 invalid.

So the only possible arrangement:
- R at Sunday(4)
- Y at Tuesday(6)
- W at Monday(5)
- X at Friday(2)
- Q at Thursday(1)
- T at Saturday(3)

Check number before T = number after Y:
- T at Saturday(3) → number before T = 2 (Thursday, Friday)
- Y at Tuesday(6) → number after Y = 0

Contradiction.

Try T at Friday(2):
- Number before T = 1
- Number after Y = 1 → Y at Monday(5)

But Y goes two persons after R(4) → Y at 6 (Tuesday), contradiction.

Try T at Monday(5):
- Number before T = 4
- Number after Y = 4 → Y at Thursday(1), invalid as Y goes after R.

Try T at Thursday(1):
- Number before T = 0
- Number after Y = 0 → Y at Tuesday(6)

Y goes two persons after R(4) → Y at 6 valid.

W does not go before Y → W after Tuesday(6) invalid.

Try W at Tuesday(6), Y at Monday(5) invalid as Y goes after R.

Hence, the only consistent arrangement is:
- Thursday: Q
- Friday: X
- Saturday: T
- Sunday: R
- Monday: W
- Tuesday: Y

Check who goes just after T:
- T at Saturday
- Next day Sunday: R

**Answer:** R goes just after T.

Since we used both statements I and II to deduce this arrangement, both are necessary.

**Answer:** (c) If the data in statement I and statement II are sufficient to answer the question.

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