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# The half-life of a radioactive element is defined as the amount of tim

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The half-life of a radioactive element is defined as the amount of tim  [#permalink]

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25 Nov 2018, 08:02
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Difficulty:

15% (low)

Question Stats:

86% (00:47) correct 14% (01:09) wrong based on 43 sessions

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The half-life of a radioactive element is defined as the amount of time required for the amount of the element to decrease by half. If the half-life of an element is 3 years, how long will it take for the element to be reduced to one-eighth of its original amount?

A. 3 years
B. 9 years
C. 21 years
D. 24 years
E. 27 years
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Re: The half-life of a radioactive element is defined as the amount of tim  [#permalink]

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25 Nov 2018, 12:51
rencsee wrote:
The half-life of a radioactive element is defined as the amount of time required for the amount of the element to decrease by half. If the half-life of an element is 3 years, how long will it take for the element to be reduced to one-eighth of its original amount?

A. 3 years
B. 9 years
C. 21 years
D. 24 years
E. 27 years

$$2M\,\,\mathop \to \limits^{3\,\,{\rm{years}}} \,\,M$$

$$8M\,\,\mathop \to \limits^{?\,\,{\rm{years}}} \,\,M$$

$$?\,\,\,\,:\,\,\,\,8M\,\,\mathop \to \limits^{3\,\,{\rm{years}}} \,\,4M\,\,\mathop \to \limits^{3\,\,{\rm{years}}} \,\,2M\,\,\mathop \to \limits^{3\,\,{\rm{years}}} \,\,M\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 3 \cdot 3\,\,{\rm{years}}\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\left( {\rm{B}} \right)$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
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Re: The half-life of a radioactive element is defined as the amount of tim  [#permalink]

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29 Nov 2018, 00:59
rencsee wrote:
The half-life of a radioactive element is defined as the amount of time required for the amount of the element to decrease by half. If the half-life of an element is 3 years, how long will it take for the element to be reduced to one-eighth of its original amount?

A. 3 years
B. 9 years
C. 21 years
D. 24 years
E. 27 years

Can someone provide more clarity on this problem? I am having trouble figuring this one out based on the half-life formula. Thx.
Re: The half-life of a radioactive element is defined as the amount of tim   [#permalink] 29 Nov 2018, 00:59
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