GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 18 Nov 2018, 14:53

Close

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • How to QUICKLY Solve GMAT Questions - GMAT Club Chat

     November 20, 2018

     November 20, 2018

     09:00 AM PST

     10:00 AM PST

    The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
  • The winning strategy for 700+ on the GMAT

     November 20, 2018

     November 20, 2018

     06:00 PM EST

     07:00 PM EST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

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

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50627
Re: At exactly what time past 7:00 will the minute and hour  [#permalink]

Show Tags

New post 19 Sep 2017, 04:05
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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
B
Joined: 14 Aug 2017
Posts: 42
Concentration: Operations, Social Entrepreneurship
GMAT 1: 610 Q48 V26
GMAT ToolKit User
Re: At exactly what time past 7:00 will the minute and hour  [#permalink]

Show Tags

New post 16 Oct 2017, 00:51
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!

Thanks in advance.
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8550
Location: Pune, India
Re: At exactly what time past 7:00 will the minute and hour  [#permalink]

Show Tags

New post 16 Oct 2017, 03:32
2
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!

Thanks in advance.


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

Answer (D)
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12882
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: At exactly what time past 7:00 will the minute and hour  [#permalink]

Show Tags

New post 06 Dec 2017, 13:05
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:

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
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Senior Manager
Senior Manager
avatar
P
Joined: 26 Jun 2017
Posts: 369
Location: Russian Federation
Concentration: General Management, Strategy
WE: Information Technology (Other)
Re: At exactly what time past 7:00 will the minute and hour  [#permalink]

Show Tags

New post 02 Mar 2018, 02:42
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)
GMAT Club Bot
Re: At exactly what time past 7:00 will the minute and hour &nbs [#permalink] 02 Mar 2018, 02:42

Go to page   Previous    1   2   [ 25 posts ] 

Display posts from previous: Sort by

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

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.