What is The Angle Between the minute and the hour hand of the Clock Which Shows 12:24? GMAT Problem Solving

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

1. 115
2. 120
3. 124
4. 130
5. 132

Correct Answer: E

Solution and Explanation
Approach Solution 1:

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

The formula is: |112m−30h|

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

The above can be derived from the fact that:

In 1 minute:
The hour hand moves 0.5 degrees,
And the minute hand moves 6 degrees.

AND

In an hour:
The hour hand moves 30 degrees,
The minute hand moves 360 degrees.

For our original question:

12:24 →
h=0 (not 12) and m=24
→ |11/2m−30h|
=|11/2*24−30∗0|
=132

Hence, the correct answer is option E.

Approach Solution 2:

From the position of hands on 12:00 (both hands are vertical) hour hands moves
360/12∗60 =0.5 degrees in 1 minute

And minute hands move
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 the minute hand will move 24∗6=144 degrees from a vertical position.
So the angle between them will be:
144−12
=132 degrees.

Approach Solution 3:
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.

“What is the angle between the minute and the hour hand of the clock which shows 12:24?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "The Official Guide for GMAT Review". To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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