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A vacuum pump reduces the number of gas molecules in a vacuum chamber

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A vacuum pump reduces the number of gas molecules in a vacuum chamber  [#permalink]

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New post 16 May 2015, 06:31
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  25% (medium)

Question Stats:

73% (02:05) correct 27% (01:57) wrong based on 212 sessions

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A vacuum pump reduces the number of gas molecules in a vacuum chamber by approximately 6.5·10^24 molecules per minute. Which of the following best approximates the time (in minutes) it takes to reduce the number of gas molecules in the vacuum chamber by 30·10^21?

A. 0.005
B. 0.03
C. 0.05
D. 2.9
E. 27

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Re: A vacuum pump reduces the number of gas molecules in a vacuum chamber  [#permalink]

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New post 16 May 2015, 16:36
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Hi reto,

This question is complex-looking (since it includes Scientific Notation), but it's really just a ratio question.

We're given the rate, per minute, that gas molecules are reduced: (6.5)(10^24) molecules/minute

We're asked, in MINUTES, how long it would take to reduce the number of molecules by (30)(10^21).

To make the comparison more "apparent", I'm going to rewrite the second number...

(30)(10^21) = (3)(10^22).

Comparing these two values...

(3)(10^22) and (6.5)(10^24)

...it should be clear that (6.5)(10^24) is LARGER. Since it takes 1 minute to clear that many molecules, it should take LESS than 1 minute to clear (3)(10^22) molecules. From here, we just need to create a ratio....

(3)(10^22) / (6.5)(10^24)

(10^22)/(10^24) = 1/(10^2)

3/6.5 is about 1/2

This leaves us with....

about 1 / (2)(10^2) = about 1/200 minutes

1/200 = .005 minutes

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Re: A vacuum pump reduces the number of gas molecules in a vacuum chamber  [#permalink]

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New post 22 Jun 2015, 05:38
Using the R x T = W chart:

(6x10^21) x T = 6 x 10^24
T = 6 x 10^24 / 6x10^21
T = 5 X 10^-3
T = 0.005 ANS A
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Re: A vacuum pump reduces the number of gas molecules in a vacuum chamber  [#permalink]

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New post 22 Jun 2015, 22:39
3
reto wrote:
A vacuum pump reduces the number of gas molecules in a vacuum chamber by approximately 6.5·10^24 molecules per minute. Which of the following best approximates the time (in minutes) it takes to reduce the number of gas molecules in the vacuum chamber by 30·10^21?

A. 0.005
B. 0.03
C. 0.05
D. 2.9
E. 27


You can also think in terms of the unitary method:

6.5 * 10^24 molecules are removed in 1 min
30 * 10^21 molecules will be removed in \(\frac{1}{6.5 * 10^{24}} * 30 * 10^{21} = .0046\)

Answer (A)
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Re: A vacuum pump reduces the number of gas molecules in a vacuum chamber  [#permalink]

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New post 23 Jun 2015, 00:28
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Answer = A = 0.005

Setting up the equation as follows:

\(\frac{30 * 10^{21}}{6.5* 10^{24}} = \frac{3}{650} = 0.004* \approx{0.005}\)
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Re: A vacuum pump reduces the number of gas molecules in a vacuum chamber  [#permalink]

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New post 09 Nov 2015, 22:50
6*5*10^21/6.5*10^24=5*1/10^3=0.005

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Re: A vacuum pump reduces the number of gas molecules in a vacuum chamber  [#permalink]

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New post 27 Jul 2018, 11:11
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Re: A vacuum pump reduces the number of gas molecules in a vacuum chamber &nbs [#permalink] 27 Jul 2018, 11:11
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