In the diagram, point $P$ is on the number line at 3 and $V$ is at 33 . The number line between 3 and 33 is divided into six equal parts by the points $Q, R, S, T, U$.

![](https://cdn.mathpix.com/cropped/2024_04_20_ac36362783317e0251fdg-026.jpg?height=127&width=683&top_left_y=1151&top_left_x=686)

What is the sum of the lengths of $P S$ and $T V$ ?
(A) 25
(B) 23
(C) 24
(D) 21
(E) 27
The segment of the number line between 3 and 33 has length $33-3=30$.

Since this segment is divided into six equal parts, then each part has length $30 \div 6=5$.

The segment $P S$ is made up of 3 of these equal parts, and so has length $3 \times 5=15$.

The segment $T V$ is made up of 2 of these equal parts, and so has length $2 \times 5=10$.

Thus, the sum of the lengths of $P S$ and $T V$ is $15+10$ or 25 .

ANSWER: (A)