What is the measure of the acute angle formed by the hands of a clock at 4:20 a.m.?
The answer is 10 deg.... Can someone explain it how?
The answer is 10 deg.... Can someone explain it how?
Swati
Hi!leonswati wrote:What is the measure of the acute angle formed by the hands of a clock at 4:20 a.m.?
The answer is 10 deg.... Can someone explain it how?
You'd definitely benefit from drawing out a clock on this question (as you would on pretty much any geometry question). Sadly, computer-generating diagrams is not one of my strengths, so we'll just visualize.
Let's think about where the hands are at 4:20: the little hand is on the 4 (20 minutes after the hour) and the big hand is somewhere between the 4 and the 5 (since it's between 4 and 5 pm). If you had provided answer choices (please always provide choices in the future, since a LOT of GMAT strategies involve working the answers), we may already have enough info to answer, since:
360 degrees/12 hours = 30 degrees per hour
and if we know that the two hands are both between 4 and 5, we know the answer must be less than 30.
If there's more than one answer under 30, then we'd go one step further. 20 minutes is 1/3 of an hour, so the big hand will be 1/3 of the way between the 4 and the 5. Since one hour is 30 degrees, 1/3 of an hour is 10 degrees.
Therefore, with the little hand right on the 4 and the big hand 10 degrees away from the 4, the two hands are 10 degrees apart!
