A certain Clock

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ST: Master | Next Rank: 500 Posts; Posts: 191; Joined: Sat Feb 14, 2009 11:56 am; Thanked: 1 times

by ST » Tue Jul 21, 2009 12:06 pm

A certain clock marks every hour by striking a number of times equal to the hour, and the time require for a stroke is exactly equal to the time interval between strokes. At 6:00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds. At 12:00, how many seconds elapse between the beginning of the first stroke and the end of the last stroke?

a. 72
b. 50
c. 48
d. 46
e. 44

Answer is D

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Source: Beat The GMAT — Problem Solving | Tue Jul 21, 2009 12:06 pm

jjk: Senior | Next Rank: 100 Posts; Posts: 43; Joined: Thu Mar 12, 2009 8:56 pmFollowed by: 1 member; Thanked: 10 times; GMAT Score:730

by jjk » Tue Jul 21, 2009 12:15 pm

"A certain clock marks every hour by striking a number of times equal to the hour, and the time required for a stroke is exactly equal to the time interval between strokes."

Based on this, you know that a stroke takes time and that the interval between strokes takes time. You also know that these time periods are equal, but you do not yet know what that time period is.

At 6:00, the clock strikes 6 times. There are also 5 time intervals between the 6 strokes. So 6 + 5 = 11 equal time periods from the first stroke of the clock to the last (at 6:00). The problem says that at 6:00 the duration from the first stroke to the last is 22 seconds. Divide this by the amount of equal time periods you discovered earlier.

22/11 = 2 seconds per stroke = 2 seconds per interval between strokes

At 12:00, you know the clock will strike 12 times and that there will be 11 time intervals between the strikes. This yields 23 equal time periods of 2 seconds each, so:

23 X 2 = 46 seconds

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ST: Master | Next Rank: 500 Posts; Posts: 191; Joined: Sat Feb 14, 2009 11:56 am; Thanked: 1 times

by ST » Wed Jul 22, 2009 6:17 am

Thank you. Make sense now.

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Thu Dec 14, 2017 5:27 pm

ST wrote:A certain clock marks every hour by striking a number of times equal to the hour, and the time require for a stroke is exactly equal to the time interval between strokes. At 6:00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds. At 12:00, how many seconds elapse between the beginning of the first stroke and the end of the last stroke?

a. 72
b. 50
c. 48
d. 46
e. 44

We are given that a certain clock marks every hour by striking a number of times equal to the hour, and the time required for a stroke is exactly equal to the time interval between strokes.

Since at 6:00 the lapse between the beginning and the last stroke is 22 seconds, we can create the following equation in which x = the time between strokes = the time for each stroke. Since there are 6 strikes at 6:00, we have:

strike - lapse - strike - lapse - strike - lapse - strike - lapse - strike - lapse - strike

There are 6 strikes and 5 lapses, and thus:

6x + 5x = 22

11x = 22

x = 2 seconds

So, at 12:00 there will be 12 strikes and 11 lapses. Thus, the total time will be:

12(2) + 11(2) = 24 +22 = 46 seconds.

Answer: D

Jeffrey Miller
Head of GMAT Instruction
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu Dec 14, 2017 6:05 pm

ST wrote:A certain clock marks every hour by striking a number of times equal to the hour, and the time require for a stroke is exactly equal to the time interval between strokes. At 6:00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds. At 12:00, how many seconds elapse between the beginning of the first stroke and the end of the last stroke?

a. 72
b. 50
c. 48
d. 46
e. 44

Answer is D

In some regards, this is more of a Reading Comprehension question than a Quantitative question.

... the time required FOR a stroke is exactly equal to the time interval BETWEEN strokes.
So, we have moments of silence and moments where the clock is ringing. Each period of silence is the same duration as each period of noise.

So, for example, at 3:00, we have (RING)(silence)(RING)(silence)(RING)

At 6:00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds
So, at 6:00, we have (RING)(silence)(RING)(silence)(RING)(silence)(RING)(silence)(RING)(silence)(RING)
Notice that, if we count RINGS and silences, we have a total of 11 periods.
If the entire event takes 22 seconds, we can conclude that each period is 2 seconds long.

At 12:00, how many seconds elapse between the beginning of the first stroke and the end of the last stroke?
We can conclude that this event will include 12 RINGS and 11 silences for a total of 23 periods.
Since each each period is 2 seconds long, the entire event will take 46 seconds
Answer: D

Aside: If you're not convinced that there will be 12 RINGS and 11 silences, you can always write it out . ..
At 12:00, we have (RING)(silence)(RING)(silence)(RING)(silence)(RING)(silence)(RING)(silence)(RING)(silence)(RING)(silence)(RING)(silence)(RING)(silence)(RING)(silence)(RING)(silence)(RING)

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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