Question

On 16th July 2022, Parvathy bought 4 new pairs of socks A, B, C and D to train herself for the Marathon race on Gandhi Jayanti. She started her training next day wearing the new socks. She trained every day, including the day of the marathon, wearing the socks (one pair every day) in the following sequence: C, A, B and D. Unfortunately, she could not train from 3^rd to 22^nd September 2022 as she was unwell. She resumed her training on 23^rd wearing pair ‘A’ socks and continued with the same sequence till the event day. Identify the pair of socks that Parvathy wore the maximum during her entire training period.

• A. C
• B. A
• C. B
• D. D

Answer 1

The Correct Option is A, B

Parvathy followed a sequence for wearing the pairs of socks: C, A, B, D. She started this sequence on 17th July 2022. To solve the problem of which pair of socks she wore the most, calculate the number of days she trained wearing each pair until Gandhi Jayanti on 2nd October.

Here's the breakdown:

• Training began on 17th July 2022 and she followed the sequence: C, A, B, D. This part of the training lasted until 2nd September 2022, since she stopped training on 3rd September. From 17th July to 2nd September: 48 days of training.
• Days per sequence cycle: C gets day 1, A gets day 2, B gets day 3, and D gets day 4, repeated ad infinitum. So, every complete cycle consists of 4 days.
• Number of complete cycles (48 days total): 48/4 = 12 complete cycles.
• She resumes training on 23rd September and continues till 2nd October: Total days = 10.
• From 23rd September onwards, she continues with the sequence starting from 'A'.

Socks	Total Days Worn
C	12
A	13
B	12
D	11

Finally, adding the numbers, pairs 'A' and 'C' are both worn on 12 days until the break. After the break, pair 'A' is worn on additional cycle days, increasing its count. Therefore, the socks that she wore the maximum number of times during her training were 'C' and 'A'.