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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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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

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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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 [#permalink] New post 11 Jul 2003, 20:54
Is it D? My Guesstimate after spending 21 minutes !
Hope GMAT is not this tough :roll:
GMAT Instructor
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Joined: 07 Jul 2003
Posts: 771
Location: New York NY 10024
Schools: Haas, MFE; Anderson, MBA; USC, MSEE
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GMAT Tests User
 [#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....

_________________

Best,

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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 [#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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 [#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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 [#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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 [#permalink] New post 12 Jul 2003, 03:56
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
GMAT Instructor
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Joined: 07 Jul 2003
Posts: 771
Location: New York NY 10024
Schools: Haas, MFE; Anderson, MBA; USC, MSEE
Followers: 9

Kudos [?]: 23 [0], given: 0

GMAT Tests User
 [#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.

_________________

Best,

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

  [#permalink] 12 Jul 2003, 07:49
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At exactly what time past 7:00 will the minute and hour

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