SAT Mathematics Practice Test 3

Question : 15 of 58

Marks: +1, -0

c=5/9(F-32)

The equation above shows how a temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?
I. A temperature increase of 1 degreeFahrenheit is equivalent to a temperature increase of

5/9

degree Celsius.
II. A temperature increase of 1 degree Celsius is equivalent to a temperature increase of

1.8

degrees Fahrenheit.
III. A temperature increase of

5/9

degree Fahrenheit is equivalent to a temperature increase of

1

degree Celsius.

I only
II only
III only
I and II only

Validate

Solution:

If C is graphed against F, the slope of the graph is equal to

5/9

degrees Celsius/degrees Fahrenheit, which means that for an increase of 1 degree Fahrenheit, the increase is

5/9

of 1 degree Celsius.
Thus, statement I is true.
This is the equivalent to saying that an increase of 1 degree Celsius is equal to an increase of

9/5

degrees Fahrenheit.
Since

9/5=1.8

, statement II is true.
On the other hand, statement III is not true, since a temperature increase of

9/5

degrees Fahrenheit, not

5/9

degree Fahrenheit, is equal to a temperature increase of 1 degree Celsius.
Choices A, B, and C are incorrect because each of these choices omits a true statement or includes a false statement.

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