At what time between 4 and 5 o’clock in a 12-hour clock, the min hand

Question

At what time between 4 and 5 o’clock in a 12-hour clock, the min hand and hour hand of the clock will be at right angle for the second time?
  A. 4:38
B. 4:38 2/11
C. 4:37
D. 4:37 2/11
E. 4:39

Source: https://www.GMATinsight.com

Reference question:
https://gmatclub.com/forum/what-is-the- ... l#p2218494

Reference Concept Video:

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Official Answer

B

Archit3110 · Answer

we can determine the angle b/w hour and min hand by ; 
angle = 11/2 * min - 30 * hour
so angle is 90
min is our target value and hour is 4
solve for min
we get
90=11/2* x - 120
x= 38 2/11 
time at clock would be 4:38 2/11 option B

swaujas · Answer

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 90degree 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.

gracie · Answer

At what time between 4 and 5 o’clock in a 12-hour clock, the min hand and hour hand of the clock will be at right angle for the second time?
  A. 4:38 
B. 4:38 2/11 
C. 4:37 
D. 4:37 2/11 
E. 4:39

let m=location of minute hand
m-(20+m/12)=15→
m=38 2/11 minutes
4:38 2/11
B

GMATinsight · Answer

Change of angle between minute and hour hand = 6-(!/2) = 11/2º

At 4 PM the angle between hands = 30*4 = 120º

Fincal angle needed = 90º

Change of angle needed = 120 + 90 = 210º (First the existing 120º will become zero and then we see the increase of 90º)

11/2º is the change in 1 min
210 will be the change in (2/11)*210 = 38 2/11º

Time : 4:38 2/11

Answer: Option B

ScottTargetTestPrep · Answer

The first time between 4 and 5 o’clock that the minute hand and the hour hand form a right angle is around 4:05. We say “around 4:05” since it’s not exactly at 4:05. That is because the hour hand is moving slightly away from the number 4 on the clock when the minute hand is exactly pointing at the number 1 on the clock. However, we don’t need to know the exact time when the minute and hour hands form a right angle the first time since what we really need to determine is the exact time the second they form a right angle.

We can test the answer choices (keep in mind that there are 60 (minute) intervals on a circular clock, so each interval is 360/60 = 6 degrees and there are 12 numbers on the clock, so each pair of consecutive numbers is separated by 360/12 = 30 degrees).

A. 4:38

At 4:38, the minute hand sweeps 6 x 38 = 228 degrees (counting from the number 12 on the clock) while the hour hand sweeps 30 x 4 + 30 x 38/60 = 120 + 19 = 139 degrees (again, counting from the number 12 on the clock). Therefore, at 4:38, the two hands of the clock form an angle of 228 - 139 = 89 degrees.

Since 90 > 89 and the minute hand moves faster than the hour hand, the exact time when they form a right angle should be greater than 4:38, so the correct answer is either B or E. Let’s test choice E first (since it’s easier and if it’s not the correct answer, then choice B must be the correct answer).

E. 4:39

At 4:39, the minute hand sweeps 6 x 39 = 234 degrees (counting from the number 12 on the clock) while the hour hand sweeps 30 x 4 + 30 x 39/60 = 120 + 19.5 = 139.5 degrees (again, counting from the number 12 on the clock). Therefore, at 4:39, the two hands of the clock form an angle of 234 - 139.5 = 94.5 degrees.

We see that this is more than 90 degrees, so the correct time must be between 4:38 and 4:39 and it will be closer to 4:38 than it is to 4:39 since 89 degrees is closer to 90 degrees than 94.5 degrees. So choice B, or 4:38 2/11, must be the correct answer.

Answer: B

bumpbot · Answer

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At what time between 4 and 5 o’clock in a 12-hour clock, the min hand

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