Directions (91-95): Study the following information carefully and answer the questions given below:
Seven persons ( A-G) work in the same organization on seven different designations (MD, CEO, SR. MGR, MGR, PO, Clerk and Typist ) but not necessarily in the same order. The designations are in the decreasing order such that MD is the senior-most position and Typist is the junior-most position.
The numbers of persons senior to A is same as the numbers of persons junior to A. B is junior to A and just senior to C. E is junior to A. The numbers of persons junior to C is same as the numbers of persons designated between B and D. At most one person between G and F. F is not the senior most.
How many persons designated between D and C?
Correct Answer :
Two
Solution :
To find the number of persons designated between D and C, let us analyze the given information step-by-step to determine the order of designations.
The designations in decreasing order of seniority (from senior-most to junior-most) are:
1. MD (Senior-most)
2. CEO
3. SR. MGR
4. MGR
5. PO
6. Clerk
7. Typist (Junior-most)
Let's represent the designations with numbers 1 to 7, where 1 is MD and 7 is Typist.
Step 1: Determine the position of A.
The number of persons senior to A is the same as the number of persons junior to A. Since there are 7 positions, the middle position (4th position) must be occupied by A.
Therefore, A is the Manager (MGR).
Step 2: Determine the positions of B and C.
B is junior to A and just senior to C. Since A is at position 4, B and C must occupy positions junior to 4 (i.e., among 5, 6, and 7).
Since B is just senior to C, they must occupy consecutive positions. The available consecutive positions junior to A are:
Case 1: B is at position 5 (PO) and C is at position 6 (Clerk).
Case 2: B is at position 6 (Clerk) and C is at position 7 (Typist).
Step 3: Analyze the condition: "The number of persons junior to C is same as the number of persons designated between B and D."
Let's test Case 1:
- A is at 4.
- B is at 5, C is at 6.
- The number of persons junior to C (at position 6) is 1 (which is the person at position 7, Typist).
- Therefore, the number of persons between B (at 5) and D must also be 1.
- Since the number of persons between B and D is 1, D could be at position 3 (SR. MGR) or position 7 (Typist). Let's check both possibilities:
Subcase 1a: D is at 3.
The arrangement so far: _ (1), _ (2), D (3), A (4), B (5), C (6), _ (7).
We are told: "E is junior to A". The positions junior to A (4) are 5, 6, and 7. Since B is at 5 and C is at 6, E must be at position 7 (Typist).
This leaves positions 1 and 2 for F and G.
We are given: "F is not the senior most." So F cannot be at position 1. Therefore, F must be at position 2 (CEO), and G must be at position 1 (MD).
The final arrangement for Subcase 1a is:
1. MD - G
2. CEO - F
3. SR. MGR - D
4. MGR - A
5. PO - B
6. Clerk - C
7. Typist - E
Let us check the remaining condition: "At most one person between G and F."
In Subcase 1a, G is at 1 and F is at 2. The number of persons between them is 0, which satisfies "at most one person between G and F". All conditions are perfectly satisfied.
Let's verify Case 2 just to be sure:
- A is at 4.
- B is at 6, C is at 7.
- The number of persons junior to C (at 7) is 0.
- Therefore, the number of persons between B (at 6) and D must be 0, which means D must be adjacent to B (at position 5).
- The arrangement so far: _ (1), _ (2), _ (3), A (4), D (5), B (6), C (7).
- Since E is junior to A, E must occupy one of the positions 5, 6, or 7. But these are already occupied by D, B, and C. Thus, Case 2 is invalid.
Conclusion:
The correct designations of the seven persons are:
MD - G
CEO - F
SR. MGR - D
MGR - A
PO - B
Clerk - C
Typist - E
Now, let's find the number of persons designated between D and C:
D is at position 3 (SR. MGR) and C is at position 6 (Clerk).
The persons designated between them are A (position 4) and B (position 5).
Thus, there are exactly 2 persons designated between D and C.
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