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If C is the temperature in degrees Celsius and F is the temperature in degrees Fahrenheit

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by BTGModeratorVI » Tue Jul 07, 2020 6:21 am

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If C is the temperature in degrees Celsius and F is the temperature in degrees Fahrenheit, then the relationship between temperatures on the two scales is expressed by the equation 9C = 5(F – 32). On a day when the temperature extremes recorded at a certain weather station differed by 45 degrees on the Fahrenheit scale, by how many degrees did the temperature extremes differ on the Celsius scale?

A. 65/9
B. 13
C. 25
D. 45
E. 81

Answer: C
Source: Official guide
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Re: If C is the temperature in degrees Celsius and F is the temperature in degrees Fahrenheit

by Jay@ManhattanReview » Tue Jul 07, 2020 10:06 pm
BTGModeratorVI wrote: ↑
Tue Jul 07, 2020 6:21 am
 If C is the temperature in degrees Celsius and F is the temperature in degrees Fahrenheit, then the relationship between temperatures on the two scales is expressed by the equation 9C = 5(F – 32). On a day when the temperature extremes recorded at a certain weather station differed by 45 degrees on the Fahrenheit scale, by how many degrees did the temperature extremes differ on the Celsius scale?

A. 65/9
B. 13
C. 25
D. 45
E. 81

Answer: C
Source: Official guide
Given the relationship 9C = 5(F – 32), we can simplify it as 9C = 5F – 32*5 => C = 5F/9 – 160/9

Note that –160/9 is a constant; thus, C is proportional to 5/9 times F

=> A variation of 45 degrees on the Fahrenheit scale would mean 5/9 x 45 = 25 degrees variation on the Celcius scale.

Correct answer: C

Hope this helps!

-Jay
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Re: If C is the temperature in degrees Celsius and F is the temperature in degrees Fahrenheit

by Brent@GMATPrepNow » Wed Jul 08, 2020 5:36 am
BTGModeratorVI wrote: ↑
Tue Jul 07, 2020 6:21 am
 If C is the temperature in degrees Celsius and F is the temperature in degrees Fahrenheit, then the relationship between temperatures on the two scales is expressed by the equation 9C = 5(F – 32). On a day when the temperature extremes recorded at a certain weather station differed by 45 degrees on the Fahrenheit scale, by how many degrees did the temperature extremes differ on the Celsius scale?

A. 65/9
B. 13
C. 25
D. 45
E. 81

Answer: C
Source: Official guide
To find the answer, let's find the Celsius conversion for two temperatures that differ by 45 degrees, on the Fahrenheit scale.

Start with 32 degrees Fahrenheit
Plug into the formula to get 9C = 5(32 – 32)
Simplify: 9C = 0
Solve: C = 0
So 32 degrees Fahrenheit = 0 degrees Celsius


32 + 45 = 77
So let's convert 77 degrees Fahrenheit into Celsius
Plug into the formula to get 9C = 5(77 – 32)
Simplify: 9C = 5(45)
Divide both sides by 9 to get: C = 5(5) = 25
So 77 degrees Fahrenheit = 25 degrees Celsius

25 - 0 = 25
So, a 45-degree difference in Fahrenheit is equal to a 25-degree difference in Celsius.

Answer: C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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Re: If C is the temperature in degrees Celsius and F is the temperature in degrees Fahrenheit

by Scott@TargetTestPrep » Sat Jul 11, 2020 1:07 pm
BTGModeratorVI wrote: ↑
Tue Jul 07, 2020 6:21 am
 If C is the temperature in degrees Celsius and F is the temperature in degrees Fahrenheit, then the relationship between temperatures on the two scales is expressed by the equation 9C = 5(F – 32). On a day when the temperature extremes recorded at a certain weather station differed by 45 degrees on the Fahrenheit scale, by how many degrees did the temperature extremes differ on the Celsius scale?

A. 65/9
B. 13
C. 25
D. 45
E. 81

Answer: C
Source: Official guide
Solution:

Notice that C = 5(F - 32)/9

We can let the low temperature of the day be 50°F; thus, the high temperature of the day is 95°F.
In Celsius, the low temperature of the day is 5(50 - 32)/9 = 5(18)/9 = 10°C, and the high temperature of the day is 5(95 - 32)/9 = 5(63)/9 = 35°C. Therefore, the difference of the temperatures on the Celsius scale is 35 - 10 = 25.

Answer: C

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