A logic problem by Samyak Sand

Logic Level 2

$C = \frac{5}{9} (F - 23)$

The equation above shows how 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 degree Fahrenheit is equivalent to a temperature increase of $\frac{5}{9}$ 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 $\frac{5}{9}$ degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.

A) I only B) II only C) III only D) I and II only

III only II only I only I and II only

2 solutions

Amy Welch
Mar 24, 2018

It should be 9/5 or 5/9 instead of 9 5 and 5 9.

Samyak Sand
Mar 24, 2018

ANSWER EXPLANATION:Think of the equation as an equation for a line

y=mx+b

where in this case

C= 5 9 (F−32)

C= 5 9 F− 5 9 (32)

You can see the slope of the graph is 5 9 , which means that for an increase of 1 degree Fahrenheit, the increase is 5 9 of 1 degree Celsius.

C= 5 9 (F)

C= 5 9 (1)= 5 9

Therefore, 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.

C= 5 9 (F)

1= 5 9 (F)

(F)= 9 5

Since 9 5 = 1.8, statement II is true.

The only answer that has both statement I and statement II as true is A, but if you have time and want to be absolutely thorough, you can also check to see if statement III (an increase of 5 9 degree Fahrenheit is equal to a temperature increase of 1 degree Celsius) is true:

C= 5 9 (F)

C= 5 9 ( 5 9 )

C= 25 81 (whichis≠1)

An increase of 5 9 degree Fahrenheit leads to an increase of 25 81 , not 1 degree, Celsius, and so Statement III is not true.

The final answer is A.

A logic problem by Samyak Sand

2 solutions

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