It is currently 22 Jun 2017, 07:48

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# In a circular clock, the long hand is the radius of the circ

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Manager
Joined: 16 May 2011
Posts: 204
Concentration: Finance, Real Estate
GMAT Date: 12-27-2011
WE: Law (Law)
In a circular clock, the long hand is the radius of the circ [#permalink]

### Show Tags

06 Jul 2011, 12:46
5
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

47% (02:17) correct 53% (01:16) wrong based on 84 sessions

### HideShow timer Statistics

In a circular clock, the long hand is the radius of the circle. At what time is the smaller angle between the hands of the clock NOT divisible by 15?

I 7:20
II 9:00
III 4:30

(A) Only I
(B) Only III
(C) I + II
(D) II+III
(E) I+II+III
[Reveal] Spoiler: OA
Manager
Joined: 29 Jun 2011
Posts: 76
Re: Clock hands [#permalink]

### Show Tags

06 Jul 2011, 13:13
1
This post received
KUDOS
Moderators : help needed here

as you can see from the diagram every division 12-1, 1-2, 2-3 etc etc makes a sector angle of 30 deg.
this can be mathematically achieved by = total central angle in the circle/total number of sector divisions = 360/12 =30 (because clock divisions make 12 sectors in the clock)

now see :
I says 7:20
so here one hand points at 7 and the other at 20 (ie 4). Now count number of divisions from 7 to 4. div = 3
convert div to angle. each div = 30 deg so div(from 7 to 4) = 3*30 = 90 which is divisible by 15

II says : 9:00 ie angle made between 9 and 00(or 12) which is 3 divisions = 3*30 =90 divisible by 15

III says : 430 ie 2 divisions ie 60deg = divisible by 15

so IMO the options provided are debatable. please check and confirm.

whats the OE and OA?
Attachments

File comment: clock angles.

15deg3.jpg [ 39.48 KiB | Viewed 11600 times ]

_________________

It matters not how strait the gate,
How charged with punishments the scroll,
I am the master of my fate :
I am the captain of my soul.
~ William Ernest Henley

Manager
Joined: 07 Jun 2011
Posts: 73
Re: Clock hands [#permalink]

### Show Tags

06 Jul 2011, 17:23
2
This post received
KUDOS
in one minute hand take a 360 Degree circle and the hour hand take a 30 degree circle

For the hour hand 30 degree movement is accomplished in 1 hour,(60 Min) so in one minute 30/60 = .5 degree (hour hand travels that much in one minute)
The minute hand accomplish 6 degree rotation in one minute

No to the problem at 7.20

Position of hour hand from 12(0 degree) is = 30*7 + 20*.5 = 210 + 10 = 220

Position of minute hand is 20*6 = 120 degrees from 12(0 degree)

the difference in angles is 100 degrees Not divisible by 15...

Employing the same priciple on the rest I get answer A
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2010
Re: Clock hands [#permalink]

### Show Tags

06 Jul 2011, 18:04
fivedaysleft wrote:
Moderators : help needed here

as you can see from the diagram every division 12-1, 1-2, 2-3 etc etc makes a sector angle of 30 deg.
this can be mathematically achieved by = total central angle in the circle/total number of sector divisions = 360/12 =30 (because clock divisions make 12 sectors in the clock)

now see :
I says 7:20
so here one hand points at 7 and the other at 20 (ie 4). Now count number of divisions from 7 to 4. div = 3
convert div to angle. each div = 30 deg so div(from 7 to 4) = 3*30 = 90 which is divisible by 15

II says : 9:00 ie angle made between 9 and 00(or 12) which is 3 divisions = 3*30 =90 divisible by 15

III says : 430 ie 2 divisions ie 60deg = divisible by 15

so IMO the options provided are debatable. please check and confirm.

whats the OE and OA?

manishgeorge already answered.

7:20 means smaller hand also moved (30*4/360)*30= 10 deg; So angle between hands= 30*3+10=100
_________________
Intern
Joined: 14 Mar 2010
Posts: 16
Re: Clock hands [#permalink]

### Show Tags

28 Jul 2011, 08:15
2
This post received
KUDOS
Formula for angle between Hour ( H) and minute ( m ) hand is

(60H-11m)/2

using this : 7.20 ->60*7 -11*20 /2 = 100 not divisible by 15
9:00 -> 180 divisible by 15
4:30 -> 105 divisible by 15

SO answer is A

br,
Binu
Intern
Joined: 27 Feb 2011
Posts: 48
Re: Clock hands [#permalink]

### Show Tags

28 Jul 2011, 13:22
7:20
1. Hours hand = 7* 30 + 1/3 (30) = 210 + 10 = 220
2. Mins hand = 4* 30 = 120

diff = 100 deg. NOT divisible by 15..

9:00 and 4:30 are pretty easy
Intern
Joined: 05 Oct 2010
Posts: 13
Re: Clock hands [#permalink]

### Show Tags

28 Jul 2011, 14:19
dimri10 wrote:
In a circular clock, the long hand is the radius of the circle. At what time is the smaller
angle between the hands of the clock NOT divisible by 15?
I 7:20
II 9:00
III 4:30
(A) Only I
(B) Only III
(C) I + II
(D) II+III
(E) I+II+III

I just do not get it!

The clock/circle has 360". Nowto figure out the SMALL angle between
hands of the clock I asigned a 30" value between the numbers on its face (360/12=30)
Now, at 7.20 one hand is on 7 and the other is on 4, thus, the small angle is 90" while the outside angle is 270". As follows, at 9.00 one hand is at nine while the other is on 12 - We have an angle formed by 3 intervals of 30". Small angle is 90".
In the last scenario, 4.30, One hand is at 4 and the other at 6 so the angle is 60. Everything divisible by 15...
Where do I go wrong
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7438
Location: Pune, India
Re: Clock hands [#permalink]

### Show Tags

28 Jul 2011, 21:20
5
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
katealpha wrote:
dimri10 wrote:
In a circular clock, the long hand is the radius of the circle. At what time is the smaller
angle between the hands of the clock NOT divisible by 15?
I 7:20
II 9:00
III 4:30
(A) Only I
(B) Only III
(C) I + II
(D) II+III
(E) I+II+III

I just do not get it!

The clock/circle has 360". Nowto figure out the SMALL angle between
hands of the clock I asigned a 30" value between the numbers on its face (360/12=30)
Now, at 7.20 one hand is on 7 and the other is on 4, thus, the small angle is 90" while the outside angle is 270". As follows, at 9.00 one hand is at nine while the other is on 12 - We have an angle formed by 3 intervals of 30". Small angle is 90".
In the last scenario, 4.30, One hand is at 4 and the other at 6 so the angle is 60. Everything divisible by 15...
Where do I go wrong

At 7:20, is the hour hand at 7 or a third between 7 and 8?
At 4:30, is the hour hand at 4 or mid way between 4 and 5?

You have to account for the little bit of distance covered by the hour hand too.
Employ Relative Speed here.
Minute hand covers 360 degrees in an hour.
Hour hand covers 360/12 = 30 degrees in an hour.
Speed of minute hand relative to hour hand is 360 - 30 = 330 degrees per hour.

At 7 o clock, the minute hand is 210 degrees behind the hour hand. In 20 minutes (at 7:20), it makes up 330/3 = 110 degrees. Now it will be 100 degrees behind the hour hand. The smaller angle between them is 100 degrees.

At 4 o clock, the minute hand is 120 degrees behind the hour hand. In half an hour, it covers 330/2 = 165 degrees to get 45 degrees ahead of the hour hand. The smaller angle between them is 45 degrees.

At 9 o clock, the angle between the two hands is 90 degrees.

(Such clock questions are applications of Relative Speed. Do you remember 'A cop is running after a crook at a speed of ... Initial distance between them is ... When will he catch up?' kind of questions? The principle employed is exactly the same here.)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Status: On... Joined: 16 Jan 2011 Posts: 188 Re: Clock hands [#permalink] ### Show Tags 30 Jul 2011, 19:31 @Karishma +1 Kudos Loved the approach. Yes it is a relative speed problem and I like your way to approach the problem. Do post any variant of the question popping up because I am too lazy to create a variant. _________________ Labor cost for typing this post >= Labor cost for pushing the Kudos Button http://gmatclub.com/forum/kudos-what-are-they-and-why-we-have-them-94812.html Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7438 Location: Pune, India Re: Clock hands [#permalink] ### Show Tags 01 Aug 2011, 02:30 krishp84 wrote: @Karishma +1 Kudos Loved the approach. Yes it is a relative speed problem and I like your way to approach the problem. Do post any variant of the question popping up because I am too lazy to create a variant. Another type of clock questions that I have come across: Mr. A leaves his house between 3 and 4 pm and notices that the angle between the hour and minute hands is x degrees. He returns between 6 and 7 pm same day and notices that the angle is again x degrees. For how much time was Mr A away from home? (The value of x is given. Try putting different values (180 degrees, 170 degrees, 45 degrees etc) and you can make PS/DS questions) _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Manager
Status: On...
Joined: 16 Jan 2011
Posts: 188
Re: Clock hands [#permalink]

### Show Tags

01 Aug 2011, 17:19
VeritasPrepKarishma wrote:
Another type of clock questions that I have come across:
Mr. A leaves his house between 3 and 4 pm and notices that the angle between the hour and minute hands is x degrees. He returns between 6 and 7 pm same day and notices that the angle is again x degrees. For how much time was Mr A away from home? (The value of x is given. Try putting different values (180 degrees, 170 degrees, 45 degrees etc) and you can make PS/DS questions)

Is the answer 3 hours 18 mns ?

okay - My thought process....
Distance between Hour hand and Minute hand between 3 and 4 PM is x degree - So Time will be 3:y, where y is the distance of the minute hand from 12 position

Distance between Hour hand and Minute hand between 6 and 7 PM is x degree - So Time will be 6:z, where z is the distance of the minute hand from 12 position

y = ()+x
z = ()+x+30*3

So the difference between 6:z and 3:y is (6-3) hours + 30*3/5 minute (Minute hand covers 30 degree in 5 minutes)
= 3 hours 18minutes....

PS - I did not substitute, But I will definitely substitute the answer choices to confirm.

Do let me know your thoughts.....
_________________

Labor cost for typing this post >= Labor cost for pushing the Kudos Button
http://gmatclub.com/forum/kudos-what-are-they-and-why-we-have-them-94812.html

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7438
Location: Pune, India
Re: Clock hands [#permalink]

### Show Tags

01 Aug 2011, 22:24
krishp84 wrote:
VeritasPrepKarishma wrote:
Another type of clock questions that I have come across:
Mr. A leaves his house between 3 and 4 pm and notices that the angle between the hour and minute hands is x degrees. He returns between 6 and 7 pm same day and notices that the angle is again x degrees. For how much time was Mr A away from home? (The value of x is given. Try putting different values (180 degrees, 170 degrees, 45 degrees etc) and you can make PS/DS questions)

Is the answer 3 hours 18 mns ?

okay - My thought process....
Distance between Hour hand and Minute hand between 3 and 4 PM is x degree - So Time will be 3:y, where y is the distance of the minute hand from 12 position

Distance between Hour hand and Minute hand between 6 and 7 PM is x degree - So Time will be 6:z, where z is the distance of the minute hand from 12 position

y = ()+x
z = ()+x+30*3

So the difference between 6:z and 3:y is (6-3) hours + 30*3/5 minute (Minute hand covers 30 degree in 5 minutes)
= 3 hours 18minutes....

PS - I did not substitute, But I will definitely substitute the answer choices to confirm.

Do let me know your thoughts.....

y and z are the distances from 12 in minutes in your solution, not in degrees. I am not sure how you made these equations. The question I gave is a generic example. The actual question would have a value for x. e.g.
Mr. A leaves his house between 3 and 4 pm and notices that the angle between the hour and minute hands is 45 degrees. He returns between 6 and 7 pm same day and notices that the angle is again 45 degrees. For how much time was Mr A away from home?
Even this would be a DS question with 2 statements giving further information because multiple answers are possible. The diagram below will explain why.
Attachment:

Ques3.jpg [ 14.19 KiB | Viewed 10964 times ]

So the statements could be something like "He was out for more than 3 hr 10 minutes" etc...
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 25 Aug 2008 Posts: 223 Location: India WE 1: 3.75 IT WE 2: 1.0 IT Re: Clock hands [#permalink] ### Show Tags 02 Aug 2011, 03:58 Karishma, Shouldn't this question be like what will the maximum / minimum time was Mr A away from home, considering that we are going to have 2 possibilities. Also, how can we solve this types of ques. _________________ Cheers, Varun If you like my post, give me KUDOS!! Senior Manager Joined: 08 Nov 2010 Posts: 408 WE 1: Business Development Re: Clock hands [#permalink] ### Show Tags 02 Aug 2011, 10:19 dimri10 wrote: In a circular clock, the long hand is the radius of the circle. At what time is the smaller angle between the hands of the clock NOT divisible by 15? I 7:20 II 9:00 III 4:30 (A) Only I (B) Only III (C) I + II (D) II+III (E) I+II+III The way I would solve this Q is this: look at the answers - we want to check answer II first of all bc its easy to check and if ill cancel it, it will leave me with 2 answers. We know easily that at 0900 - the angel is 90 and therefore we can remove all the questions with answer II - meaning C,D,E - OUT. now - bc we have no answer as "none" - we need to check only one of the answers. I or III. For me, 0430 is easier bc its dealing with half and not thirds. we know that the big one is at 180, the small one is 4.5*30 = 135. 180-135=45. Done. III is out. I dont need to check answer I bc i made sure all the others are wrong. _________________ Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7438 Location: Pune, India Re: Clock hands [#permalink] ### Show Tags 02 Aug 2011, 21:44 varunmaheshwari wrote: Karishma, Shouldn't this question be like what will the maximum / minimum time was Mr A away from home, considering that we are going to have 2 possibilities. Also, how can we solve this types of ques. Yes, if you want to make it a PS question, you can definitely ask for the maximum or minimum time. There are going to be 4 possibilities (2C1 * 2C1). 2 possibilities for the time at which he leaves. 2 possibilities for the time at which he returns. How to solve it? Mr. A leaves his house between 3 and 4 pm and notices that the angle between the hour and minute hands is 45 degrees. He returns between 6 and 7 pm same day and notices that the angle is again 45 degrees. What is the minimum time for which Mr A was away from home? Let's focus on the minimum time that he was away. For that he should have left later and arrived earlier. So he should have left at around 3:25 and arrived at around 6:25 (Look at the diagram above to see the case we are talking about) At 3 o clock, the angle between the hour and minute hand is 90 degrees. The minute hand should cover the 90 degrees and then create an angle of 45 degrees between itself and the hour hand. Relative speed of minute hand is 330 degrees/hour. To cover 135 degrees relative to the hour hand, it will take 60/330 * 135 minutes = 270/11 minutes = 24(6/11) minutes He must have left at 24(6/11) minutes past 3. At 6 o clock, the angle between the hour and minute hand is 180 degrees. The minute hand should cover 135 degrees relative to the hour hand to create an angle of 45 degrees. Relative speed of minute hand is 330 degrees/hour. To cover 135 degrees relative to the hour hand, it will take 60/330 * 135 minutes = 270/11 minutes = 24(6/11) minutes. He must have arrived at 24(6/11) minutes past 6. This means he was out for exactly 3 hours. Now try the case of 'maximum time' and put it up. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Manager
Status: On...
Joined: 16 Jan 2011
Posts: 188
Re: Clock hands [#permalink]

### Show Tags

08 Aug 2011, 19:42
1
This post received
KUDOS
VeritasPrepKarishma wrote:
varunmaheshwari wrote:
Karishma,
Shouldn't this question be like what will the maximum / minimum time was Mr A away from home, considering that we are going to have 2 possibilities.
Also, how can we solve this types of ques.

Yes, if you want to make it a PS question, you can definitely ask for the maximum or minimum time. There are going to be 4 possibilities (2C1 * 2C1). 2 possibilities for the time at which he leaves. 2 possibilities for the time at which he returns.

How to solve it?
Mr. A leaves his house between 3 and 4 pm and notices that the angle between the hour and minute hands is 45 degrees. He returns between 6 and 7 pm same day and notices that the angle is again 45 degrees. What is the minimum time for which Mr A was away from home?

Let's focus on the minimum time that he was away. For that he should have left later and arrived earlier. So he should have left at around 3:25 and arrived at around 6:25 (Look at the diagram above to see the case we are talking about)

At 3 o clock, the angle between the hour and minute hand is 90 degrees.
The minute hand should cover the 90 degrees and then create an angle of 45 degrees between itself and the hour hand.
Relative speed of minute hand is 330 degrees/hour.
To cover 135 degrees relative to the hour hand, it will take 60/330 * 135 minutes = 270/11 minutes = 24(6/11) minutes
He must have left at 24(6/11) minutes past 3.

At 6 o clock, the angle between the hour and minute hand is 180 degrees.
The minute hand should cover 135 degrees relative to the hour hand to create an angle of 45 degrees.
This is because 180-45 = 135 degrees and not 90+45 degrees - Highlighted to see that evryone gets the reason. Anyway it will become clear in the Maximum example
Relative speed of minute hand is 330 degrees/hour.
To cover 135 degrees relative to the hour hand, it will take 60/330 * 135 minutes = 270/11 minutes = 24(6/11) minutes.
He must have arrived at 24(6/11) minutes past 6.

This means he was out for exactly 3 hours.

Now try the case of 'maximum time' and put it up.

Mr. A leaves his house between 3 and 4 pm and notices that the angle between the hour and minute hands is 45 degrees. He returns between 6 and 7 pm same day and notices that the angle is again 45 degrees. What is the maximum time for which Mr A was away from home?

Now we need -
Earliest time that Mr. A left b/w 3 and 4 PM
Latest time when Mr. A returned b/w 6 and 7 PM

Relative speed of Minute hand w.r.t Hour hand = 330 degrees per hour

At 3 PM, the angle b/w hour and minute hand = 90 degree
So earliest time when Mr. A leaves will be 90-45 = 45 degrees to be covered by the minute hand relative to Hour hand = (60/330)45 minutes past 3

At 6 PM, the angle b/w hour and minute hand = 180 degree
So latest time when Mr. A returns will be 180+45 = 225 degrees to be covered by the minute hand relative to Hour hand = (60/330)225 minutes past 6

So maximum time for which Mr A was away from home
= (60/330)225 minutes past 6 - (60/330)45 minutes past 3
= 3 hrs (60/330)180minutes
= 3 hours (360/11) minutes
= $$3 hours 34\frac{6}{11} minutes$$

_________________

Labor cost for typing this post >= Labor cost for pushing the Kudos Button
http://gmatclub.com/forum/kudos-what-are-they-and-why-we-have-them-94812.html

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7438
Location: Pune, India
Re: Clock hands [#permalink]

### Show Tags

09 Aug 2011, 03:43
Expert's post
1
This post was
BOOKMARKED
krishp84 wrote:
Mr. A leaves his house between 3 and 4 pm and notices that the angle between the hour and minute hands is 45 degrees. He returns between 6 and 7 pm same day and notices that the angle is again 45 degrees. What is the maximum time for which Mr A was away from home?

Now we need -
Earliest time that Mr. A left b/w 3 and 4 PM
Latest time when Mr. A returned b/w 6 and 7 PM

Relative speed of Minute hand w.r.t Hour hand = 330 degrees per hour

At 3 PM, the angle b/w hour and minute hand = 90 degree
So earliest time when Mr. A leaves will be 90-45 = 45 degrees to be covered by the minute hand relative to Hour hand = (60/330)45 minutes past 3

At 6 PM, the angle b/w hour and minute hand = 180 degree
So latest time when Mr. A returns will be 180+45 = 225 degrees to be covered by the minute hand relative to Hour hand = (60/330)225 minutes past 6

So maximum time for which Mr A was away from home
= (60/330)225 minutes past 6 - (60/330)45 minutes past 3
= 3 hrs (60/330)180minutes
= 3 hours (360/11) minutes
= $$3 hours 34\frac{6}{11} minutes$$

Yes, that's right. Though, in the last step, 360/11 minutes would be 32(8/11) minutes
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Manager
Status: On...
Joined: 16 Jan 2011
Posts: 188
Re: Clock hands [#permalink]

### Show Tags

09 Aug 2011, 04:41
VeritasPrepKarishma wrote:
krishp84 wrote:
Mr. A leaves his house between 3 and 4 pm and notices that the angle between the hour and minute hands is 45 degrees. He returns between 6 and 7 pm same day and notices that the angle is again 45 degrees. What is the maximum time for which Mr A was away from home?

Now we need -
Earliest time that Mr. A left b/w 3 and 4 PM
Latest time when Mr. A returned b/w 6 and 7 PM

Relative speed of Minute hand w.r.t Hour hand = 330 degrees per hour

At 3 PM, the angle b/w hour and minute hand = 90 degree
So earliest time when Mr. A leaves will be 90-45 = 45 degrees to be covered by the minute hand relative to Hour hand = (60/330)45 minutes past 3

At 6 PM, the angle b/w hour and minute hand = 180 degree
So latest time when Mr. A returns will be 180+45 = 225 degrees to be covered by the minute hand relative to Hour hand = (60/330)225 minutes past 6

So maximum time for which Mr A was away from home
= (60/330)225 minutes past 6 - (60/330)45 minutes past 3
= 3 hrs (60/330)180minutes
= 3 hours (360/11) minutes
[color=#FF0000]= $$3 hours 34\frac{6}{11} minutes$$

[/color]

Yes, that's right. Though, in the last step, 360/11 minutes would be 32(8/11) minutes

Yeah silly me
Any one should have said it is 32.xxx minutes just by dividing mentally
_________________

Labor cost for typing this post >= Labor cost for pushing the Kudos Button
http://gmatclub.com/forum/kudos-what-are-they-and-why-we-have-them-94812.html

Manager
Status: On...
Joined: 16 Jan 2011
Posts: 188
Re: Clock hands [#permalink]

### Show Tags

09 Aug 2011, 04:50
VeritasPrepKarishma wrote:
varunmaheshwari wrote:
Karishma,
Shouldn't this question be like what will the maximum / minimum time was Mr A away from home, considering that we are going to have 2 possibilities.
Also, how can we solve this types of ques.

Yes, if you want to make it a PS question, you can definitely ask for the maximum or minimum time. There are going to be 4 possibilities (2C1 * 2C1). 2 possibilities for the time at which he leaves. 2 possibilities for the time at which he returns.

How to solve it?
Mr. A leaves his house between 3 and 4 pm and notices that the angle between the hour and minute hands is 45 degrees. He returns between 6 and 7 pm same day and notices that the angle is again 45 degrees. What is the minimum time for which Mr A was away from home?

Let's focus on the minimum time that he was away. For that he should have left later and arrived earlier. So he should have left at around 3:25 and arrived at around 6:25 (Look at the diagram above to see the case we are talking about)

At 3 o clock, the angle between the hour and minute hand is 90 degrees.
The minute hand should cover the 90 degrees and then create an angle of 45 degrees between itself and the hour hand.
Relative speed of minute hand is 330 degrees/hour.
To cover 135 degrees relative to the hour hand, it will take 60/330 * 135 minutes = 270/11 minutes = 24(6/11) minutes
He must have left at 24(6/11) minutes past 3.

At 6 o clock, the angle between the hour and minute hand is 180 degrees.
The minute hand should cover 135 degrees relative to the hour hand to create an angle of 45 degrees.
Relative speed of minute hand is 330 degrees/hour.
To cover 135 degrees relative to the hour hand, it will take 60/330 * 135 minutes = 270/11 minutes = 24(6/11) minutes.
He must have arrived at 24(6/11) minutes past 6.

This means he was out for exactly 3 hours.

Now try the case of 'maximum time' and put it up.

One more important thing to note here -
At 3 o clock, the angle between the hour and minute hand is 90 degrees.
The minute hand should cover the 90 degrees and then create an angle of 45 degrees between itself and the hour hand.

Relative speed of minute hand is 330 degrees/hour.
To cover 135 degrees relative to the hour hand, it will take 60/330 * 135 minutes = 270/11 minutes = 24(6/11) minutes

When minute hand moves, Hour hand will also move, but the distance in degree b/w both the hands will remain same.

Let Hour hand move by h degrees when minute hands moves ...
The minute hand would be 135+h degrees from 12'o clock position.....
But here we ae speaking about relative speed and
NOT ABSOLUTE SPEEDcolor=#0000BF], so relative to hour hand , the speed will remain constant (135 degrees)[/color]

These are simple points but make the difference to understand the core concepts
_________________

Labor cost for typing this post >= Labor cost for pushing the Kudos Button
http://gmatclub.com/forum/kudos-what-are-they-and-why-we-have-them-94812.html

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15911
Re: Clock hands [#permalink]

### Show Tags

21 Sep 2013, 18:29
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: Clock hands   [#permalink] 21 Sep 2013, 18:29

Go to page    1   2    Next  [ 21 posts ]

Similar topics Replies Last post
Similar
Topics:
1 The number of degrees that the hour hand of a clock moves through betw 1 14 May 2016, 08:12
How often between 11 O'clock and 12 O'clock are the hands of the clock 2 05 Aug 2011, 12:59
11 The minute hand of a clock overtakes the hour hand at intervals of 65 2 24 Oct 2010, 12:30
9 What is the angle between the minute and the hour hand of the clock wh 5 25 Oct 2014, 05:33
48 What is the angle between the minute and the hour hand of the clock wh 14 02 Jan 2017, 20:36
Display posts from previous: Sort by

# In a circular clock, the long hand is the radius of the circ

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.