Q21. - Algebra 2

Question

Compare the quantity in Column A and the quantity in Column B. Then determine whether:

 

A. the quantity in Column A is greater;

 

B. the quantity in Column B is greater;

 

C. the two quantities are equal;

 

D. the relationship cannot be determined from the information given.

 

 

$0<\text{s}<\frac{3}{4}$

 

Column A     Column B

 

      $1$                   $3\text{s}$

Step-by-Step Solution

Answer

The relationship between the quantity in Colum A and the quantity in Column B cannot be determined. So, the correct option is D.

Step 1 - Consider the two quantities.

The range of $s$ is:

 

$0<s<\frac{3}{4}$

 

The quantity in column A is:

 

$1$

 

The quantity in column B is:

 

$3s$

Step 2 - Evaluate the two quantities.

Write the range of s as:

 

$0<s<\frac{3}{4}=0<s<0.75$.

 

The quantity in column B is $3s$.

 

Minimum value of s is $0$ and maximum value of s is $0.75$.

 

So, the range of $3s$ is:

 

$0<s<0.75=0<3s<2.25$

 

Now the quantity in column B is 1.

 

As $3s$ can take any value from 0 to $2.25$. And no specific value of s is given. So, no specific value for 3s can be obtained. Thus, it cannot be said which quantity is greater and hence the relationship cannot be determined.

Step 3 - State the conclusion.

The relationship between the quantities cannot be determined. Therefore, option D is correct.