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fractions

by Ankitaverma » Wed Dec 04, 2013 10:28 am
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
Q/A-a
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by Brent@GMATPrepNow » Wed Dec 04, 2013 10:35 am
Ankitaverma 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
Q/A-a
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

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by GMATGuruNY » Wed Dec 04, 2013 12:25 pm
Ankitaverma 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
Q/A-a
The amount of air is reduced by 1/2 four times.
Plug in a value that can be divided by 2 four times.
Let the original amount of air = 2� = 16 units.

After 1 stroke, the remaining amount of air = 8 units.
After 2 strokes, the remaining amount of air = 4 units.
After 3 strokes, the remaining amount of air = 2 units.
After 4 strokes, the remaining amount of air = 1 unit.
.
Since only 1 unit remains, the amount removed = 15 units.
(amount removed)/(original amount) = 15/16.

The correct answer is A.
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by [email protected] » Wed Dec 04, 2013 2:16 pm
Hi Ankitaverma,

Both Brent and Mitch provide logical solutions to this problem. Here's another way to look at it:

Since we don't know how much air we're starting with, the tank could technically have any amount of air, so we can TEST a Value. Instead of randomly choosing a number, you should take a quick look at the answer choices. Notice how the common-denominator is 16? That number will likely be the best choice for your starting value.

Now, all you have to do is the basic "math", removing half after each stroke (with 4 strokes total):

Start = 16
remove half = 16 - 8 = 8
remove half = 8 - 4 = 4
remove half = 4 - 2 = 2
remove half = 2 - 1 - 1

So, 1/16 is left and 15/16 is removed.

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