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A group of no more than 9 companies

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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

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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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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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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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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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