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

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At exactly what time past 7:00 will the minute and hour [#permalink] New post 11 Jul 2003, 18:41
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A
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D
E

Difficulty:

  75% (hard)

Question Stats:

59% (03:18) correct 41% (03:19) wrong based on 212 sessions
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
[Reveal] Spoiler: OA

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AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

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Re: At exactly what time past 7:00 will the minute and hour [#permalink] New post 11 Jul 2003, 20:54
Is it D? My Guesstimate after spending 21 minutes !
Hope GMAT is not this tough :roll:
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Re: At exactly what time past 7:00 will the minute and hour [#permalink] New post 11 Jul 2003, 21:06
Sorry. Guessing not allowed. Show me how you solved it.

(It is NOT that hard if you take the right approach).

Motto: Spoonfed knowledge is not well retained, but knowledge worked hard for will be cherished for a long time....
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AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

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Re: At exactly what time past 7:00 will the minute and hour [#permalink] New post 11 Jul 2003, 22:36
Dear AkamaiBrah,

Thank you for not only posting such a nice questions, but also soving
the tough ones. Wish I had a teahcer like you when I was in school.

Here is my ans: D

A1 = hour angle
A2 = minute angle
A1-A2 = 90
Assume the minutes = M
A1 = (7*60+M)/12*60 )*360
A2 = M*360/60

Solving all three equation , results in the answer D
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Re: At exactly what time past 7:00 will the minute and hour [#permalink] New post 11 Jul 2003, 22:38
BTW:

Which one is correct? "Such a nice questions" or "Such nice questions" or "Such a nice question"
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Re: At exactly what time past 7:00 will the minute and hour [#permalink] New post 11 Jul 2003, 23:04
210 + M/12 - M = 90

Let M be the degrees covered by minute hand from zero. (7:00 pm is the reference point)
initially difference is 210 deg. Hour hand will move at the rate of M/12, so after M minutes hour hand will be at 210+M/12 and minute hand will be at M. The difference should be 90. Find M and divide by 6, which will give you the minutes.

Answer comes out to D
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Re: At exactly what time past 7:00 will the minute and hour [#permalink] New post 12 Jul 2003, 03:56
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OKies my idea of solution,

I found it the fastest way,

Speed of hour hand/min = 360/12*60 = 1/2.

Speed of minuted hand/min = 360/60 = 6.

Relative speed = 11/2 degrees/min

Now at 7 the two are 210 degrees apart.
From 210 degress to 90 degrees. Minute has to gain 120 over the hour hand.

So time required will be = 120/Relative speed = 120*2/11 = 21 9/11 = D
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Re: At exactly what time past 7:00 will the minute and hour [#permalink] New post 12 Jul 2003, 07:49
The answer is D. Evensflow did it the fastest although all of the solutions were fine. The key is computing the rate of each hand and solving for when they are 90 deg apart.

Good job all.
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AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
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MFE, Haas School of Business, UC Berkeley, Class of 2005
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At exactly what time past 7:00 will the minute and hour [#permalink] New post 03 Sep 2014, 12:33
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At 7:00, hour hand must be at 210 degree from 12 (clock wise).
Minute hand of the clock moves with 6 degree per minute speed and hour hand moves at 1/2 degree per minute.
Therefore in x min hour hand will travel (1/2)*x degree further 210 degree from initial position; meanwhile minute hand must cover 6x degrees. Difference between minute and hour hand is required 90 degree. Formed following equation and solved for x.

\((\frac{1}{2}x + 210) - 6x = 90\)
Solve: x=240/11

Ans D.
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At exactly what time past 7:00 will the minute and hour [#permalink] New post 12 May 2015, 13:02
Anotehr way to solve this problem is to use the formula that we have for the angle of the clock needels.

\(angle of clock needels =\frac{(60H + 11M)}{2}\) where H is the hour and the M is the minutes.
We can imply that the H= 7 because the strating point is 7:00 any way and just need to find the M in the equation with making teh equation equal to 90 since that is what is being asked.
Do the math and you will see that \(M=21\frac{9}{11}\)

So not bad to learn the formula at beggiging I was struguling with teh question and trying to go figure out some other stuff, but than I remmeberd on this formula and applied it.

hope it helps
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Re: At exactly what time past 7:00 will the minute and hour [#permalink] New post 20 May 2015, 19:10
PiyushK wrote:
At 7:00, minute hand must be at 210 degree from 12 (clock wise).
Minute hand of the clock moves with 6 degree per minute speed and hour hand moves at 1/2 degree per minute.
Therefore in x min hour hand will travel (1/2)*x degree further 210 degree from initial position; meanwhile minute hand must cover 6x degrees. Difference between minute and hour hand is required 90 degree. Formed following equation and solved for x.

\((\frac{1}{2}x + 210) - 6x = 90\)
Solve: x=240/11

Ans D.



Thanks for the solution. This cleared up the confusions I had in my head, bigtime!
Re: At exactly what time past 7:00 will the minute and hour   [#permalink] 20 May 2015, 19:10
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