The volume of water inside a swimming pool doubles every hour. If the

in 8th hour it is full its capacity
thus in 7th it will be half of full capacity (since it doubles /hr)
so in 6th Hr. it will be only x/4 or quarter filled of the capacity

Ans D

We can observe this question as the question of Geometric Progression which is also the basis of Compound Interest

Since Water doubles every hour and it was filled after 8 hours that means it was half of it's current capacity an hour ago i.e. it was 1/2 (a half) filled an hour ago i.e. 7 hours from the start
and it was 1/4th (a Quarter) filled an hour ago before it was half filled i.e. 6 hours from the start

Answer: option D

Hi All,

This question can be solved in a couple of different ways (depending on how quickly you 'see' the pattern involved). You can also TEST VALUES to define the pattern.

We're told that a swimming pool doubles its volume of water every hour...

IF... you start at the beginning....

Start = 1 gallon
Hour 1 = 2 gallons
Hour 2 = 4 gallons
Hour 3 = 8 gallons
Hour 4 = 16 gallons
Hour 5 = 32 gallons
Hour 6 = 64 gallons
Hour 7 = 128 gallons
Hour 8 = 256 gallons = FULL

The question asks at what point the pool was 1/4 full. Since 1/4 of 256 = 64, we know exactly when it was 1/4 full.

IF... you start from the end....

Hour 8 = FULL
Hour 7 = 1/2 full
Hour 6 = (1/2)(1/2) = 1/4 full

Either way, you have the correct answer.

Final Answer:

GMAT assassins aren't born, they're made,
Rich

If the pool is full in 8 hours, it will be half in 7 hours and it will be quarter full in 6 hours.

Take the total capacity as 10.
On or before 8 hrs it is 10
In 7 hours it was 5
In 6 hours it was 2.5 = quarter of 10. Hence answer is 6 or D

This is a tricky question. The text 'full within 8 hours' does not make things easy.

I also think that the pool could have filled by hour 4, using your approach. This means it is full at hour 8 even though it is overflowing. IMHO this is somewhat vague for a GMAT question.

30 Secs Approach

Let's assume the pool capacity is 100 liters. 1/4 of the capacity is 25 liters.
Assume the pool is filled with 25 at time t. at t+1 the pool will be filled with 50 and at t+2 it will be filled with 100.
In other words, from 1/4 capacity it takes 2 hours to reach full capacity.

0----------------------------------25 liters-----------50 liters------------100 liters
0h----------------------------------6h---------------------------------------8h

Answer is D.

Since the volume of water inside the swimming pool doubles every hour and the pool is filled to its full capacity in 8 hours, then it must be filled to half of its capacity in 7 hours and a quarter of its capacity in 6 hours.

Answer: D

1. Assume that \(x\) liters were filled during the first hour
2. Below table shows the growth in quantity with every passing hour and the final quantity after \(8\) hours

| Hr | Qty |
| 1 | x |
| 2 | 2x |
| 3 | 4x |
| 4 | 8x |
| 5 | 16x |
| 6 | 32x |
| 7 | 64x |
| 8 | 128x |

3. Total quantity is \(128x\), hence \(\frac{1}{4}\) of the total is \(128x * \frac{1}{4}\) \(= 32x\)
4. Referring to the table above, we see that \(32x\) was filled at the \(6^{th}\) hour

Ans. D

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