In a courtyard, one bell rings every 1/4 hour and another

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 am; Followed by:3 members

In a courtyard, one bell rings every 1/4 hour and another

by VJesus12 » Fri Apr 06, 2018 2:42 am

In a courtyard, one bell rings every 1/4 hour and another bell rings every 1/5 hour. Both bells ring together at exactly the beginning of each hour. Which of the following gives all the intervals that occur between any two rings of the bells in minutes?

A. 6 and 9 only
B. 3, 6 and 9
C. 3, 12 and 15
D. 3, 6, 9 and 12
E. 3, 6, 10 and 12

The OA is D.

I don't understand this question. May someone help me, please? Thanks in advanced.

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Source: Beat The GMAT — Problem Solving | Fri Apr 06, 2018 2:42 am

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Sionainn@PrincetonReview: GMAT Instructor; Posts: 41; Joined: Mon Mar 12, 2018 9:54 am; Followed by:1 members

by Sionainn@PrincetonReview » Fri Apr 06, 2018 4:20 am

Make a list of times the bells ring for an hour.

Bell A: noon, 12: 15, 12:30, 12:45 and 1.
Bell B: noon, 12:12, 12:24, 12:36, 12:48 and 1

Now combine the lists (deleting any repeated times):
noon, 12:12, 12:15, 12:24, 12:30, 12:36, 12:45, 12:48, 1

12 minute gap between noon and 12: 12. Eliminate A and B.

The next gap is between 12:12 - 12: 15 or 3 minutes. But all of our remaining answers have 3 so we can't eliminate anything.

But the next gap is between 12:15 -12:24 or 9 minutes. Eliminate C and E. Only D remains.

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Instructor, tutor for Princeton Review and Airbnb host
In other words a blend of Jamie Escalante from Stand and Deliver, Julie from The Love Boat, and Schneider the Super from One Day at a Time.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Fri Apr 06, 2018 5:25 am

VJesus12 wrote:In a courtyard, one bell rings every 1/4 hour and another bell rings every 1/5 hour. Both bells ring together at exactly the beginning of each hour. Which of the following gives all the intervals that occur between any two rings of the bells in minutes?

A. 6 and 9 only
B. 3, 6 and 9
C. 3, 12 and 15
D. 3, 6, 9 and 12
E. 3, 6, 10 and 12

To make the math easier, let the total timeline = the LCM of the two denominators 4 and 5 = 20 minutes.

Dividing a 20-minute timeline into 5ths and 4ths, we get:
0....4...5...8...10...12...15...16...20.
Each of the values above represents a ring.
The timeline yields the following intervals between successive rings:
4 minutes (from 0 to 4 and from 16 to 20).
1 minute (from 4 to 5 and from 15 to 16).
2 minutes (from 8 to 10 and from 10 to 12).
3 minutes (from 5 to 8 and from 12 to 15).

Since the actual timeline is 60 minutes -- 3 times as long -- the intervals above must all be multiplied by a factor of 3, yielding the following intervals between successive rings:
12 minutes
3 minutes
6 minutes
9 minutes.

The correct answer is D.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8085; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Mon Apr 16, 2018 4:17 pm

VJesus12 wrote:In a courtyard, one bell rings every 1/4 hour and another bell rings every 1/5 hour. Both bells ring together at exactly the beginning of each hour. Which of the following gives all the intervals that occur between any two rings of the bells in minutes?

A. 6 and 9 only
B. 3, 6 and 9
C. 3, 12 and 15
D. 3, 6, 9 and 12
E. 3, 6, 10 and 12

For every 4th of an hour, bell one rings on minutes 15, 30, 45, and 60.

For every 5th of an hour, bell two rings on minutes 12, 24, 36, 48, and 60.

Since 15 - 12 = 3, 30 - 24 = 6, 45 - 36 = 9 and 60 - 48 = 12, the intervals are 3, 6, 9 and 12.

Answer: D

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