Directions: Read the following information carefully and answer the question.…
2020
Directions: Read the following information carefully and answer the question.
Twelve persons were born on one of two dates — either the 7th or the 16th — across six different months of a year, namely January, March, June, July, September and October, but not necessarily in that order.
Persons whose name starts with a letter before 'M' were born in the first half of the year; persons whose name starts with a letter after 'M' were born in the second half of the year (letters follow the English alphabet). Example: a person named Rajesh would be born in the second half of the year.
A person whose name has an even number of letters was born on an odd-numbered date, and vice versa. Example: 'Ramesh' has 6 letters (even), so that person was born on the 7th.
Only two persons were born between Pranav and Kumar. The number of persons born before Gaurav is the same as the number born after Yaati. Only four persons were born between Kunal and Gaurav. The number of persons born between Kunal and Sriti is one more than the number of persons born between Puja and Ram. Ayush was born before Kishan and Gopi. Puja was born in a month having 31 days. Not more than two persons were born between Kishan and Ram. Swathi is one of the persons.
Which of the following statements is/are true?
I. Gopi was born before Kishan.
II. Kunal was born in the month of March.
III. Three persons were born between Ayush and Kunal.
- A.
Both I and II
- B.
Only III
- C.
All I, II and III
- D.
Only II
- E.
Both I and III
Attempted by 2 students.
Show answer & explanation
Correct answer: E
Concept
This is a chronological scheduling puzzle. Twelve people occupy twelve fixed time slots — the 7th and 16th of six months (January, March, June, July, September, October). The governing rules first PLACE each person into a half-year and onto a date, then a chain of "between" and "before/after" clues pins the exact order. The method is: (1) translate each fixed rule into the set of slots a person can occupy, (2) use the gap clues to lock relative distances, then (3) read the statements off the single completed table.
Fixed-placement rules (applied to every name)
Half-year by first letter: a name starting with a letter BEFORE 'M' goes to the first half (Jan, Mar, Jun); a name AFTER 'M' goes to the second half (Jul, Sep, Oct). This splits the twelve names into two groups of six — Kumar, Gaurav, Kunal, Ayush, Kishan, Gopi in the first half; Pranav, Yaati, Sriti, Puja, Ram, Swathi in the second half. (Note: P, R, S all come AFTER M, so Puja, Ram, Swathi are second-half — the group sizes are 6 and 6, with no contradiction.)
Date by letter count: an EVEN number of letters means the 7th (an odd date); an ODD number of letters means the 16th (an even date). So Gaurav(6), Puja(4), Kishan(6), Gopi(4), Pranav(6), Swathi(6) take the 7th; Kumar(5), Kunal(5), Ayush(5), Yaati(5), Sriti(5), Ram(3) take the 16th.
Locking the order with the gap clues
"Puja was born in a month having 31 days": among second-half months Jul/Sep/Oct, only Jul and Oct have 31 days, and Puja must be on a 7th — narrowing her to Jul-7 or Oct-7.
"Only four persons between Kunal and Gaurav" fixes their gap at exactly five slots apart; both are first-half, so the only fit is Gaurav at Jan-7 and Kunal at Jun-16.
"Persons before Gaurav = persons after Yaati": with Gaurav first overall (none before him), Yaati must be last overall (none after) — Yaati at Oct-16.
"Only two persons between Pranav and Kumar" (gap of three) with Kumar on a 16th first-half slot forces Kumar to Mar-16 and Pranav to Jul-7.
"Ayush before Kishan and Gopi", "between Kunal and Sriti is one more than between Puja and Ram", and "not more than two between Kishan and Ram" together leave exactly one consistent filling, giving the complete table below.
The unique arrangement
Slot | Person |
|---|---|
Jan 7 | Gaurav |
Jan 16 | Ayush |
Mar 7 | Gopi |
Mar 16 | Kumar |
Jun 7 | Kishan |
Jun 16 | Kunal |
Jul 7 | Pranav |
Jul 16 | Ram |
Sep 7 | Swathi |
Sep 16 | Sriti |
Oct 7 | Puja |
Oct 16 | Yaati |
Testing the three statements
I. Gopi before Kishan: Gopi sits at Mar-7 and Kishan at Jun-7, so Gopi is indeed earlier — TRUE.
II. Kunal in March: Kunal sits at Jun-16, not March — FALSE.
III. Three persons between Ayush and Kunal: Ayush at Jan-16 and Kunal at Jun-16 have Gopi, Kumar and Kishan between them — exactly three — TRUE.
Cross-check
Re-reading every clue against the table confirms all of them hold and that no other arrangement survives, so the table is unique. Statements I and III are true and II is false, so the true set is "Both I and III".