At What Time between 4 and 5’o clock, the Min Hand GMAT Problem Solving

Question: At what time between 4 and 5’o clock, the min hand and hour hand of the clock will be the right angle for the second time?

1. 4 : 38
2. 4 : 38 2/11
3. 4 : 37
4. 4 : 37 2/11
5. 4 : 39

Answer:
Approach Solution (1):
We can determine the angle b/w hour and minute hand by:
Angle = 11/2 * minute – 30 * hour
So angle is 90
Minute is our target value and hour is 4
Solve for minute
We get:
90 = 11 / 2 * x – 120
x = 38 2/11
Time at clock would be 4 : 38 2/11
Correct option: B

Approach Solution (2):
The relative speed of Minute hand w.r.t Hour hand is 11/2 degrees/min.
Let's start at 4:00PM. Initially they have a 120degree difference between them.
The time taken by the minute hand to have zero degree difference with hour hand (i.e. just overtake the Hour Hand) is 120*2/11=240/11 mins.
Note that by this time, before overtaking, the minute hand has already made a 90 degree with hour hand for the first time. After this point in time, we just need another 90 degrees difference. So that takes 90*2/11=180/11 mins.
So total time is (180+240)/11 mins, i.e. 38,2/11 mins
Correct option: B

Approach Solution (3):
Change of the angle between minute and hour hand = 6 – (1/2) = 11/2 degrees
At 4 PM the angle between hands = 30 * 4 = 120 degrees
Final angle needed = 90 degrees
Change of angle needed = 120 + 90 = 210 degrees (First the existing 120 degrees will become zero and then we see the increase the 90 degrees)}
11/2 degrees is the change in 1 minute
210 will be the change in {2/11} * 210 = 38 2/11 degrees
Time: 4 : 38 2/11
Correct option: B

“At what time between 4 and 5’o clock, the min hand and hour hand of the clock will be the right angle for the second time?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. 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.

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