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Arithmetic

by anirudhbhalotia » Thu Jan 13, 2011 10:14 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

This question is from OG-12, the answer mentioned is A, but am unable to understand the explanation. I had chosen E as the answer.
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by Anurag@Gurome » Thu Jan 13, 2011 10:57 pm
anirudhbhalotia 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
In each stroke it removes (1/2) of the air in the tank. Therefore after each stroke the amount of remaining air in the tank is (1/2) of what was before the stroke. Thus,
  • After 1st stroke : Remaining air = (1/2) of original amount
    After 2nd stroke : Remaining air = (1/2)*(1/2) of original amount
    After 3rd stroke : Remaining air = (1/2)*(1/2)*(1/2) of original amount
    After 4th stroke : Remaining air = (1/2)*(1/2)*(1/2)*(1/2) of original amount
Hence after four strokes remaining air in the tank = (1/16) of the original amount

Hence the amount of air removed = [1 - (1/16)] of the original amount = (15/16) of the original amount

The correct answer is A.[/list]
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by towerSpider » Thu Jan 13, 2011 10:59 pm
anirudhbhalotia 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

This question is from OG-12, the answer mentioned is A, but am unable to understand the explanation. I had chosen E as the answer.
(1/2)^4=1/16 This is amount left, so amount removed: 15/16
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by GMATGuruNY » Fri Jan 14, 2011 4:34 am
anirudhbhalotia 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

This question is from OG-12, the answer mentioned is A, but am unable to understand the explanation. I had chosen E as the answer.
We can plug in a value for the tank. Since each stroke of the pump removes 1/2 the tank, we should plug in a value that can divided by 2 four times

Let tank = 16.
Stroke 1 removes 1/2*16 = 8, so 16-8 = 8 left.
Stroke 2 removes 1/2*8 = 4, so 8-4 = 4 left.
Stroke 3 removes 1/2*4 = 2, so 4-2 = 2 left.
Stroke 4 removes 1/2*2 = 1, so 2-1 = 1 left.
Since 1 is left, 16-1 = 15 was removed.
Amount removed/Tank = 15/16.

The correct answer is A.
Last edited by GMATGuruNY on Sun Jan 16, 2011 3:14 am, edited 1 time in total.
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by anirudhbhalotia » Sun Jan 16, 2011 2:22 am
I am not understanding this one...if 1/16 is removed...thats the answer right?

Why are we subtracting from 1...if we subtract that much remains...is it not?
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by ankur.agrawal » Sun Jan 16, 2011 2:35 am
anirudhbhalotia wrote:I am not understanding this one...if 1/16 is removed...thats the answer right?

Why are we subtracting from 1...if we subtract that much remains...is it not?
Ur Point makes sense. lets analyze it this way:

Let tank = 16.
Stroke 1 removes 1/2*16 = 8
Stroke 2 removes 1/2*8 = 4
Stroke 3 removes 1/2*4 = 2
Stroke 4 removes 1/2*2 = 1

So Total Removed=8+4+2+1 = 15

So the fraction of the original amount of air has been removed after 4 strokes= 15/16.

Hope this helps.
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by anirudhbhalotia » Sun Jan 16, 2011 2:47 am
ankur.agrawal wrote:
anirudhbhalotia wrote:I am not understanding this one...if 1/16 is removed...thats the answer right?

Why are we subtracting from 1...if we subtract that much remains...is it not?
Ur Point makes sense. lets analyze it this way:

Let tank = 16.
Stroke 1 removes 1/2*16 = 8
Stroke 2 removes 1/2*8 = 4
Stroke 3 removes 1/2*4 = 2
Stroke 4 removes 1/2*2 = 1

So Total Removed=8+4+2+1 = 15

So the fraction of the original amount of air has been removed after 4 strokes= 15/16.

Hope this helps.
I think I got it now...I was looking at it a different way...your adding up somewhat got it cleared for me.

Thanks!
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