QUESTION 16 Direction: Study the information given below and answer the question that follows.
Qualcomm technical mcq question, verified with a worked answer. Free to practise - no sign-up.
QUESTION 16
Direction: Study the information given below and answer the question that follows.
Four organizations P, Q, R and S rated five companies A, B, C, D and E on a scale of one to ten (All ratings are integer values). The higher the numerical value the better the rating. No organization gave any two companies the same rating. No company received the same rating from any two organizations. The total rating of a company is the sum of ratings from P, Q, R and S.
I. Further, it is also known that B was rated two by organization S. A was rated seven and nine by organizations P and R respectively.
II. Q rated A, C, D and E one, five, six and seven respectively. B received a rating of nine by organization Q.
III. Only one organization rated B less than five. P gave a rating of six to E which is the lowest rating given to any company by P. P gave D the highest rating of 10.
IV. The total rating of E is 16. The highest rating given to any company by S is five. C got the second highest total rating. A's total rating is less than 21.
Show answer & explanation
By systematically applying all constraints: E's total is 16 with P=6, Q=7 leaves R+S=3. Since S max is 5 and B got S=2, E must get R=2, S=1. A's total < 21 with P=7, Q=1, R=9 means S=3. Only S rated B < 5 (with 2), so P and R both ≥5. With P's constraints (lowest=6, highest=10), B from R must be 5 to satisfy all uniqueness and rating constraints across the matrix.
Step-by-step Derivation:
- E's ratings: P=6, Q=7, need R+S=3 → R=2, S=1 (since S max=5, B used S=2)
- A's ratings: P=7, Q=1, R=9, S=3 (gives total 20 < 21)
- P's ratings used: 7(A), 6(E), 10(D) → remaining 8,9 for B,C
- Only S < 5 for B, so P,R ≥ 5 for B
- Q rates B=9, S rates B=2
- With remaining values and uniqueness: R rates B=5
- Final: B's total = 8+9+5+2 = 24