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, or

(D) The relationship cannot be determined from the information given.

 

21. $3x+12=5x-3$

Column A: The sum of two different prime numbers if each number is less than 8.

 

Column B: The sum of two different positive even integers if each integer is less than 8.

Step-by-Step Solution

Answer

The correct option is (D), and, the other options are wrong because one cannot determine a relationship between the quantities, because of more possibilities.

Step 1 – Compute the value of the quantity in column A.

Find the sum of two different prime numbers if each number is less than 8.

 

The prime numbers that are less than 8 are $1,2,3,5,$and 7.

Find the possible sum of two different prime numbers:

$\begin{array}{c}1+2=3\\ 1+3=4\\ 1+5=6\\ 1+7=8\\ 2+3=5\\ 2+5=7\\ 2+7=9\\ 3+5=8\\ 3+7=10\\ 5+7=12\end{array}$

Step 2 – Compute the value of the quantity in column B.

Find the sum of two different positive even integers if each integer is less than 8..

 

The even integers that are less than 8 are 2,4,and 6.

 

Find the possible sum of two different even integers:

$\begin{array}{c}2+4=6\\ 2+6=8\\ 6+4=10\end{array}$

Step 3 – Check whether the option A is correct or incorrect.

For example, the value of the quantity in column A is 12 and the quantity in column B is 10.

 

This means the quantity in column A is greater.

So, the option A is correct.

 

For example, the value of the quantity in column A is 8 and the quantity in column B is 10.

This means the quantity in column A is not greater.

So, the option A is incorrect.

So, we cannot conclude the relation.

Step 4 – Check whether the option B is correct or incorrect.

For example, the value of the quantity in column A is 12 and the quantity in column B is 10.

 

This means the quantity in column B is not greater.

So, the option B is incorrect.

 

For example, the value of the quantity in column A is 3 and the quantity in column B is 10.

This means the quantity in column B is greater.

So, the option B is correct.

So, we cannot conclude the relation.

Step 5 – Check whether the option C is correct or incorrect.

For example, the value of the quantity in column A is 10 and the quantity in column B is 10.

 

Here the values of the two quantities in column A and column B are same.

So, the option C is correct.

 

For example, the value of the quantity in column A is 3 and the quantity in column B is 8.

 

Here the values of the two quantities in column A and column B are different.

So, the option C is incorrect.

So, we cannot conclude the relation.

Step 6 – Check whether the option D is correct or incorrect.

Here, one cannot determine a relationship between the quantities, because of more possibilities.

So, the option D is correct.

 

Hence, the correct option is (D), and, the other options are wrong because one cannot determine a relationship between the quantities, because of more possibilities.