Q22. - 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.

 

Integers p, q, r, s, t, and u are equally spaced on the number line.

Column A: t — s.

 

Column B: 8. 

Step-by-Step Solution

Answer

The correct option is (C), and, the other options are wrong because the value of $t-s$is 8, both the quantities in column A and column B be are equal.

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

From the figure, notice that the distance between p to u is given by u-p=40.

This distance 40 is divided into 5 equal parts, as $pq,qr,rs,st,tu$.

So,

$\begin{array}{c}u-p=40\\ \frac{u-p}{5}=\frac{40}{5}\\ \frac{u-p}{5}=8\end{array}$

So, the distance between each part is 8.

That is, $q-p=8, r-q=8, s-r=8, t-s=8, u-t=8.$

Step 2 – Check whether the option A is correct or incorrect.

The quantity in column A is $t-s$ and the quantity in column B is 8.

From the given data and the calculated values, one can conclude that $t-s=8$.

So, the option A is incorrect.

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

The quantity in column A is $t-s$ and the quantity in column B is 8.

From the given data and the calculated values, one can conclude that $t-s=8$.

So, the option B is incorrect.

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

The quantity in column A is $t-s$ and the quantity in column B is 8.

From the given data and the calculated values, one can conclude that $t-s=8$.

So, the option C is correct.

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

The quantity in column A is $t-s$ and the quantity in column B is 8.

From the given data and the calculated values, one can conclude that $t-s=8$.

So, one can determine a relationship.

So, the option D is incorrect.

 

Hence, the correct option is (C), and, the other options are wrong because the value of $t-s$ is 8, both the quantities in column A and column B be are equal.