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CAT 2003 Slot 1 — QA Question 38

SphereEasy
Passage / Data

Each question is followed by two statements, A and B. Answer each question using the following instructions

Choose 1 if the question can be answered by using one of the statements alone but not by using the other statement alone.
Choose 2 if the question can be answered by using either of the statements alone.
Choose 3 if the question can be answered by using both statements together but not by either statement alone.
Choose 4 if the question cannot be answered on the basis of the two statements.

There are 8436 steel balls, each with a radius of 1 centimetre, stacked in a pile, with 1 ball on top, 3 balls in the second layer, 6 in the third layer, 10 in the fourth, and so on. The number of horizontal layers in the pile is

Answer & solution

  • A

    34

  • B

    38

  • 36

  • D

    32

Solution

The first layer has 1 ball.

Second layer has 1 + 2 = 3 balls

Third layer has 1 + 2 + 3 = 6 balls

∴ The nth layer of the stack would have [n(n+1)2] balls

∴ Total balls in all the layers = ∑[n(n+1)2] = 8436

∴ 12×[n(n+1)(2n+1)6+n(n+1)2] = 8436

Only n = 36 satisfies the above equation.

Hence, option (c).

CAT 2003 Slot 1 QA Q38: There are 8436 steel balls, each with a radius of 1 centimetre, stacked in a pile, with 1 ball on top, 3 balls — Solution | TheCATExam