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Radioactive - Tougher problem

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Radioactive - Tougher problem

by charlie33 » Sun Jul 05, 2009 9:53 am
The radioactive element americium has a half-life of 432 years. Suppose we start with a 20-g mass of americium.
How much will be left after 367 years?


A. 17.0 g
B. 11.1 g
C. 15.5 g
D. 8.8 g
E. 18.0 g
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Re: Radioactive - Tougher problem

by real2008 » Sun Jul 05, 2009 10:38 am
charlie33 wrote:The radioactive element americium has a half-life of 432 years. Suppose we start with a 20-g mass of americium.
How much will be left after 367 years?


A. 17.0 g
B. 11.1 g
C. 15.5 g
D. 8.8 g
E. 18.0 g
is the OA B? If so, I can explain....
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by charlie33 » Sun Jul 05, 2009 10:47 am
I don't know I am having trouble working it out, doesn't seem much like a GMAT style question.
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by charlie33 » Sun Jul 05, 2009 10:50 am
I get A but I am not sure. I will have to find the answer book.

367/432 = approx .85
20*.85=17
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by real2008 » Sun Jul 05, 2009 11:02 am
charlie33 wrote:I get A but I am not sure. I will have to find the answer book.

367/432 = approx .85
20*.85=17
I think it is 20/{2^(367/432)} i.e. 11.099

Can you tell me the source please?
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by charlie33 » Sun Jul 05, 2009 11:04 am
Yes B is correct, I found the answer sheet.

It is from a class I took at my local university for the GMAT.
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by ssmiles08 » Sun Jul 05, 2009 3:00 pm
Is there some sort of formula for these kind of problems? It would be nice to know some solid way of going about this.

I would have just approximated 11.1 as the answer b/c you know in 432 years, the radioactive element would be 10g.

367 years a little more than 80% of 432 years which means it would have decayed about 80% of its first half life. 80% of 10 = 8 so 20 - 8 ~ 12

would have guesstimated it around 11-12% which would be B in this case.
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by Ian Stewart » Sun Jul 05, 2009 3:51 pm
You'll never see a question like this on a real GMAT, first because you'd need to know what 'half-life' means, which is not something you're assumed to know on the GMAT (it's not a physics test), and second because the calculation is impossible without a calculator. Sure, you can tell from the answer choices which must be right, but if the GMAT were to design a question around this concept, they would not use numbers like 432 and 367 in the question; instead they'd use numbers that were manageable.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by real2008 » Mon Jul 06, 2009 12:03 am
Ian Stewart wrote:You'll never see a question like this on a real GMAT, first because you'd need to know what 'half-life' means, which is not something you're assumed to know on the GMAT (it's not a physics test), and second because the calculation is impossible without a calculator. Sure, you can tell from the answer choices which must be right, but if the GMAT were to design a question around this concept, they would not use numbers like 432 and 367 in the question; instead they'd use numbers that were manageable.
Exactly.....
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