How often between 11 O'clock and 12 O'clock are the hands of the clock

Question

How often between 11 O'clock and 12 O'clock are the hands of the clock together at an integral number value?

(1) 55
 (2) 56
 (3) 4
 (4) 5

GyanOne · Answer

Lets take up the challenge! As it turns out, the answer is  really  simple, and can even be done just mentally.

The assumption here is that 11'o clock is not included, and 12'o clock is included.

For both the hands to be at integral values, the hour hand must take integral values, and for these values, the minute hand HAS to be at integral values. This is because for the hour hand to move an integral value (from 11 to one tick past 11), the minute hand must move 12 times the movement of the hour hand. For example, (talking in terms of the minute markings on the clock face now) if the hour hand moves from 55 to 56, the minute hand will move from 60 (or 0) to 12.

The hour hand can move from 55 to 56,57,58,59,and finally 60 (when it will be 12'o clock). At these times, the minute hand will respectively be at 12,24,36,48,and 60.

Therefore there are five such values. The answer is (D).

gladvijay · Answer

I cant seem to agree with this assumption .. the question doesnt specify whether 11:00 and 12:00 are included or not, in this case I would assume both to be included OR both to be excluded..

the clock hands will be on integral numbers at 11:00; 11:12; 11:24; 11:36; 11:48; 12:00 => 6 values..

if both 11:00 and 12:00 are included .. then 6 values
if both are not included then.. 4 values..

I will go with (3) 4 values as the answer..

NanditaParmar · Answer

Answer - 5 times. At 56th, 57th, 58th, 59th and 60th minute.

griffith7 · Answer

Interesting question, but I am in agreement that the question does not adequately clarify whether 11:00 and 12:00 are included or not. My understanding is that the GMAT is supposed to clarify this with inclusivity language. "Between" 11 and 12, without stating that 11:00 and 12:00 are explicitly to be included (in this case only one being included is contemplated in the answer), could very plausibly indicate that neither are to be included, which would render the answer 4 (C).

12:00 is "between" 11 and 12 while 11:00 is not similarly "between" 11 and 12?

12:00 is "between" 11 and 12 while 11:00 is not similarly "between" 11 and 12?

How often between 11 O'clock and 12 O'clock are the hands of the clock

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How often between 11 O'clock and 12 O'clock are the hands of the clock

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