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Transferring Water Between Drums

XAT 2020 · Quantitative Ability & Data Interpretation · Medium · Quantitative Aptitude

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Six drums are used to store water. Five drums are of equal capacity, while the sixth drum has double the capacity of each of these five drums. On one morning, three drums are found half full, two are found two-thirds full and one is found completely full. It is attempted to transfer all the water to the smaller drums. How many smaller drums are adequate to store the water?

  1. A.

    Three but not two

  2. B.

    Four but not three

  3. C.

    Three or four, depending on which drum had how much water initially

  4. D.

    Five but not four

  5. E.

    Five may be inadequate, depending on which drum had how much water initially

Answer

D

Explanation

Let capacity of a small drum = 1 unit, double capacity drum = 2 units. Total water calculation:

  • Minimum possible water occurs when the double drum is 1/2 full (1 unit of water): 1+2×(1/2)+2×(2/3)+1=1+1+4/3+1=4.331 + 2 \times (1/2) + 2 \times (2/3) + 1 = 1 + 1 + 4/3 + 1 = 4.33 units.
  • Maximum possible water occurs when the double drum is 100% full (2 units of water): 2+3×(1/2)+2×(2/3)=2+1.5+1.33=4.8332 + 3 \times (1/2) + 2 \times (2/3) = 2 + 1.5 + 1.33 = 4.833 units.

In all cases, total water volume VV satisfies 4.33<V<4.8334.33 < V < 4.833. Since each smaller drum holds 1 unit, 4 smaller drums can hold at most 4 units (inadequate), while 5 smaller drums can hold 5 units (adequate). Thus, five but not four smaller drums are adequate.

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