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# Challenge 25 Question (derived rate problem)

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Challenge 25 Question (derived rate problem) [#permalink]

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31 May 2006, 16:08
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Hello everyone,

This question is from the challenge 25 (i believe). I don't completely understand the explanation. Can someone please explain? Thanks.

The gold depreciated at a rate of X% per year between 2000 and 2005. If the gold cost S dollars in 2001 and T dollars in 2003, how much did it cost in 2002?

Thanks again.

Mike

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Re: Challenge 25 Question (derived rate problem) [#permalink]

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31 May 2006, 17:16
If gold costs S in 2001 and T in 2003 and is steadily depreciating at X%,
T = S*(1-X/100)^2 .................A
After a year of 2001 (when gold was S), in 2002, the gold would cost S(1-X/100) .............................B

Therefore, gold in 2002
= S*(T/S)^1/2 = (S^1/2)/T.

In a simpler way, you can see it as a GP.
S Sr Sr^2, where r = (1-X/100).
Since Sr^2 = T, r = (T/S)^(1/2).
Therefore, Sr = S*(T/S)^(1/2) = (S^(1/2))/T
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Re: Challenge 25 Question (derived rate problem) [#permalink]

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31 May 2006, 17:32
kapslock wrote:
If gold costs S in 2001 and T in 2003 and is steadily depreciating at X%,
T = S*(1-X/100)^2 .................A
After a year of 2001 (when gold was S), in 2002, the gold would cost S(1-X/100) .............................B

Therefore, gold in 2002: = S*(T/S)^1/2 = (S^1/2)/T.

In a simpler way, you can see it as a GP.
S Sr Sr^2, where r = (1-X/100).
Since Sr^2 = T, r = (T/S)^(1/2).
Therefore, Sr = S*(T/S)^(1/2) = (S^(1/2))/T

great work.

but i guess, S*(T/S)^1/2 = (ST)^1/2.

How you arrived here? "Gold in 2002 = = S*(T/S)^1/2 = (S^1/2)/T."?

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Senior Manager
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Re: Challenge 25 Question (derived rate problem) [#permalink]

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31 May 2006, 22:28
Professor wrote:
kapslock wrote:
If gold costs S in 2001 and T in 2003 and is steadily depreciating at X%,
T = S*(1-X/100)^2 .................A
After a year of 2001 (when gold was S), in 2002, the gold would cost S(1-X/100) .............................B

Therefore, gold in 2002: = S*(T/S)^1/2 = (S^1/2)/T.

In a simpler way, you can see it as a GP.
S Sr Sr^2, where r = (1-X/100).
Since Sr^2 = T, r = (T/S)^(1/2).
Therefore, Sr = S*(T/S)^(1/2) = (S^(1/2))/T

great work.

but i guess, S*(T/S)^1/2 = (ST)^1/2.

How you arrived here? "Gold in 2002 = = S*(T/S)^1/2 = (S^1/2)/T."?

Good catch Prof. My mind was not properly working - that's what happens when you're solving GMAT problems at work
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question regarding the final step [#permalink]

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01 Jun 2006, 00:33
Hello,

This may not be the most intelligent question but...

how does S*(T/S)^1/2 = (ST)^1/2 ?

If you have sqrt (T/S) * S, where <i>sqrt (T/S)</I> represents the rate of decline expressed in T and S, does that come out to sqrt(ST)?

Thanks.

Mike

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Re: question regarding the final step [#permalink]

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01 Jun 2006, 04:42
mrmikec wrote:
Hello,

This may not be the most intelligent question but...

how does S*(T/S)^1/2 = (ST)^1/2 ?

If you have sqrt (T/S) * S, where <i>sqrt (T/S)</I> represents the rate of decline expressed in T and S, does that come out to sqrt(ST)?

Thanks.

Mike

Sqrt (T/S) * S
= { Sqrt(T)/Sqrt(S) } * S
= Sqrt (T) * S/Sqrt(S)
= Sqrt (T) * Sqrt (S)
= Sqrt (ST)

Hope that helps.
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Re: question regarding the final step [#permalink]

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01 Jun 2006, 10:23
kapslock wrote:
mrmikec wrote:
Hello,

This may not be the most intelligent question but...

how does S*(T/S)^1/2 = (ST)^1/2 ?

If you have sqrt (T/S) * S, where <i>sqrt (T/S)</I> represents the rate of decline expressed in T and S, does that come out to sqrt(ST)?

Thanks.

Mike

Sqrt (T/S) * S
STEP 2 = { Sqrt(T)/Sqrt(S) } * S
= Sqrt (T) * S/Sqrt(S)
= Sqrt (T) * Sqrt (S)
= Sqrt (ST)

Hope that helps.

One claification though on Step 2- > [ Sqrt(T/S) * S = Sqrt(T)*Sqrt(1/S)*S ] ? Correct?

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Re: question regarding the final step   [#permalink] 01 Jun 2006, 10:23
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