A digital watch X beeps every 30 seconds while watch Y beeps every 32 seconds. They beeped together at 10 AM. The immediate next time that they will beep together is ________. A. 10:08 AM B. 10:10 AM C. 11:00 AM D. 10:10 PM

GATE 2021 · General Aptitude · Clock Time · medium

Answer: The watches next beep together at 10:08 AM. Answer: A. 10:08 AM.

1. Find GCD(30, 32): 30 = 2 x 3 x 5. 32 = 2^5. GCD(30, 32) = 2 (only common prime factor).
2. Compute LCM(30, 32): LCM(30, 32) = 30 x 32 / 2 = 960 / 2 = 480 seconds.
3. Convert to clock time: 480 / 60 = 8 minutes. Next simultaneous beep = 10:00 AM + 8 minutes = 10:08 AM.