Directions: Read the given information carefully and answer the question below.

Six executives – P, Q, R, S, T and U sit in a row facing north, but not necessarily in the same order. Each of them scored a different number of points in an assessment, between 10 and 50. Only two persons sit between P and the one who scored 25 points, and neither of them sits at the extreme ends of the row. The number of persons sitting to the right of P is one more than the number of persons sitting to the left of Q. U, who sits adjacent to Q, sits second to the left of the person who scored 5 points less than U. R sits to the immediate right of T, who scored a perfect square number of points. P scored 12 points less than R, who scored 15 points more than T. S scored a prime number of points, which is 7 points more than the person sitting two places away from R.

What is the total number of points scored by the executives sitting at the extreme ends of the row?

The correct answer is 69.

Step 1: Determine the seating positions of P, Q, and the 25-point scorer
There are 6 positions numbered 1 to 6 from left to right facing North.
Only two persons sit between P and the person who scored 25 points, and neither sits at the extreme ends (positions 1 and 6). Therefore, P and the 25-point scorer must occupy positions 2 and 5 in some order.
The number of persons sitting to the right of P is one more than the number of persons sitting to the left of Q.
If P were at position 5, there would be 1 person to his right, meaning 0 persons to the left of Q (so Q would be at position 1). However, testing this arrangement leads to an out-of-range score for T. Thus, P must be at position 2.
With P at position 2, there are 4 persons to his right, which means there are 3 persons to the left of Q. Hence, Q is at position 4, and the person who scored 25 points is at position 5.

Step 2: Determine the positions of U, T, R, and S
U sits adjacent to Q (position 4), so U can be at position 3 or 5. Since position 5 is occupied by the 25-point scorer, if U were at position 5, U would sit second to the left of position 7, which does not exist in a 6-person row. Therefore, U must be at position 3.
U sits second to the left of the person who scored 5 points less than U. The person second to the right of U (position 3) is at position 5:

$3+2=5$

Since the person at position 5 scored 25 points, U's score is:

$\text{Score of U}=25+5=30$

R sits to the immediate right of T. The remaining vacant adjacent seats are positions 5 and 6. Thus, T is at position 5 (scoring 25 points, which is a perfect square, 5²) and R is at position 6.
The remaining person S must sit at position 1.
The seating arrangement from left to right (positions 1 to 6) is: S, P, U, Q, T, R.

Step 3: Calculate the scores of R, P, and S
R scored 15 points more than T:

$\text{Score of R}=25+15=40$

P scored 12 points less than R:

$\text{Score of P}=40-12=28$

The person sitting two places away from R (position 6) is Q at position 4:

$6-2=4$

S scored a prime number of points, which is 7 points more than Q:

$\text{Score of S}=\text{Score of Q}+7$

Step 4: Calculate the total points of the executives at the extreme ends
The executives at the extreme ends of the row are S (position 1) and R (position 6).
Given R = 40, to get the total points of the extreme ends:

$\text{Score of S}+\text{Score of R}=29+40=69$

If S scored 29 points (which is a prime number), then Q scored 22 points (29 − 7 = 22), which perfectly satisfies all conditions.

Thus, the total score of the executives sitting at the extreme ends is 69.