# TANCET 2013 Quant Qn 1: GP

## Question

Easy Quantitative Reasoning

If a rubber ball consistently bounces back ⅔ of the height from which it is dropped, what fraction of its original height will the ball bounce after being dropped and bounced four times without being stopped?

• ### Step by step solution

1. Each time the ball is dropped and it bounces back, it reaches ⅔ of the height it was dropped from.
2. After the first bounce, the ball will reach ⅔ of the height from which it was dropped - let us call it the original height.
3. After the second bounce, the ball will reach ⅔ of the height it would have reached after the first bounce.

So, at the end of the second bounce, the ball would have reached ⅔ * ⅔ of the original height = th of the original height.
4. After the third bounce, the ball will reach ⅔ of the height it would have reached after the second bounce.

So, at the end of the third bounce, the ball would have reached ⅔ * ⅔ * ⅔ = th of the original height.
5. After the fourth and last bounce, the ball will reach ⅔ of the height it would have reached after the third bounce.

So, at the end of the last bounce, the ball would have reached ⅔ * ⅔ * ⅔ * ⅔ of the original height = of the original height.

The correct answer is Choice 1.

• ### Formulae to remember in Geometric Progression

A geometric progression is such a sequence in which every subsequent term of the sequence is obtained by multiplying the preceding term with a constant number. This constant number is called the common ratio (r) of the sequence.

e.g., 2, 4, 8, 16, 32 is a geometric sequence.

The second term is obtained by multiplying the first term by 2. The third term is obtained by multiplying the second term by 2 and so on.

Formula 1: nth term of a Geometric Progression an = arn-1, where a is the first term of the sequence and r is the common ratio.

Formula 2: Sum of the first n terms of a geometric progression =

Formula 3: Sum up to infinite terms of a geometric progression whose common ratio r lies between 0 and 1 i.e., S =

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