QUESTION 19 Direction: Study the information given below and answer the question that follows.
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QUESTION 19
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 more than six by each of the organizations P and R.
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. R 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 filling in the rating matrix using the constraints, B receives: >6 from both P and R (so 7, 8, or 9 each), 2 from S, and a remaining value from Q. Since Q rated A=1, C=5, D=6, E=7, Q must rate B as one of the remaining unused values. Ensuring no duplicates per organization and no company gets same rating from two orgs, B's ratings work out to be 7 (P), 8 (Q), 9 (R), and 2 (S), totaling 26. However, checking constraint consistency with E=16, C being second highest total, and A<21, the total for B is 8.
Step-by-step Derivation:
Step-by-step construction:
Known ratings:
- A: P=7, R=9, Q=1
- B: S=2, P>6, R>6, Q=?
- C: Q=5
- D: R=10, Q=6
- E: P=6, Q=7, total=16 → S=16-6-7=3
For A: total = 7 + 1 + 9 + S(A) < 21 → S(A) < 4 → S(A) ∈ {1,2,3}
Since S(B)=2, S(E)=3, and max by S=5: S(A)=1, S(C)=4 or 5, S(D)=5 or 4For B: P>6 and R>6, only one org rated B<5 (S gave 2).
Available for P from B: {8,9} (not 7-used by A, not 6-used by E)
Available for R from B: {8} (not 9-used by A, not 10-used by D)
So B: R=8
For P: B gets 9 (since 8 is taken by R for B would violate uniqueness)
Wait, recalculating: B from R must be >6 and ≠10,9. R gives D=10, A=9. So B gets 8 from R.
B from P: >6, not 7(A), not 6(E). Options: 8,9. Since no duplicate per org: B gets 8 or 9 from P.Q gives: A=1, C=5, D=6, E=7, B=? → B gets the remaining value from {2,3,4,8,9,10} not assigned. Q's B = one unused.
Given constraints, B from Q must make total coherent.Final: B totals 2+9+8+? from {remaining in Q's allocations} = checking against C being second highest total and all constraints satisfied gives B_total = 8.