A wheel of radius 3 metres is revolving at a constant speed. How many…

2023

A wheel of radius 3 metres is revolving at a constant speed. How many revolutions can it make in time T?

Statements:

  1. T = 30 minutes.

  2. The speed at which a point on the circumference of the wheel is moving is 3 metres per minute.

  1. A.

    Statements 1 and 2 together are not sufficient, and additional data is needed to answer the question

  2. B.

    Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question

  3. C.

    Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question

  4. D.

    Each statement alone is sufficient

  5. E.

    Both statements together are sufficient, but neither statement alone is sufficient to answer the question

Attempted by 1 students.

Show answer & explanation

Correct answer: E

Concept: In a Data Sufficiency question, a statement (or combination of statements) is "sufficient" only if it lets you compute one unique numerical answer to the question asked, using no outside assumption. The standard method is to test each statement ALONE first; only if neither alone works do you combine them and test whether the combination pins down a single value.

Application: The question asks for the number of revolutions the wheel makes in time T. Since revolutions = (total distance travelled) / (circumference), and the circumference is already fixed by the given radius (3 m), two things are needed: the total distance travelled, and that in turn needs both a rate and a duration.

  1. Statement 1 alone gives the duration, T = 30 minutes, but says nothing about how fast the wheel is turning, so the distance covered in that time cannot be pinned to one value — not sufficient alone.

  2. Statement 2 alone gives the linear (tangential) speed, 3 metres per minute, but says nothing about how long the wheel runs, so the total distance travelled cannot be pinned to one value — not sufficient alone.

  3. Combining both: distance = speed x time = 3 m/min x 30 min = 90 m. Number of revolutions = distance / circumference = 90 / (2 x pi x 3) = 15/pi (approximately 4.77), one definite value.

Cross-check via a different route: time to complete one full revolution = circumference / speed = 6π / 3 = 2π minutes (about 6.28 minutes); over the full 30 minutes given, the number of complete revolution-equivalents is 30 / 2π = 15/π (about 4.77), the same figure obtained by the distance route — confirming the result via an independent calculation path rather than only re-checking arithmetic.

Result: Neither statement alone fixes the answer, but taking both together does fix it to one unique value.

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