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Company H distributed $4,000 and 180 pencils evenly among it

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GMAT Club Legend
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Joined: 07 Jun 2014
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GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Kudos [?]: 1613 [1] , given: 375

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Company H distributed $4,000 and 180 pencils evenly among it [#permalink] New post 12 Aug 2018, 15:32
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Question Stats:

70% (01:02) correct 30% (00:34) wrong based on 10 sessions
Company H distributed $4,000 and 180 pencils evenly among its employees, with each employee getting an equal integer number of dollars and an equal integer number of pencils. What is the greatest number of employees that could work for company H?

(A) 9
(B) 10
(C) 20
(D) 40
(E) 180
[Reveal] Spoiler: OA

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2 KUDOS received
GMAT Club Legend
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Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1613 [2] , given: 375

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Re: Company H distributed $4,000 and 180 pencils evenly among it [#permalink] New post 15 Aug 2018, 05:17
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Explanation

In order to distribute $4,000 and 180 pencils evenly, the number of employees must be a factor of each of these two numbers. Because the question asks for the greatest number of employees possible, start by checking the greatest choices:

(E) $4,000 could not be evenly distributed among 180 employees (although 180 pencils could).

(D) $4,000 could be evenly divided among 40 people, but 180 pencils could not.

(C) is the greatest choice that works—$4,000 and 180 pencils could each be evenly distributed among 20 people.


Alternatively, find the greatest common factor (GCF) of the two numbers. Factor: \(4,000 = 2 \times 2 \times 2 \times 2 \times 2 \times 5 \times 5 \times 5 = 2^5 \times 5^3\) and \(180 = 2 \times 2 \times 3 \times 3 \times 5 = 2^2 \times 3^2 \times 5\). These numbers have 2 × 2 × 5 in common, so 20 is the GCF.
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Re: Company H distributed $4,000 and 180 pencils evenly among it [#permalink] New post 15 Aug 2018, 17:57
The answer has to be a factor of both, so substitution will solve this problem quickly.
Re: Company H distributed $4,000 and 180 pencils evenly among it   [#permalink] 15 Aug 2018, 17:57
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Company H distributed $4,000 and 180 pencils evenly among it

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