Directions: Each of the following questions consists of a question and three…
2021
Directions: Each of the following questions consists of a question and three statements numbered I, II and III given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the statements and give the answer.
Six persons Q, R, T, W, X and Y go to the market on six different consecutive days, starting from Thursday (Thursday to Tuesday).
Who among the following goes just after T?
Statement I. Q goes two persons before R, who does not go last. The number of persons who go before T is the same as the number of persons who go after Y.
Statement II. W does not go before Y, and Y goes two persons after R. One person goes between X and W, and W goes after Sunday.
Statement III. T goes before the person who goes two persons after Q. Y and W go one immediately after the other, but not on Thursday.
- A.
If the data in statement I alone is sufficient to answer the question.
- B.
If the data in statement II alone is sufficient to answer the question.
- C.
If the data in statement I and statement II together are sufficient to answer the question.
- D.
If the data in all three statements I, II and III together are necessary to answer the question.
- E.
If the data in statement III alone is sufficient to answer the question.
Attempted by 4 students.
Show answer & explanation
Correct answer: C
Concept
In a data-sufficiency arrangement problem, a statement (or a set of statements) is "sufficient" only when it pins the required fact down to one unique value. A single arrangement is not required; what is required is that every arrangement allowed by the data give the same answer to the asked question. So the test is: does the data leave more than one possibility for "the person just after T"? If yes, that data is insufficient; if it forces exactly one person, it is sufficient.
Frame: six consecutive days Thursday, Friday, Saturday, Sunday, Monday, Tuesday (call them seats 1 to 6). Treat "X goes two persons before Y" as a gap of two seats (one person sits between them), and "persons before / after" as counting seats to the left / right.
Applying each statement on its own
Statement I: R = Q + 2 seats, R is not in seat 6, and (seats before T) = (seats after Y). These leave several valid orders, and the person right after T is not fixed — so I alone does not give a single answer.
Statement II: Y is after R by two seats, W is not before Y, exactly one person sits between X and W, and W is after Sunday (seat 5 or 6). These too allow more than one order — for instance W can land on Monday in one and on Tuesday in another — so the person right after T is still not fixed; II alone does not give a single answer.
Statement III: T is before the person two seats after Q, and Y, W are adjacent but neither on Thursday. This is very loose and allows many orders — III alone does not give a single answer.
Combining I and II
Now read the two together; each fact narrows the line until only one order survives:
II puts W after Sunday (seat 5 or 6) with exactly one person between X and W, and not before Y. On its own that still allows W on Monday, so bring in I.
I forces R = Q + 2 with R not last, and II forces Y = R + 2. Chaining these places Q (Thursday), R (Saturday), Y (Monday); R-not-last rules out the order that would have put W on Monday, so W is now driven to the last seat (Tuesday) and X two seats before it (Sunday).
The only seat left for T is Friday, which also matches I's "persons before T = persons after Y" (one person before T, one after Y).
The unique resulting order is:
Day | Person |
|---|---|
Thursday | Q |
Friday | T |
Saturday | R |
Sunday | X |
Monday | Y |
Tuesday | W |
The person who goes just after T (Friday) is R (Saturday). Because the two read together collapse to exactly one order while each on its own does not, the pair is jointly sufficient and statement III is not needed.
Cross-check
Neither I alone nor II alone narrows "the person after T" to a single name (each permits different people in that position), and the loose statement III is not required once I and II are combined. Hence the data in statements I and II together are sufficient, and that is the answer.