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vacuum pump

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by BlueDragon2010 » Sun Mar 02, 2014 1:48 pm
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) 7/8
C) 1/4
D) 1/8
E) 1/16
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by Patrick_GMATFix » Sun Mar 02, 2014 1:57 pm
The quickest approach is probably to pick a number to represent the amount of starting air. It should be a power of 2 since 1/2 the amount is removed after every stroke. For instance, if starting amount is 16, we can figure out that after four strokes we'll have just 1 left, so 15/16 was removed. The answer is A. I go through the question in detail in the full solution below (taken from the GMATFix App).

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by [email protected] » Sun Mar 02, 2014 2:36 pm
Hi BlueDragon2010,

TESTing Values will work well on this question. A quick look at the answers tells us that the common denominator for all 5 options is 16; THAT is a huge clue that 16 would be a great number to TEST.

We're told that 1/2 of the air in a tank is removed with each stroke. We're asked what fraction has been removed after 4 strokes....

Full = 16
1st = 16-8 = 8 left
2nd = 8-4 = 4 left
3rd = 4-2 = 2 left
4th = 2-1 = 1 left

So 1/16 is LEFT; thus, 15/16 was REMOVED

Final Answer: A

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by Brent@GMATPrepNow » Mon Mar 03, 2014 7:32 am
BlueDragon2010 wrote: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) 7/8
C) 1/4
D) 1/8
E) 1/16
Another approach is to stick with fractions:


Start: All of the air is in the tank
After 1st stroke: 1/2 of the air REMAINS in tank
After 2nd stroke: 1/4 of the air REMAINS in tank
After 3rd stroke: 1/8 of the air REMAINS in tank
After 4th stroke: 1/16 of the air REMAINS in tank

We want to determine the fraction of air that has been REMOVED
So, if 1/16 of the air REMAINS in the tank, we know that [spoiler]15/16[/spoiler] has been REMOVED

Answer: A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Abhishek009 » Mon Mar 03, 2014 8:44 am
BlueDragon2010 wrote: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) 7/8
C) 1/4
D) 1/8
E) 1/16
Let the total volume be 1

Since the action is repeated every time we can condense the form to find air removed is -

1 - (1/2)^4

1 - 1/16

15/16
Abhishek
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