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Major Timing Issue - Coffee (GMAT PREP) - need expert's help

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Source: — Problem Solving |
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by VP_Jim » Mon Sep 01, 2008 4:31 pm
Well, I'm not sure how you solved it, but here's what I did.

First, we have to solve for "a", so we have to plug in what we know: we know that the coffee was 120 degrees after 10 minutes, so:

120=120(2^-10a)+60

We can solve for a there and find that a=.1.

Now that we know "a", we can create a new equation to solve for the temperature after 30 minutes:

F=120(2^(30*.1))+60

Now we can solve for F, which would = 75.

Let me know if you want more details re: how to do the calculations - it's hard to type them out! I agree that this problem is pretty time consuming and I don't see much of a shortcut at first glance...
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by sushilmore » Mon Sep 01, 2008 4:45 pm
Ans is 75
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by Fab » Mon Sep 01, 2008 8:28 pm
Hey Jim, how do you get a=1?

This is my procedure:

120=120(2^-10a)+60
60=120(2^-10a)
1/2=(2^-10a) so,
1/2=1/2^10a

so a=1/10..

please correct me if i'm wrong...

THANKS
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by VP_Jim » Mon Sep 01, 2008 9:38 pm
.1 .... not 1.

.1 = 1/10

Hope that clears it up!
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by nervesofsteel » Mon Sep 01, 2008 11:40 pm
Yes the answer is 75...
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by rosh26 » Tue Sep 02, 2008 10:09 am
Yeah that's what I did, but it took me a long time to arrive at the answer, especially under time pressure.
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by dferm » Tue Sep 02, 2008 10:57 am
How did you arrive @ 75?
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by dferm » Tue Sep 02, 2008 11:13 am
GOT IT....
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by ddm » Thu Sep 04, 2008 5:22 pm
120=120(2^-10a)+60
60=120(2^-10a)
1/2=(2^-10a) so,
1/2=1/2^10a

How do u solve for "a" after this?


Since it is already mentioned in few posts that a= .1, after substituting the value for a the equation is:

F= 120(2^30*.1)+60
= 120(2^3)+60

.....solving got this equation gives a huge number....

where am i going wrong in solving for "a" n then in the substitution?
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by kshankker » Thu Sep 04, 2008 6:09 pm
hey... a= 1/10..... not 1.

here is the method , i think so you stuked at 1/2 = (1/2^a)^10,

cross multiplication..... 2^10a = 2 ^ 1
.....10a = 1
........a = 1/ 10 ....
Then substitute this a into that equation.....youw will be getting 15 + 60.
Hope thats clear
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