Which among the following statement is false? Study the following information carefully and answer the questions given below:
Nine persons - P, Q, R, S, T, U, V, W and X are working in the company at different designations such as MD, CEO, CFO, CRO, COO, GM, DM, HR and TL but not necessarily in the same order. The designations are given in decreasing order, such that MD is the senior-most designation and TL is the junior-most designation.
X is four persons junior to Q who is senior to CRO. The number of persons senior to Q is one less than the number of persons junior to S. Only three persons are designated between S and T. P is two persons junior to T. The number of persons designated between P and U is one less than the number of persons designated between U and V who is senior to X. W is senior to R who is not TL.
Correct Answer :
R is immediately junior to X
Solution :
To determine which statement is false, let us first establish the step-by-step ranking of the nine designations from senior-most to junior-most:
1. MD (Senior-most)
2. CEO
3. CFO
4. CRO
5. COO
6. GM
7. DM
8. HR
9. TL (Junior-most)
Let us analyze the clues provided in the question:
1. Q and X: X is four designations junior to Q. Thus, if Q is at rank , then X is at rank .
2. Q's rank: Q is senior to CRO (rank 4), which means Q can only be at rank 1 (MD), 2 (CEO), or 3 (CFO). Correspondingly, X can be at rank 5, 6, or 7.
3. S's rank: The number of persons senior to Q is one less than the number of persons junior to S.
Simplifying this gives:
4. T's rank: There are exactly three persons between S and T, so:
5. P's rank: P is two persons junior to T, meaning:
Now, let us evaluate the possible cases:
Case 1: Q is at rank 1 (MD)
• X must be at rank 5 (COO).
• S must be at rank (HR).
• T must be at rank (CRO).
• P must be at rank (GM).
This leaves ranks 2, 3, 7, and 9 empty.
Case 2: Q is at rank 2 (CEO)
• X must be at rank 6 (GM).
• S must be at rank (DM).
• T must be at rank (CFO).
• P must be at rank (COO).
This leaves ranks 1, 4, 8, and 9 empty.
Case 3: Q is at rank 3 (CFO)
• X must be at rank 7 (DM).
• S must be at rank (GM).
• T must be at rank (CEO).
• P must be at rank (CRO).
This leaves ranks 1, 5, 8, and 9 empty.
Now let us apply the final clues: "The number of persons designated between P and U is one less than the number of persons designated between U and V who is senior to X. W is senior to R who is not TL."
Testing Case 2 (Q = 2, T = 3, P = 5, X = 6, S = 7):
• Since V is senior to X (6), V must be at rank 1 or 4.
• If V is at rank 4, and we place U at rank 9:
The number of persons between P (5) and U (9) is 3.
The number of persons between U (9) and V (4) is 4.
Since 3 is indeed one less than 4, this configuration satisfies the condition.
• This leaves ranks 1 and 8 for W and R. Since W is senior to R, W is at rank 1 (MD) and R is at rank 8 (HR).
• Since R is at rank 8, R is not TL (which is rank 9), satisfying all rules.
Thus, the final sequence of designations from senior-most (1) to junior-most (9) is:
1. W (MD)
2. Q (CEO)
3. T (CFO)
4. V (CRO)
5. P (COO)
6. X (GM)
7. S (DM)
8. R (HR)
9. U (TL)
Let us verify the statements against our final sequence:
• "U is junior to X": U is TL (9) and X is GM (6), which is true.
• "X is not designated as TL": X is GM (6), which is true.
• "R is immediately junior to X": R is HR (8), which is junior to S (7), not X (6). Thus, this statement is false.
• "T is senior to R": T is CFO (3) and R is HR (8), which is true.
Therefore, the false statement is "R is immediately junior to X".
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