What is the angle between the minute and the hour hand of the clock wh

Question

What is the angle between the minute and the hour hand of the clock which shows 12:24?

A. 115
B. 120
C. 124
D. 130
E. 132

M12-26

Bunuel · Accepted Answer

You just should substitute h=0 in it, not h=12.

General formula is:

|\frac{11}{2}m - 30h|

If the result is greater than 180 degrees, subtract it from 360 to get the included angle.

The above can be derived from the fact that:
In 1 minute:
Hour hand moves 0.5 degrees,
Minute hand moves 6 degrees.

AND

In an hour:
Hour hand moves 30 degrees,
Minute hand moves 360 degrees.

Hope it's clear.

Bunuel · Answer

From the position of hands on 12:00 (both hands are vertical) hour hands moves  \frac{360}{12*60}=0.5  degrees in 1 minute and minute hands moves  \frac{360}{60}=6  degrees in 1 minute.

Hence at 12:24, after 24 minutes from 12:00, when both hands are vertical, hour hand will move  24*0.5=12  degrees from the vertical position and minute hand will move  24*6=144  degrees from vertical position. So the angle between them will be  144-12=132  degrees.

Answer: E.

There is general formula for this, (though no need to memorize):

|\frac{11}{2}m - 30h|

If the result is greater than 180 degrees, subtract it from 360 to get the included angle.

The above can be derived from the fact that:
In 1 minute:
Hour hand moves 0.5 degrees,
Minute hand moves 6 degrees.

AND

In an hour:
Hour hand moves 30 degrees,
Minute hand moves 360 degrees.

For our original question:
12:24 -->  h=0  (not 12) and  m=24  -->  |\frac{11}{2}m - 30h|=|\frac{11}{2}24 - 30*0|=132

Answer: E.

Hope it's clear.

alpha_plus_gamma · Answer

At 12:24 
-minute hand will be at 24*6 = 144 degrees from position of 12.
- Hour hand will move by 2*6 = 12 degree during the same time

So the difference between the two hands will be 144-12 = 132 degrees.

gameCode · Answer

hour hand moves 5 minutes when minute hand moves 60 minutes. Hence when minute hand moved 24 minutes, hour hand moved 24 *5 / 60 i.e. 2 minutes.

alpha_plus_gamma · Answer

yeah, exactly in the way provided by gameCode

KocharRohit · Answer

I read somewhere there is a direct formula to solve this question..2) 
Angle between m and h hand is ( 11/2) *m – 30 * h
 can this be apply here? if yes should i take the value of h =12 ..taking this I am not getting the answer..
Please suggest

b2bt · Answer

such questions are asked on GMAT? I have never encountered this type in OG, gmatprep or any other test prep material

Bunuel · Answer

What is the angle between the minute and the hour hand of the clock which shows 12:24?

A. 115
B. 120
C. 124
D. 130
E. 132
 
From the position of hands on 12:00 (both hands are vertical) hour hand moves  \frac{360}{12*60}=0.5  degrees in 1 minute and minute hand moves  \frac{360}{60}=6  degrees in 1 minute.
 
Hence at 12:24, after 24 minutes from 12:00, when both hands are vertical, hour hand will move  24*0.5=12  degrees from the vertical position and minute hand will move  24*6=144  degrees from vertical position.
 
So the angle between them will be  144-12=132  degrees.

Answer: E

Manonamission · Answer

This Q reminds me of good old school days.

Formula for included angle between minute hand and a hour hand = 11/2m - 30h

Since the hour hand is at 12 , we have h =0

Putting the values in formula above

11/2 * 24 - 0 = 132 Option E

gracie · Answer

What is the angle between the minute and the hour hand of the clock which shows 12:24?

A. 115
B. 120
C. 124
D. 130
E. 132

24-(0+24/12)=22
22*6°=132°

WilDThiNg · Answer

Please can anyone elaborate on when to assign positive and negative signs when opening the modulus in the general formula given above?

Thanks

Bunuel · Answer

You should take the absolute value of  \frac{11}{2}m - 30h , so if  \frac{11}{2}m - 30h  is negative you should make it positive.

WilDThiNg · Answer

thanks for clarifying

gracie · Answer

24-(24/12)=22 minutes difference
22*6=132°
E

rsmalan · Answer

Hi Ritula

Good question here. Doubt if one should expect this kind of question in GMAT.

Nevertheless, lets try to solve this question.

Degrees of movement by minute hand in 24 minutes:
 \frac{24}{60}  x 360
= 144 degrees

Given that hour hand moves 30 degrees in 60 minutes,
Degrees of movement by hour hand in 24 minutes:
 \frac{24}{60}  x 30
= 12

Thus angle between hour and minute hand = 144 - 12
=132 degrees

Answer (E)

Is there anything you would like me to clarify further?
All the best!!!

CEdward · Answer

I like this question.

24 minutes / 60 minutes = 2/5 ---> 2/5 x 360 = 144 ---> 144/360 is the amount of rotation that the minute hand has accomplished

360/12 = 30 degrees <--- This is the amount of degrees that each hour takes up in the circle.

2/5 x 30 = 12 <---This is the amount of rotation that the hour hand has finished

144 - 12 = 132

Answer is E.

Bambi2021 · Answer

Minute moves 24/60 = 4/10 
Hour moves 4/10 * 1/12 = 4/120

48/120 - 4/120 = 44/120

44/120 * 360 = 44*3*120 / 120 = 132

Posted from my mobile device

CrackverbalGMAT · Answer

Solution: 
In 1 hour ( 60 mins), A minute hand covers 360°
i.e minute hand moves 6 ° in every 1 minute

Similarly, in 12 hours, the hour hand moves 360°
==> in 1 hour , hour hand moves 360/12 = 30 °
i.e in 1 minute, the hour hand will move 30/60 = 1/2 °
 
At 12:24, 24 minutes past 12.
in 24 mins, the minute hand moves 24* 6 = 144 °
The hour hand will move 24*1/2 = 12° in 24 mins

So the angle between the minute and the hour hand of the clock will be 144- 12 = 132 °
 Option E is the answer.

Thanks,
Clifin J Francis
GMAT SME

bumpbot · Answer

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What is the angle between the minute and the hour hand of the clock wh

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