Interview Q&A / Aptitude

1. How many times in a day do the hands of a clock coincide, and how many times are they at right angles?

   They coincide 22 times in 24 hours (11 times every 12 hours, since the coincidence between 11 and 1 happens only once, at 12). They are at right angles 44 times a day and opposite each other 22 times.

   BeginnerQuick answer1 min read
2. What is the angle between the hour and minute hands of a clock at 3:40?

   130 degrees. The minute hand is at 40 x 6 = 240 degrees. The hour hand is at 3 x 30 + 40 x 0.5 = 110 degrees. The difference is 130 degrees (the reflex angle on the other side is 230).

   BeginnerQuick answer1 min read
3. At what time between 4 and 5 o'clock are the hands of a clock together?

   At 21 9/11 minutes past 4 (about 4:21:49). At 4:00 the minute hand is 120 degrees behind, and it gains 5.5 degrees a minute, so it catches up in 120/5.5 = 240/11 = 21 9/11 minutes.

   IntermediateQuick answer1 min read
4. The minute hand of a clock overtakes the hour hand every 64 minutes of correct time. How much does the clock gain or lose in a day?

   It gains 32 8/11 minutes a day. In a correct clock the hands meet every 65 5/11 minutes. Here they meet after only 64 real minutes, so the clock runs fast: it shows 65 5/11 minutes in 64 real minutes, gaining 16/11 minutes every 64 minutes, which is 360/11 = 32 8/11 minutes in 1,440 minutes.

   AdvancedQuick answer1 min read