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

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

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New post 25 May 2016, 10:48
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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
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Re: A chemist is testing the properties of a certain gas that are inside a  [#permalink]

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New post 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:

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

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

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

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New post 25 May 2016, 13:33
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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 :-)
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Re: A chemist is testing the properties of a certain gas that are inside a  [#permalink]

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New post 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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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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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