A group of no more than 9 companies

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guerrero: Master | Next Rank: 500 Posts; Posts: 227; Joined: Sun Apr 08, 2012 4:53 amFollowed by: 3 members; Thanked: 12 times

by guerrero » Thu Mar 21, 2013 12:57 am

A group of no more than 9 companies are sending their selected employees to attend a technical conference. How many slots for participants should the organizers allocate so that each company will have the same number of slots?

(A)20
(B)60
(C)420
(D)840
(E)2520

OAE

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Source: Beat The GMAT — Problem Solving | Thu Mar 21, 2013 12:57 am

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Anju@Gurome: GMAT Instructor; Posts: 511; Joined: Wed Aug 11, 2010 9:47 amFollowed by: 86 members; Location: Delhi, India; Thanked: 344 times

by Anju@Gurome » Thu Mar 21, 2013 1:01 am

guerrero wrote:A group of no more than 9 companies are sending their selected employees to attend a technical conference. How many slots for participants should the organizers allocate so that each company will have the same number of slots?

There may be 1, 2, 3, 4, ..., 8, or 9 companies.
The organizers have to allocate slots so that each company will have the same number of slots.

Hence, number of slots = LCM of 1, 2, 3, 4, ..., 8, and 9 = 9*8*7*5 = 2520

The correct answer is E.

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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 » Thu Mar 21, 2013 2:08 am

The answer should be able to evenly divide numbers 1 through 9
only option E does that.

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Anju@Gurome: GMAT Instructor; Posts: 511; Joined: Wed Aug 11, 2010 9:47 amFollowed by: 86 members; Location: Delhi, India; Thanked: 344 times

by Anju@Gurome » Thu Mar 21, 2013 3:30 am

The least time consuming method to solve this problem is to check the options for a number divisible by 9.

If a number is divisible by 9, the sum of the digits of the number will be divisible by 9 too.

(A)20 --> (2 + 0) = 2 --> NO
(B)60 --> (6 + 0) = 6 --> NO
(C)420 --> (4 + 2 + 0) = 6 --> NO
(D)840 --> (8 + 4 + 0) = 12 --> NO
(E)2520 --> (2 + 5 + 2 + 0) = 9 --> YES

The correct answer is E.

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

by GMATGuruNY » Thu Mar 21, 2013 3:34 am

guerrero wrote:A group of no more than 9 companies are sending their selected employees to attend a technical conference. How many slots for participants should the organizers allocate so that each company will have the same number of slots?

(A)20
(B)60
(C)420
(D)840
(E)2520

OAE

The question stem should ask for the LEAST number of slots that must be allocated.

Each company that attends must be given the same number of slots.
Since 9 companies could attend, the correct answer choice must be a multiple of 9.
For an integer to be a multiple of 9, the SUM OF ITS DIGITS must be a multiple of 9.
Of the answer choices, only E works:
2+5+2+0 = 9.

The correct answer is E.

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