Arithmetic

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anirudhbhalotia: Master | Next Rank: 500 Posts; Posts: 123; Joined: Tue Nov 23, 2010 7:18 pmFollowed by: 4 members; Location: Mumbai, India; Thanked: 5 times

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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Source: Beat The GMAT — Problem Solving | Thu Jan 13, 2011 10:14 pm

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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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towerSpider: Master | Next Rank: 500 Posts; Posts: 155; Joined: Mon Dec 13, 2010 11:02 am; Thanked: 3 times

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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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

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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anirudhbhalotia: Master | Next Rank: 500 Posts; Posts: 123; Joined: Tue Nov 23, 2010 7:18 pmFollowed by: 4 members; Location: Mumbai, India; Thanked: 5 times

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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ankur.agrawal: Master | Next Rank: 500 Posts; Posts: 261; Joined: Wed Mar 31, 2010 8:37 pmFollowed by: 3 members; Location: Varanasi; Thanked: 11 times

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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anirudhbhalotia: Master | Next Rank: 500 Posts; Posts: 123; Joined: Tue Nov 23, 2010 7:18 pmFollowed by: 4 members; Location: Mumbai, India; Thanked: 5 times

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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