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.

Four of the following five options share a common characteristic and thus form a group. Which of the following does not belong to that group?

The correct answer is S.

Step-by-step Explanation:

1. Understanding the Row Positions:
There are 6 executives: P, Q, R, S, T, and U sitting in a single row facing North. Let the positions be numbered 1 to 6 from left to right.

2. Determining the Positions of P, Q, and the 25-Point Scorer:
It is given that only two persons sit between P and the person who scored 25 points, and neither of them sits at the extreme ends of the row (positions 1 and 6). Therefore, P and the person who scored 25 points must occupy positions 2 and 5.

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 sits at position 2, there are 4 persons to the right of P (positions 3, 4, 5, and 6). Thus, there must be $4-1=3$ persons to the left of Q, which places Q at position 4.

Consequently, the person who scored 25 points is at position 5.

3. Determining the Position and Score of U:
U sits adjacent to Q, meaning U can be at position 3 or position 5. Since position 5 is occupied by the executive who scored 25 points, U must sit at position 3.

U sits second to the left of the person who scored 5 points less than U. The person sitting second to the right of U (at position 3) is at position 5, who scored 25 points.

Therefore:

$U-5=25$

$U=30$

So, U scored 30 points.

4. Determining the Positions and Scores of T, R, and P:
R sits to the immediate right of T. The only adjacent vacant positions available are positions 5 and 6. Thus, T is at position 5 and R is at position 6.

Since T is at position 5, T scored 25 points (which is a perfect square: $5^2=25$).

R scored 15 points more than T:

$R=25+15=40$

P scored 12 points less than R:

$P=40-12=28$

5. Placing S:
The only remaining executive, S, must occupy position 1 (the extreme left end of the row).

6. Final Seating Arrangement (Left to Right):
• Position 1: S (Extreme Left End)
• Position 2: P (28 points)
• Position 3: U (30 points)
• Position 4: Q
• Position 5: T (25 points)
• Position 6: R (40 points, Extreme Right End)

7. Identifying the Common Characteristic and Odd One Out:
Looking at the five options (U, P, T, Q, S):
• U, P, T, and Q all sit in middle (non-extreme) positions of the row.
• S is the only executive among the options who sits at an extreme end of the row (Position 1).

Thus, S does not belong to the group.