If 1/2 of the air in a tank is removed with each stroke of a

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. 7/8 
C. 1/4 
D. 1/8 
E. 1/16

sudhir18n · Accepted Answer

The best thing to do here is plug in 
Assume that there is 16 units of air in the tank 
first stroke = 1/2*16 = 8 ( we are left ith 8 now)
second stroke = 1/2*8 = 4( left ith 4 units now)
third stoke = 1/2*4 = 2( left with 2 units)
4th stroke = 1/2* 2 = 1 (left with 1 unit)

total units removed = 8+4+2+1 = 15
total unis in the tank at the begining = 16
thus its A . 15/16

Hope this helps

puneetj · Answer

A - 15/16..

Left After 1st stroke = 1/2
Left After 2nd stroke = 1/2 * 1/2 = 1/4
Left After 3rd stroke = 1/2 * 1/4 = 1/8
Left After 4th stroke = 1/2 * 1/8 = 1/16

So removed = 1- 1/16 = 15/16

jallenmorris · Answer

A

First you have 1

so 
first stroke = 1/2
second stroke = 1/4
third stroke = 1/8
fourth stroke = 1/16

8/16 + 4/16 + 2/16 + 1/16 = 15/16

2010mba · Answer

I get A, too.

Let X = air in the tank.

Plug in 240 = X.

First stroke = 1/2 * 240 = 120
Second stroke = 1/2 * 120 = 60
Third stroke = 1/2 * 60 = 30
Fourth stroke = 1/2 * 30 = 15

So 15 remains, which is the amount of air left.

240 - 15 = 225 (amount of air removed). 225/240 = 15/16

mrblack · Answer

This is a decay-type problem...the tank is halved after each stroke. Therefore:

(0.5)^4 = 1/16 --> 0.5 for halving, 4 for strokes

so 1/16 of air is left in the tank => 15/16 of the air was removed

srivats212 · Answer

Oh, I get it..! Thanks..!!!
I think the catch over here is.."the tank is halved after each stroke"....failed to understand the question properly.
Thought that a single stoke halves the air in it...so after 2 strokes guessed there wont be any air in it

Bunuel · Answer

Similar questions to practice: if-2-3-of-the-air-in-a-tank-is-removed-with-each-stroke-of-a-128432.html if-3-4-of-the-mineral-deposits-in-a-reservoir-of-water-are-97300.html on-january-1-2076-lake-loser-contains-x-liters-of-water-b-82667.html Hope it helps.

mvictor · Answer

let's assign a nice number..16 (divisible by 2 and 4), for total Air..
after 1st stroke, we are left with 8
after 2nd stroke, we are left with 4
after 3rd stroke, we are left with 2
after 4th stroke, we are left with 1

we removed 15 parts out of 16.
A: 15/16

EMPOWERgmatRichC · Answer

Hi All,

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

GMAT assassins aren't born, they're made, 
Rich

BrentGMATPrepNow · Answer

Strategy: Since the question is asking us to find a certain  fraction  (and not the actual volume of air that has been removed), let's assign a nice, easy-to-work-with value for the original volume of air in the tank .  
Since we keep halving the volume of air, let's say there are 64 liters of are in the tank at the beginning, and will keep track of the volume after each stroke.

Initial volume:  64  liters
Volume of air remaining after 1 stroke: 32 liters
Volume of air remaining after 2 strokes: 16 liters
Volume of air remaining after 3 strokes: 8 liters
Volume of air remaining after 4 strokes:  4  liters

If  4  liters of air remain in the tank, then the volume of air that was removed =  64  -  4  =  60  liters

So, the fraction of the original amount of air has been removed after 4 strokes =  60 / 64  = 30/32 = 15/16

Answer: A

Elite097 · Answer

What's a fast way to solve such questions? WHat if we had 10 strokes? Pls also explain the strategy  avigutman   ThatDudeKnows

avigutman · Answer

Elite097  this question is describing a geometric sequence. An analogous question could ask what fraction of the atomic nuclei of a radioactive sample would decay after 100 years, if it has a  half-life  of 25 years.
The strategy is to figure our how many times we're multiplying by (1/2). In the original question, that's clearly four times, so we have a change factor of (1/2)^4 = 1/16. If that fraction remains, then the remaining 15/16 is gone.
If we had 10 strokes, our change factor would be (1/2)^10 = 1/1,024, so the answer would be 1,023/1,024.
By the way, I have a chapter on geometric sequences in my book. First week access is free with a trial membership at  quantreasoning.com

ThatDudeKnows · Answer

Elite097

I agree with Avi's comments.

One thing to think about is that GMAC will never give us a question that REQUIRES us to do too much math to make sense in the context of a timed exam. If you encounter a question for which you think your solution is going to take far too long, that's an indication that you should take a moment to see if you can find a different path to the finish line. Can you ballpark? Can you use some logic to eliminate incorrect answer choices (e.g. you need a negative odd number, and there is only one)? Can you Plug In The Answers? Can you Plug In for variables? Can you spot a pattern by testing a subset and then apply a rule for the pattern to a larger number (e.g. what if we had 243 strokes?)?

I'm curious what approach you took on this that prompted you to post? I can't come up with a way to solve this question that would take more than just a few seconds. What was your method? And what would be the answer if it were 243 strokes?

egmat · Answer

Hey there! Let's think about this vacuum pump problem together - it's one of those questions where tracking what happens at each step really matters.

Understanding What's Happening: 
Each stroke removes  \frac{1}{2}  of the air that's  currently  in the tank. Here's what you need to see: if half is removed each time, then half  remains  each time. This is the key insight that makes everything click!

Let's Track What Remains: 
Starting with the full tank (let's call it 1 for simplicity):
- After stroke 1:  \frac{1}{2}  remains
- After stroke 2:  \frac{1}{2} 	imes \frac{1}{2} = \frac{1}{4}  remains 
- After stroke 3:  \frac{1}{4} 	imes \frac{1}{2} = \frac{1}{8}  remains
- After stroke 4:  \frac{1}{8} 	imes \frac{1}{2} = \frac{1}{16}  remains

Notice how we're just multiplying by  \frac{1}{2}  each time? That's the pattern!

Converting to What's Removed: 
Now here's where students often slip up - the question asks for what's been  removed , not what remains! If  \frac{1}{16}  of the air is still in the tank, then:

Fraction removed =  1 - \frac{1}{16} = \frac{16}{16} - \frac{1}{16} = \frac{15}{16}

Answer: A  ( \frac{15}{16} )

You can check out the  step-by-step solution on Neuron by e-GMAT  to master the exponential decay pattern systematically - they show you alternative approaches including a smart numbers technique that makes these calculations even faster. You can also explore other GMAT official questions with detailed solutions on Neuron for structured practice  here  to build consistent accuracy with word problems.

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