In a group of 36 trainees, each trainee is ranked in a written test and in an interview, with no two trainees sharing a rank in either list. Aditi is 11th from the top in the written test and 15th from the bottom in the interview. Balraj is 7 ranks below Aditi in the written test and 4 ranks above Aditi in the interview.
Which of the following statements are correct?
(A) Balraj has the same rank from the top in both lists.
(B) Aditi’s interview rank from the top is 21st.
(C) In the written test, 18 trainees are ranked below Balraj.
(D) Balraj’s interview rank from the bottom is 19th.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A), (C) and (D) only
Turn every rank into a rank from the top first, using rank from the top = 36 − rank from the bottom + 1. A rank below means a larger number; a rank above means a smaller number.
Written test: Aditi is 11th from the top; Balraj is 7 ranks below: \(11+7=18\)th from the top
Interview: Aditi is \(36-15+1=22\)nd from the top; Balraj is 4 ranks above: \(22-4=18\)th from the top
Checking the statements
(A) Balraj has the same rank from the top in both lists. — Correct. Balraj is 18th from the top in the written test and also 18th from the top in the interview.
(B) Aditi’s interview rank from the top is 21st. — Incorrect. Being 15th from the bottom of 36, Aditi is \(36-15+1=22\)nd from the top, not 21st.
(C) In the written test, 18 trainees are ranked below Balraj. — Correct. Balraj is 18th from the top, so the trainees below him are \(36-18=18\).
(D) Balraj’s interview rank from the bottom is 19th. — Correct. Balraj is 18th from the top in the interview, so from the bottom he is \(36-18+1=19\)th.