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# At exactly what time past 7:00 will the minute and hour

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Math Expert
Joined: 02 Sep 2009
Posts: 44421
Re: At exactly what time past 7:00 will the minute and hour [#permalink]

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19 Sep 2017, 05:05
sinhap07 wrote:
Engr2012 wrote:
baharemustafa wrote:
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

5.5 is the angle between minute n hour, this is what I was taught...so shouldn't it be solve by dividing 90 with 5.5?

That would have been the case if your initial difference between the hour and the minute hand was = 0 degrees or in other words, both minute and hour hands were at the same location. But as per the question, you are asked for time AFTER 7:00. At 7:00, the angle between the hour and the minute hand is 210 degrees. you need to take this into account as well.

So in order for the difference to decrease to 90 degrees, the minute hand must eat away this difference of 210-90 = 120 degree at the rate of 5.5 degrees per minute ---> 120/5.5 = 21 9/11 minutes.

Thus, D is the correct answer.

Hope this helps.

P.S.: If what you are saying was correct, then you should have calculated 16 4/11 minutes and this is not present in the given options. This should have told you that you are making a mistake somewhere.

Hi
Why shouldnt I consider the initial distance between the hour and minute hand be 150 degrees?

The hands of the clock move so that 150 degree angle increases and 210 degree angle decreases, so that will be the angle which will be 90 degree.
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Re: At exactly what time past 7:00 will the minute and hour [#permalink]

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16 Oct 2017, 01:51
Bunuel karishma - Can we look at this question from an angle of relative change as at 7.00 PM the change in the angle would be 210 deg and to make it perpendicular post 7 PM as per the question stem the total relative change would be 300 (210+90).

Which can be derived as 300/360*11/2 which is the total change in the hourly and the minute hand of the clock.

If yes, i have solved the question as 300/360*11/2 which is coming at 55/12 and i am stuck here!

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Re: At exactly what time past 7:00 will the minute and hour [#permalink]

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16 Oct 2017, 04:32
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Expert's post
siddyj94 wrote:
Bunuel karishma - Can we look at this question from an angle of relative change as at 7.00 PM the change in the angle would be 210 deg and to make it perpendicular post 7 PM as per the question stem the total relative change would be 300 (210+90).

Which can be derived as 300/360*11/2 which is the total change in the hourly and the minute hand of the clock.

If yes, i have solved the question as 300/360*11/2 which is coming at 55/12 and i am stuck here!

Yes, you can. I have given the link to the relevant post on the previous page.
Here is what it says: the minute hand covers 11/2 degrees per minute relative to the hour hand.

Note that position of the hour hand and the minute hand at 7. The larger angle between them is 210 degrees which needs to be brought down to 90 degrees (Think why - the hour hand will barely move but the minute hand will need to cover most of the difference between them and when it is closer to the hour hand, at some time, angle between them will be 90 degrees)

Relative to the hour hand, the minute hand has to cover 210 - 90 = 120 degrees.

Time taken for that will be $$\frac{120}{(11/2)} = \frac{240}{11} = 21(\frac{9}{11})$$ mins

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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 11312 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Re: At exactly what time past 7:00 will the minute and hour [#permalink] ### Show Tags 06 Dec 2017, 14:05 Hi All, 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: [Reveal] Spoiler: D GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: At exactly what time past 7:00 will the minute and hour [#permalink]

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02 Mar 2018, 03:42
AkamaiBrah wrote:
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

Of course not as good as previous solutions, but may be helpful.
If hour hand stands at 7, the minute hand has to stand at 4 (it is not possible, but approximately). So it will be 90% between them.
20 mins - it is 1/3 of the whole circle (20 of 60) ----> So the hour tand has to move 1/3 distance toward 8 ---->
-----> the minute hand has to move 1/3 distance toward 5 (1/3*5 = 5/3) -----> so we already have 20 + 5/3 = 21 and 2/3 mins (A, B, C are out) --->
----> since now minute hand has moved more than 1/3 distance toward 5, so the hour hand has moved a little more than 1/3 toward 8, so we have to add some more ---> it is D (E is too much)
Re: At exactly what time past 7:00 will the minute and hour   [#permalink] 02 Mar 2018, 03:42

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