The Minute Hand of a Clock Overtakes the Hour Hand at Intervals of 65 GMAT Problem Solving

Question: The minute hand of a clock overtakes the hour hand at intervals of 65 minutes of the correct time. How much a day (24Hours) does the clock gain or lose?

  1. 1440/143 Min
  2. 720/11 Min
  3. 5/11 Min
  4. 340/41 Min
  5. 511/11 Min


Correct Answer: A

Solution and Explanation
Approach Solution 1:

In a correct clock, the minute hand gains 55 min. spaces over the hour hand in 60 minutes.
To be together again, the minute hand must gain 60 minutes over the hour
hand.
55 min. are gained in 60 min.
60 min are gained in (60/55) x 60 min =720/11 min.
But, they are together after 65 min.
Gain in 65 min =(720/11)-65 =5/11min.
Gain in 24 hours =(5/11 * (60*24)/65)min =1440/143
The clock gains 1440/143 minutes in 24 hours.

Approach Solution 2:
In 12 hours hour clock covers 360 degree => 1 hour = 30 degree => 60 min = 30 degree
=> hour clock covers 1/2 degree in 1 minute.

the minute clock covers 360 degree in 6 minutes => 6 degree in 1 minute

=> relative time between them = 6 -1/2 = 11/2 minute.

Time taken by their relative distance to be zero = 11/2 * 360 degree = 720/11

but it is taking 65 minutes.

thus time gained = 720/11 - 65 = (720-715)/11 = 5/11

But this time is gained in 65 minutes.
Time gained in 24 * 60 minutes = 5/11 * 1/65 *24*60
=1440/143
The clock gains 1440/143 minutes in 24 hours.

Approach Solution 3:
For a normal clock, time taken by minute hand to overtake the hour hand = 65 + 5/11 minutes.
Since for this clock, the minute hand takes only 65 minutes, the clock gains 5/11 minutes every 65 minutes.
Therefore, in 24 hours, the clock gains 1440/143 minutes.

“The minute hand of a clock overtakes the hour hand at intervals of 65”- is a topic of the GMAT Quantitative reasoning section of GMAT. 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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