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Company H distributed $4,000 and 180 pencils evenly among it
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12 Aug 2018, 15:32
12 Aug 2018, 15:32
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Question Stats:
82% (01:16) correct
17% (01:19) wrong based on 94 sessions
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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
(A) 9
(B) 10
(C) 20
(D) 40
(E) 180
Re: Company H distributed $4,000 and 180 pencils evenly among it
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15 Aug 2018, 05:17
15 Aug 2018, 05:17
2
Expert Reply
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.
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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Joined: 13 Jul 2018
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GRE 1: Q159 V151
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Re: Company H distributed $4,000 and 180 pencils evenly among it
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15 Aug 2018, 17:57
15 Aug 2018, 17:57
The answer has to be a factor of both, so substitution will solve this problem quickly.
