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The temperature of a certain cup of coffee 10 minutes it was

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The temperature of a certain cup of coffee 10 minutes it was

by imane81 » Thu Feb 18, 2010 12:29 pm
Please help on this one


The temperature of a certain cup of coffee 10 minutes it was poured was 120 degree Fahrenheit> If temperature F of the coffee t minutes after it was poured can be determined by the formula F = 120*(2^-at) + 60where F is in degree Fahrenheit and a is a constant , then the temperature of the coffee 30 minutes after it was poured was how many degree Fahrenheit?
A. 65
B. 75
C. 80
D. 85
E. 90
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by harsh.champ » Thu Feb 18, 2010 12:37 pm
imane81 wrote:Please help on this one


The temperature of a certain cup of coffee 10 minutes it was poured was 120 degree Fahrenheit> If temperature F of the coffee t minutes after it was poured can be determined by the formula F = 120*(2^-at) + 60where F is in degree Fahrenheit and a is a constant , then the temperature of the coffee 30 minutes after it was poured was how many degree Fahrenheit?
A. 65
B. 75
C. 80
D. 85
E. 90
Now,
F = 120*(2^-at) + 60

Putting t=10 we get F=120
=>120 = 120*(2^-10a) + 60
=>2 = 2*(2^-10a) + 1 [we know that 2^0 is 1]
=>2-1 = 2^(1-10a)
=>2^0 = 2^(1-10a) [since 2^0 =1]
=>10a =1
=>a = 0.1
Putting value of a in the original eqn.,it becomes
F = 120*[2^(-0.1*t)] + 60
Putting t=30 ,
we get F = 120*[2^-3] + 60
[spoiler]=15 + 60
=75
Hence,B.[/spoiler]
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by ajith » Thu Feb 18, 2010 12:48 pm
imane81 wrote:Please help on this one


The temperature of a certain cup of coffee 10 minutes it was poured was 120 degree Fahrenheit> If temperature F of the coffee t minutes after it was poured can be determined by the formula F = 120*(2^-at) + 60where F is in degree Fahrenheit and a is a constant , then the temperature of the coffee 30 minutes after it was poured was how many degree Fahrenheit?
A. 65
B. 75
C. 80
D. 85
E. 90
120 = 120*(2^-10a) + 60
2= 2*(2^-10a) + 1
2^1-10a = 1
10a =1

Temp after 30 mins = 120*2^-30a +60 = 120*2^-3 +60 = 120/8+60 = 75
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by shashank.ism » Sun Feb 21, 2010 3:51 pm
imane81 wrote:Please help on this one


The temperature of a certain cup of coffee 10 minutes it was poured was 120 degree Fahrenheit> If temperature F of the coffee t minutes after it was poured can be determined by the formula F = 120*(2^-at) + 60where F is in degree Fahrenheit and a is a constant , then the temperature of the coffee 30 minutes after it was poured was how many degree Fahrenheit?
A. 65
B. 75
C. 80
D. 85
E. 90
Initial temp = 120 F
also temp decreases as , F = 120*(2^-at) + 60
temp after 10 min = 120*(2^-a10 ) + 60 = 120
-->
2(2^-10a)+1 = 2 -> 2(2^-10a )=1 --> 2^-10a = 2^-1
-10a = -1 --> a= 1/10
temp after 30 min = 120*(2^-at) + 60 = 120 * (2 ^ -30a ) + 60 = 120 x(2^-30/10) +60 = 120 (2^-3) +60
120/8 +60 = 15+60 = [spoiler]75 Ans B
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by akmba » Mon Jul 14, 2014 6:22 am
These are Leavo on my strategy ! :)
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by Brent@GMATPrepNow » Mon Jul 14, 2014 8:10 am
The temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees Fahrenheit. if the temperature f of the coffee t minutes after it was poured can be determined by the formula f = 120 * 2^(-at) + 60, where f is in degrees Fahrenheit and a is a constant, then the temperature of the coffee 30 minutes after it was poured was how many degrees Fahrenheit?
A. 65
B. 75
C. 80
D. 85
E. 90
The temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees Fahrenheit.

So, 120 = 120 * 2^[(-a)(10)] + 60
Divide both sides by 60: 2 = 2 * 2^[(-a)(10)] + 1
1 = 2 * 2^[(-a)(10)]
1/2 = 2^[(-a)(10)]
Since 2^(-1) = 1/2, we know that (-a)(10) = -1
So, a = 1/10

So, the formula is f = 120 * 2^[(-1/10)(t)] + 60

The temperature of the coffee 30 minutes after it was poured was how many degrees Fahrenheit?
f = 120 * 2^[(-1/10)(30)] + 60
= 120 * 2^[-3] + 60
= 120 * (1/8) + 60
= 15 + 60
= 75
= B

Cheers,
Brent
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by GMATinsight » Mon Jul 14, 2014 8:31 am
akmba wrote:These are Leavo on my strategy ! :)
Hi akmba,

I suggest that such questions should NOT be left and MUST be attempted as these are pretty straight forward questions for a 700 score (your target score) aspirant. This questions should be categorized as MEDIUM DIFFICULTY LEVEL Question.
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by Brent@GMATPrepNow » Mon Jul 14, 2014 8:48 am
akmba wrote:These are Leavo on my strategy ! :)
It's a good idea to have in mind some question types that you typically find difficult (and time-consuming), especially if you find it difficult to complete each section in the allotted time. Keep in mind that you can have incorrect responses on the GMAT and still score 800.

Cheers,
Brent
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by RosalineJWilson » Tue May 19, 2015 8:30 pm
These are Leavo on my strategy !
Brent@GMATPrepNow wrote:
akmba wrote:These are Leavo on my strategy ! :)
It's a good idea to have in mind some question types that you typically find difficult (and time-consuming), especially if you find it difficult to complete each section in the allotted time. Keep in mind that you can have incorrect responses on the GMAT and still score 800.

Cheers,
Brent
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