Question: At 3:30 P.M. the angle between the hands of a clock is

(A) 90°
(B) 80°
(C) 75°
(D) 72°
(E) 65°

“At 3:30 P.M. the angle between the hands of a clock is”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GRE-GMAT Math Review: The Mathworks Program”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:
Approach Solution 1:
Angular speed of hour hand = 30° = 0.5 degree/minute
In 30 mins, the angle swept by an hour hand is 30*0.5 = 15 degree
At 3:30, the minute hand is at number 6.
At 3:30 the hour hand is at 3.
Now it has moved 15 degrees.
Hence the angle between the two is (90-15) = 75°

Correct Answer: C

Approach Solution 2:
We know that the hour hand of a clock completes one rotation in 12 hours.

Therefore, angle traced by the hour hand is 12 hours = 360 degree

Now,

Angle traced by the hour hand in 8 hrs 30 mins. i.e., 17/2 = (360/12* 17/2)= 255 degree

We also know that the minute hand of a clock completes one rotation in 60 minutes.

Therefore, angle traced by the minute hand in 60 minutes = 360 degree

Now,

Angle traced by the minute hand in 30 mins = (360/60*30 degree)= 180 degree
Therefore, required angle between two hands of the clock = 255-180= 75°

Correct Answer: C

Approach Solution 3:
Formula:

The angle between hours and minutes hands (h hours and m minutes) is |30∗h−11∗m/2|

|30∗3−11∗30/2| = |−75| = 75°

Correct Answer: C

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