Question: Among A, B, C, D and E, who is in the middle while standing in a row…

2023

Question: Among A, B, C, D and E, who is in the middle while standing in a row ?

Statements:

C, who is third to the left of D, is to the immediate right of A and second to the left of E.

C is second to the left of E, who is not at any of the ends and who is third to the right of A. D is at one of the ends.

  1. A.

    I alone is sufficient while II alone is not sufficient

  2. B.

    II alone is sufficient while I alone is not sufficient

  3. C.

    Either I or II is sufficient

  4. D.

    Neither I nor II is sufficient

Attempted by 1 students.

Show answer & explanation

Correct answer: C

Concept: In data sufficiency for seating/ordering puzzles, a statement is sufficient on its own only if applying just its own clues fixes one unique arrangement of everyone; if more than one arrangement stays possible, that statement alone is not sufficient.

Applying Statement I on its own:

  1. A is immediately to the left of C, so C sits right after A.

  2. C is third to the left of D, so D sits three seats to the right of C.

  3. C is second to the left of E, so E sits two seats to the right of C.

  4. Placing A first and C next fixes C at position 2 (from the left); E then falls at position 4 and D at position 5, leaving B as the only person for position 3.

  5. This gives one unique order: A, C, B, E, D — with B in the middle (position 3 of 5).

Applying Statement II on its own:

  1. E is second to the right of C, and E is also third to the right of A, so C is exactly one seat to the right of A.

  2. E is not at either end, so E cannot occupy position 1 or 5; combined with E being three seats after A, the only fit is A at position 1, C at position 2, E at position 4.

  3. D is at one of the ends; position 1 already belongs to A, so D must be at position 5, leaving B for position 3.

  4. This again gives the unique order: A, C, B, E, D — with B in the middle.

Cross-check: Both statements are worked independently using only their own clues, and both land on the identical unique arrangement, so neither statement needs the other's information to settle who is in the middle.

Conclusion: Since Statement I alone fixes a unique arrangement and Statement II alone also fixes that same unique arrangement, each statement is independently sufficient.

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