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George claims that with each breath he takes, he can suck 1/3 of the a

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Senior DS Moderator
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George claims that with each breath he takes, he can suck 1/3 of the a  [#permalink]

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New post 27 Oct 2018, 09:16
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A
B
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Difficulty:

  45% (medium)

Question Stats:

45% (01:23) correct 55% (01:41) wrong based on 18 sessions

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George claims that with each breath he takes, he can suck 1/3 of the air out of his room. If this were true, what, after 4 breaths, would be the ratio of
the air that George has sucked out of the room to the air that still remains in the room? Assume no air is breathed back into the room.
A) 65:81
B) 65:16
C) 8:9
D) 13:27
E) 40:81

Weekly Quant Quiz #6 Question No 5


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Senior DS Moderator
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Re: George claims that with each breath he takes, he can suck 1/3 of the a  [#permalink]

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New post 27 Oct 2018, 09:16
1

Official Solution


Since George can suck \(1/3\) of air at a time, the remaining are after each breath = \(2/3\) of initial air.
After 4 breath , air remaining = \((\frac{2}{3})^4\) = \(\frac{16}{81}\) of initial air .
Air sucked = \(1-\frac{16}{81} = \frac{65}{81}\)
Air remaining = \(\frac{16}{81}\)
Required Ratio = \(\frac{65}{16}\)

Answer B
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Re: George claims that with each breath he takes, he can suck 1/3 of the a  [#permalink]

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New post 27 Oct 2018, 09:35
Answer is B

Take the air in the room to be x
1st breath: (1/3*x)sucked, 2x/3 left
2nd breath: (1/3*2x/3)sucked, (2x/3-2x/9)left
3rd breath: (1/3*4x/9)sucked, (4x/9-4x/27)left
4th breath: (1/3*8x/27)sucked, (8x/27-8x/81)left

adding up the sucked out air gives 65x/81
and air left is 16x/81
therefore ratio is 65x/81:16x/81 which is 65:16
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Re: George claims that with each breath he takes, he can suck 1/3 of the a  [#permalink]

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New post 27 Oct 2018, 11:55
My approach-
let the air in the room be a multiple of 3 as the air getting sucked out is 1/3 of total
now filtering the answer choices we can see that A and E has 81 , B,C and D are out
1/3 -> 81* (1/3) = 27 left
1/3 -> 27* (1/3) = 9 left
1/3 -> 9* (1/3) = 3 left
1/3 -> 3* (1/3) = 1 left
total left= 40

Ans I think is -E
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Re: George claims that with each breath he takes, he can suck 1/3 of the a  [#permalink]

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New post 27 Oct 2018, 12:41
Suppose there is 81 units air in the room.
George sucks 1/3 out. 2/3 still remains after each breath
Air after 4 breaths = 81 * 2^4/3^4 = 16 units
Air sucked = 65 units
65:16
GMAT Club Bot
Re: George claims that with each breath he takes, he can suck 1/3 of the a &nbs [#permalink] 27 Oct 2018, 12:41
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George claims that with each breath he takes, he can suck 1/3 of the a

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