hand on a standard clock

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Wed Mar 23, 2011 2:13 am

At 4:40, what is the minor angle between the hour hand and the minute hand on a standard clock?
A. 100
B. 110
C. 120
D. 130
E. 140

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Source: Beat The GMAT — Problem Solving | Wed Mar 23, 2011 2:13 am

AIM GMAT: Legendary Member; Posts: 857; Joined: Wed Aug 25, 2010 1:36 amFollowed by: 15 members; Thanked: 56 times

by AIM GMAT » Wed Mar 23, 2011 2:37 am

IMO A . 100

4:40 --- minute hand will be at 8 .

At 4 hour hand will be at 4 , now we need to calculate how many degrees hour hand will move in 40mins.

12 hrs hour hand moves 360 degree
1 hr ---------------------------30 degree
60 min-------------------------30 degree
1 min---------------------------0.5 degree
40min---------------------------20degree

so still 10 degrees are left to cover till hour hand moves to 5 .

Degree between 5 to 8 = 3 * 30 = 90 +10 [left] = 100

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AIM GMAT

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srcc25anu: Master | Next Rank: 500 Posts; Posts: 423; Joined: Fri Jun 11, 2010 7:59 amFollowed by: 2 members; Location: Seattle, WA; Thanked: 86 times

by srcc25anu » Wed Mar 23, 2011 2:37 am

(* for degrees)
at 4:00 pm, hour and minute hand are 120 * apart
in 1 minute - hour hand moves 1/2 *
in 1 min minute hand moves 6*

in 40 mins minute hand moves 6 * x 40 = 240*
in 40 mins hour hand moves 0.5 * x 40 = 20*

hour hand moves 20* further of 120* ie its at 140*
minute hand moves 240* from 0* (at 4 o clock)

hence the difference between 2 hands = 240* - 140* = 100*

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HSPA: Legendary Member; Posts: 1101; Joined: Fri Jan 28, 2011 7:26 amFollowed by: 13 members; Thanked: 47 times; GMAT Score:640

by HSPA » Wed Mar 23, 2011 2:40 am

ideally 120 ... but the hours hand will be btw 4 and 5 on the 4th minor point

4*6= 24

120-24 = 96

96deg is the minor angle

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Wed Mar 23, 2011 2:54 am

srcc25anu wrote:(* for degrees)
at 4:00 pm, hour and minute hand are 120 * apart
in 1 minute - hour hand moves 1/2 *
in 1 min minute hand moves 6*

in 40 mins minute hand moves 6 * x 40 = 240*
in 40 mins hour hand moves 0.5 * x 40 = 20*

hour hand moves 20* further of 120* ie its at 140*
minute hand moves 240* from 0* (at 4 o clock)

hence the difference between 2 hands = 240* - 140* = 100*

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The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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