Directions: Each of the questions below consists of a question and two…

2022

Directions: Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both statements and answer accordingly.

Eight balls are scattered on the floor at various distances and directions from one another. In which direction is ball R with respect to ball O?
Statement I: Ball R is 15 m west of ball P. Ball M is 6 m south of ball R. Ball T is 12 m north of ball Q.
Statement II: Ball S is 15 m south of ball P. Ball O is 6 m south of ball N. Ball T is 18 m west of ball O. Ball N is 9 m east of ball S.

  1. A.

    If the data in statement I alone are sufficient to answer the question

  2. B.

    If the data in statement II alone are sufficient to answer the question

  3. C.

    If the data either in statement I alone or in statement II alone are sufficient to answer the question

  4. D.

    If the data given in both I and II together are not sufficient to answer the question

  5. E.

    If the data given in both statements I and II together are necessary to answer the question

Show answer & explanation

Correct answer: E

Concept

In a data-sufficiency direction problem, a single statement is sufficient only if it lets you connect the two target objects (here R and O) through an unbroken chain of relative positions. If a statement never mentions one of the two targets, it cannot, by itself, fix their relative direction — no matter how many other points it locates.

Applying it to this question

Place P at the origin and use east as +x, north as +y.

  1. Statement I locates R, M, Q and T relative to P and Q only: R is 15 m west of P, M is 6 m south of R, T is 12 m north of Q. Ball O never appears, so I alone leaves R and O unconnected — insufficient.

  2. Statement II locates S, N, O and T relative to P: S is 15 m south of P, N is 9 m east of S, O is 6 m south of N, T is 18 m west of O. Ball R never appears, so II alone leaves R and O unconnected — insufficient.

  3. Using both together, P is the shared anchor. From I, R = P + (−15, 0) = (−15, 0). From II, S = P + (0, −15) = (0, −15), N = (9, −15), O = (9, −21).

  4. Therefore R − O = (−15 − 9, 0 − (−21)) = (−24, +21): R lies 21 m north and 24 m west of O, i.e. to the north-west of O. The direction is now fixed.

Cross-check

Note that T appears in both statements, but in statement I it is tied only to Q (which is otherwise free-floating), so T creates no shortcut that would let either statement work alone. Only the common point P links the two halves, so both statements are required and together they are sufficient.

Hence both statements I and II together are necessary to answer the question.

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