Directions (74-78): Study the information carefully and answer the questions given below.
Ten persons were born in five different months of the same year starting from August to December, but on two different dates, i.e., 10th and 15th. K was born in the month which has odd number of days. Six persons were born in between K and D who was born after K. D was not born in the last. Two persons were born between D and S. The number of persons born before S is same as the number of persons born after G. R was born on an even number date and the month which has even number of days. Five persons were born between R and F who was born in the same month as P. Z was born before V but after H.
H was born in which of the following month?
Correct Answer :
August
Solution :
The correct option is August.
Let us analyze the given information step-by-step to determine the order of birth of all ten persons.
1. Understanding the Time Frame & Structure:
The ten persons were born in five months: August, September, October, November, and December.
Each month has two dates: 10th and 15th.
The number of days in each month:
- August: 31 days (Odd)
- September: 30 days (Even)
- October: 31 days (Odd)
- November: 30 days (Even)
- December: 31 days (Odd)
The 10 possible positions in chronological order are:
1. August 10th
2. August 15th
3. September 10th
4. September 15th
5. October 10th
6. October 15th
7. November 10th
8. November 15th
9. December 10th
10. December 15th
2. Analyzing Clues for K and D:
- K was born in a month with an odd number of days (August, October, or December).
- Six persons were born between K and D, and D was born after K.
- D was not born last (position 10, December 15th).
If D cannot be at position 10, then D can be at position 8 or 9:
- If D is at position 9 (Dec 10), then counting 6 persons back puts K at position 2 (Aug 15). August has 31 days (odd), which satisfies the condition.
- If D is at position 8 (Nov 15), counting 6 persons back puts K at position 1 (Aug 10). August has 31 days (odd), which also satisfies the condition.
Let's check the position of S and G:
- Two persons were born between D and S.
- The number of persons born before S is the same as the number of persons born after G.
If D is at position 9 (Dec 10):
Two persons between D and S puts S at position 6 (Oct 15).
Number of persons before S = 5.
Therefore, the number of persons after G must also be 5, which means G is at position 5 (Oct 10).
If D were at position 8 (Nov 15):
Two persons between D and S would put S at position 5 (Oct 10).
Number of persons before S = 4, so G would be at position 6 (Oct 15).
3. Analyzing R, F, and P:
- R was born on an even-numbered date (10th) and in a month with an even number of days (September or November).
So R can be on Sept 10th (position 3) or Nov 10th (position 7).
- Five persons were born between R and F.
- F was born in the same month as P.
If R is on Nov 10th (position 7):
5 persons between R and F means F must be at position 1 (Aug 10th).
Since F was born in the same month as P, P must be at position 2 (Aug 15th).
However, we already established K is at position 2 (Aug 15th). This creates a conflict!
Therefore, R must be on Sept 10th (position 3).
5 persons between R and F puts F at position 9.
Wait, position 9 is occupied by D! But if R is at position 3 (Sept 10th), 5 persons between R and F means F is at position 9 (Dec 10th) or 3 + 5 + 1 = 9th position. Let's re-verify the counting:
Positions between 3 and 9: 4, 5, 6, 7, 8 (which is exactly 5 persons).
So F would be at position 9. But D is at position 9!
Let's re-evaluate D at position 8 (Nov 15th) and K at position 1 (Aug 10th):
- K = Position 1 (Aug 10th)
- 6 persons between K and D (Positions 2, 3, 4, 5, 6, 7)
- D = Position 8 (Nov 15th)
- 2 persons between D and S: S = Position 5 (Oct 10th)
- Number of persons before S = 4, so number of persons after G = 4 => G = Position 6 (Oct 15th)
- R is on an even date (10th) and even month (Sept or Nov): R can be at position 3 (Sept 10th) or position 7 (Nov 10th).
If R = Position 3 (Sept 10th): 5 persons between R and F (Positions 4, 5, 6, 7, 8) puts F at Position 9 (Dec 10th).
Since F and P were born in the same month, P must be at Position 10 (Dec 15th).
Now let's check remaining spots for H, Z, V:
Remaining positions available: Position 2 (Aug 15th), Position 4 (Sept 15th), Position 7 (Nov 10th).
- Z was born before V but after H (H ... Z ... V).
So:
- H = Position 2 (Aug 15th)
- Z = Position 4 (Sept 15th)
- V = Position 7 (Nov 10th)
4. Final Complete Arrangement:
1. August 10th: K
2. August 15th: H
3. September 10th: R
4. September 15th: Z
5. October 10th: S
6. October 15th: G
7. November 10th: V
8. November 15th: D
9. December 10th: F
10. December 15th: P
Therefore, H was born in the month of August (specifically August 15th).
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