Read the following data and answer the questions that follow: Bhim has…

2023

Read the following data and answer the questions that follow:

Bhim has assembled a basket of fruit as a holiday gift for each of his four friends — Santosh, Tarun, Ujjwal, and Varun. A total of fifteen pieces of fruit — five apples, five oranges, and five pears — are distributed among the four baskets according to the following conditions:

  • Santosh, Tarun, and Ujjwal will each receive exactly two different types of fruit.

  • Varun will receive only apples.

  • Tarun will receive more pieces of fruit than Santosh.

  • Each basket includes at least three pieces of fruit.

Which of the following statements could be true?

  1. A.

    Tarun will receive three pieces of fruit.

  2. B.

    Santosh will receive exactly three pieces of fruit.

  3. C.

    Varun will receive exactly seven pieces of fruit.

  4. D.

    None

Show answer & explanation

Correct answer: B

Concept:

For a 'could be true' question built on distribution constraints, first derive the necessary bounds every valid arrangement must obey (from the minimum-per-basket rule and the given inequalities) to eliminate options that violate them outright, then confirm any surviving option by exhibiting one complete, constraint-satisfying distribution — a single valid case is enough to prove a 'could be true' claim.

Application:

  1. Every basket must hold at least three pieces, so Santosh receives at least three pieces.

  2. Tarun must receive more pieces than Santosh, so Tarun's minimum possible count is three plus one, i.e. four pieces — Tarun can never receive exactly three.

  3. Varun receives fruit only of the apple type, and only five apples exist in total, so Varun's count can never exceed five — Varun can never receive seven.

  4. To test whether Santosh can receive exactly three, construct one full distribution: give all five apples to Varun. With no apples left, Santosh, Tarun, and Ujjwal must each draw their two fruit types from the remaining oranges and pears. Split the five oranges as 1-2-2 and the five pears as 2-2-1 across Santosh, Tarun, and Ujjwal respectively: Santosh gets one orange plus two pears equals three pieces, Tarun gets two oranges plus two pears equals four pieces, Ujjwal gets two oranges plus one pear equals three pieces.

  5. This distribution uses all five apples plus five oranges plus five pears equals fifteen pieces, gives every basket at least three pieces, keeps Tarun's count above Santosh's, and gives Santosh, Tarun, and Ujjwal exactly two fruit types each — every condition holds, so Santosh receiving exactly three pieces is a valid, achievable scenario.

  6. Since one valid scenario exists, the claim that none of the statements could be true is also ruled out.

Cross-check:

Re-adding the four basket totals, three plus four plus three plus five, gives fifteen, matching the fruit supply exactly, and re-checking the type count for each of Santosh, Tarun, and Ujjwal confirms exactly two non-zero fruit types apiece — the constructed distribution is fully consistent.

Result:

So Santosh receiving exactly three pieces of fruit is the option that could be true.

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