Problem Solving

BTGmoderatorDC wrote: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

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

Hi All,

We're told that C is the temperature in degrees Celsius and F is the temperature in degrees Fahrenheit, and 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, we're asked by how many degrees did the temperature extremes differ on the Celsius scale. This question can be solved rather easily by TESTing VALUES (as Brent has shown in his post). In addition, the answer choices are sufficiently 'spread out' that we can use a little logic and a little math to answer this question without too much work.

The equation 9C = 5(F - 32) can be 'rewritten' as...

C = 5(F - 32)/9

5/9 is a little more than 1/2.... so we can 'rewrite' the equation again as....

C = (a little more than 1/2)(F - 32)

Thus, for every degree that F 'changes', the value of C will change by a little more than 1/2 of a degree.

In this question, F changes by 45 degrees, so the value of C will change by (a little more than 1/2)(45) degrees. Half of 45 is 22.5, so we're looking for an answer that's a little more than 22.5 degrees. There's only one answer that matches...

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

BTGmoderatorDC wrote: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


OA C

Source: Official Guide

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