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# A chemist is testing the properties of a certain gas that are inside a

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Intern
Joined: 06 Apr 2010
Posts: 14
A chemist is testing the properties of a certain gas that are inside a  [#permalink]

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25 May 2016, 10:48
4
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Difficulty:

45% (medium)

Question Stats:

68% (01:59) correct 32% (02:15) wrong based on 82 sessions

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A chemist is testing the properties of a certain gas that are inside a balloon that contains an unknown number of molecules of this gas. On Monday the chemist stained 5 × 10^6 gas molecules so that those gas molecules could be easily recognizable in the future. Then on Tuesday, 5 x 10^6 gas molecules were taken from the balloon randomly. From these gas molecules 1,000 were found to be stained. If the percent of stained gas molecules found on Tuesday is representative of the number of stained gas molecules in the balloon, what is that number of gas molecules in the balloon?

A) 2.5 x 10^4
B) 2.5 x 10^7
C) 2.5 x 10^12
D) 2.5 x 10^10
E) 2.5 x 10^16
Math Expert
Joined: 02 Sep 2009
Posts: 52285
Re: A chemist is testing the properties of a certain gas that are inside a  [#permalink]

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25 May 2016, 13:30
1
ninayeyen wrote:
A chemist is testing the properties of a certain gas that are inside a balloon that contains an unknown number of molecules of this gas. On Monday the chemist stained 5 × 10^6 gas molecules so that those gas molecules could be easily recognizable in the future. Then on Tuesday, 5 x 10^6 gas molecules were taken from the balloon randomly. From these gas molecules 1,000 were found to be stained. If the percent of stained gas molecules found on Tuesday is representative of the number of stained gas molecules in the balloon, what is that number of gas molecules in the balloon?

A) 2.5 x 10^4
B) 2.5 x 10^7
C) 2.5 x 10^12
D) 2.5 x 10^10
E) 2.5 x 10^16

The percent of stained gas molecules found on Tuesday is representative of the number of stained gas molecules in the balloon, means that:

$$\frac{1000}{(5 * 10^6)} = \frac{(5 * 10^6)}{(total)}$$;

$$(total) = \frac{(5 * 10^6)^2}{100} = \frac{(25 * 10^{12})}{10^3} =25* 10^{9}=2.5* 10^{10}$$.

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Re: A chemist is testing the properties of a certain gas that are inside a  [#permalink]

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25 May 2016, 13:33
1
2
ninayeyen wrote:
A chemist is testing the properties of a certain gas that are inside a balloon that contains an unknown number of molecules of this gas. On Monday the chemist stained 5 × 106 gas molecules so that those gas molecules could be easily recognizable in the future. Then on Tuesday, 5 x 10^6 gas molecules were taken from the balloon randomly. From these gas molecules 1,000 were found to be stained. If the percent of stained gas molecules found on Tuesday is representative of the number of stained gas molecules in the balloon, what is that number of gas molecules in the balloon?

A) 2.5 x 10^4
B) 2.5 x 10^7
C) 2.5 x 10^12
D) 2.5 x 10^10
E) 2.5 x 10^16

Dear ninayeyen,
I'm happy to respond.

For the Monday amount, I assume 5 x 106 is a misprint, and you mean 5 x 10^6.

I will say that the premise of this word problem is so entirely absurd that it is embarrassing. There is no way to "stain" a molecule: all pigments themselves are made of molecules, typically much larger than gas molecules. This question appears to be written by someone with less than a middle school understanding of physical science. Truly embarrassing.

If we ignore the obvious inaccuracies of the scenario, this is intended to be a proportion problem

$$\frac{1000}{5 \times 10^6} = \frac{5 \times 10^6}{N}$$

where N is the total number of gas molecules in the balloon. Cross-multiply.

1000N = (5 x 10^6)^2 = 25 x 10^12

N = 25 x 10^9 = 2.5 x 10^10

OA = (D)

Mike
_________________

Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Math Expert
Joined: 02 Sep 2009
Posts: 52285
Re: A chemist is testing the properties of a certain gas that are inside a  [#permalink]

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25 May 2016, 13:35
mikemcgarry wrote:
ninayeyen wrote:
A chemist is testing the properties of a certain gas that are inside a balloon that contains an unknown number of molecules of this gas. On Monday the chemist stained 5 × 106 gas molecules so that those gas molecules could be easily recognizable in the future. Then on Tuesday, 5 x 10^6 gas molecules were taken from the balloon randomly. From these gas molecules 1,000 were found to be stained. If the percent of stained gas molecules found on Tuesday is representative of the number of stained gas molecules in the balloon, what is that number of gas molecules in the balloon?

A) 2.5 x 10^4
B) 2.5 x 10^7
C) 2.5 x 10^12
D) 2.5 x 10^10
E) 2.5 x 10^16

Dear ninayeyen,
I'm happy to respond.

For the Monday amount, I assume 5 x 106 is a misprint, and you mean 5 x 10^6.

I will say that the premise of this word problem is so entirely absurd that it is embarrassing. There is no way to "stain" a molecule: all pigments themselves are made of molecules, typically much larger than gas molecules. This question appears to be written by someone with less than a middle school understanding of physical science. Truly embarrassing.

If we ignore the obvious inaccuracies of the scenario, this is intended to be a proportion problem

$$\frac{1000}{5 \times 10^6} = \frac{5 \times 10^6}{N}$$

where N is the total number of gas molecules in the balloon. Cross-multiply.

1000N = (5 x 10^6)^2 = 25 x 10^12

N = 25 x 10^9 = 2.5 x 10^10

OA = (D)

Mike

Dear Mike,

Edited the highlighted part. Thank you.
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Joined: 09 Sep 2013
Posts: 9431
Re: A chemist is testing the properties of a certain gas that are inside a  [#permalink]

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17 Dec 2018, 15:07
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Re: A chemist is testing the properties of a certain gas that are inside a &nbs [#permalink] 17 Dec 2018, 15:07
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