sequences topic

Question

if 1/2 of the air in a tank is removed with each stroke of a vacuum pump ,what fraction of the original amount of air has been removed after 4 strokes 

 

(a) 15/16

 

(b)12/56

 

(c)55/16

 

(d)12/46

Answer 1

Stroke 1 of the vacuum pump will lead to 1/2 of the air in a full container being removed. 1 * (1/2) = 1/2

Stroke 2 will remove 1/2 of the air still in the container, which is now 1/2, not 1. (1/2) * (1/2) = 1/4

Stroke 3 removes 1/2 of the 1/4 of air in the container from stroke #2. (1/2) * (1/4) = 1/8

Stroke 4 removes 1/2 of the air in the container again. (1/2) * (1/8) = 1/16

However, the question is asking how much air was removed after all 4 strokes. 1 - (1/16) = 15/16

 

The answer is A

Answer 2

Since 1/2 of the air is removed with each stroke, you can also say that 1/2 of what was there before the stroke is remaining after the stroke.

 

So after the first stroke there is 1/2 remaining.

 

After the second stroke, there is 1/2 of 1/2 remaining = 1/4.

 

After the third there is 1/2 of 1/4 = 1/8.

 

After the fourth, there is 1/2 of 1/8 = 1/16.

 

Since there is 1/16 remaining, that means that 1 - 1/16 was removed = 15/16.  So the answer is (a).