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clock problem...How to think and solve

This topic has 1 expert reply and 1 member reply
Mo2men Legendary Member Default Avatar
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clock problem...How to think and solve

Post Wed Sep 20, 2017 9:44 am
At exactly what time past 7:00 will the minute and hour hands of an accurate working clock be precisely perpendicular to each other for the first time ?

(A) 20 13/21 minutes past 7:00
(B) 20 13/17 minutes past 7:00
(C) 21 3/23 minutes past 7:00
(D) 21 9/11 minutes past 7:00
(E) 22 4/9 minutes past 7:00

Source: 800 Score
OA: D



Last edited by Mo2men on Wed Sep 20, 2017 10:32 am; edited 1 time in total

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Mo2men Legendary Member Default Avatar
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Post Wed Sep 20, 2017 10:26 am
Rich.C@EMPOWERgmat.com wrote:
Hi Mo2men,

To start, given the correct answer, the 5 answer choices should be ordered from 'least' to 'greatest', meaning that they should be:

a) 20 13/21 minutes past 7:00
b) 20 13/17 minutes past 7:00
c) 21 3/23 minutes past 7:00
d) 21 9/11 minutes past 7:00
e) 22 4/9 minutes past 7:00

When dealing with a clock face, there are several pieces of information to consider:
1) A clock face is 360 degrees, so each "hour mark" represents 30 degrees and each "minute mark" represents 6 degrees.
2) As the minute hand moves, the hour hand ALSO moves (a little). Over the course of 1 full hour of time, the minute hand will move 360 degrees and the hour hand will move 30 degrees.
3) For each MINUTE that the minute hand moves, the hour hand moves 0.5 DEGREES.

To find the first time AFTER 7:00 that the hour hand and minute hand are PERPENDICULAR (meaning that their positions are 90 degrees apart), you might find it useful to work in small increments. From the answer choices, we see that the correct answer has to be fairly close to 7:20, so we'll 'work up' to there:

At 7:00...
the minute hand is at 0 degrees
the hour hand is at 210 degrees

At 7:20...
the minute hand is at 120 degrees
the hour hand has moved to 210 + 10 = 220 degrees
So the arms are getting closer to where we want them to be, but they're not there yet (they're 100 degrees apart)...

At 7:21...
the minute hand is at 126 degrees
the hour hand has moved to 220 + 0.5 = 220.5 degrees
So the arms are getting closer to where we want them to be, but they're not there yet (now they're 94.5 degrees apart)...

At 7:22...
the minute hand is at 132 degrees
the hour hand has moved to 220.5 + 0.5 = 221 degrees
Here, the minute hand has 'overshot' just a little bit (now they're 89 degrees apart)... Thus, the correct answer has to be just a little 'earlier' than 7:22

Final Answer: D

GMAT assassins aren't born, they're made,
Rich
Insightful Smile

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Top Reply
Post Wed Sep 20, 2017 10:10 am
Hi Mo2men,

To start, given the correct answer, the 5 answer choices should be ordered from 'least' to 'greatest', meaning that they should be:

a) 20 13/21 minutes past 7:00
b) 20 13/17 minutes past 7:00
c) 21 3/23 minutes past 7:00
d) 21 9/11 minutes past 7:00
e) 22 4/9 minutes past 7:00

When dealing with a clock face, there are several pieces of information to consider:
1) A clock face is 360 degrees, so each "hour mark" represents 30 degrees and each "minute mark" represents 6 degrees.
2) As the minute hand moves, the hour hand ALSO moves (a little). Over the course of 1 full hour of time, the minute hand will move 360 degrees and the hour hand will move 30 degrees.
3) For each MINUTE that the minute hand moves, the hour hand moves 0.5 DEGREES.

To find the first time AFTER 7:00 that the hour hand and minute hand are PERPENDICULAR (meaning that their positions are 90 degrees apart), you might find it useful to work in small increments. From the answer choices, we see that the correct answer has to be fairly close to 7:20, so we'll 'work up' to there:

At 7:00...
the minute hand is at 0 degrees
the hour hand is at 210 degrees

At 7:20...
the minute hand is at 120 degrees
the hour hand has moved to 210 + 10 = 220 degrees
So the arms are getting closer to where we want them to be, but they're not there yet (they're 100 degrees apart)...

At 7:21...
the minute hand is at 126 degrees
the hour hand has moved to 220 + 0.5 = 220.5 degrees
So the arms are getting closer to where we want them to be, but they're not there yet (now they're 94.5 degrees apart)...

At 7:22...
the minute hand is at 132 degrees
the hour hand has moved to 220.5 + 0.5 = 221 degrees
Here, the minute hand has 'overshot' just a little bit (now they're 89 degrees apart)... Thus, the correct answer has to be just a little 'earlier' than 7:22

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

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