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

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AAPL: Moderator; Posts: 2599; Joined: Sun Oct 29, 2017 2:08 pm; Followed by:2 members

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

by AAPL » Thu Oct 03, 2019 3:43 am

Manhattan Prep

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

OA C

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Source: Beat The GMAT — Problem Solving | Thu Oct 03, 2019 3:43 am

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pm; Followed by:5 members

by deloitte247 » Sat Oct 05, 2019 7:42 pm

Each employee got equal amount of dollars and equal number of pencils all in whole numbers without remainder. The greatest number of employees that could work for company H will be the highest common factor of $4,000 and 180 pencils.
Using prime factorization,
Prime factors of 4000 = 2*2*2*2*2*5*5*5
Prime factors of 180 = 2*2*3*3*5
Common prime factor = 2*2*5
Highest common factor = 20
Hence, 180/20 = 9; and #4000/20 = $200

Therefore, the greatnest number of employees working at company H is 20 employees with each of them getting $200, and 9 pencils each. Hence, the answer is option C.

Thanks.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8083; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Mon Oct 07, 2019 10:16 am

AAPL wrote:Manhattan Prep

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

OA C

We need to determine the greatest common factor of 4,000 and 180.

Since 4,000 and 180 are divisible by 20 but not 40 nor 180, we see that the greatest common factor of 4,000 and 180 is 20.

Alternate Solution:

The prime factorization of 4,000 is 100 x 40 = 5^2 x 2^2 x 2^3 x 5 = 2^5 x 5^3.

The prime factorization of 180 = 20 x 9 = 2^2 x 5 x 3^2 = 2^2 x 3^2 x 5.

The greatest common factor (GCF) is the factors that both numbers have in common, so the GCF of 4,000 and 180 is 2^2 x 5 = 4 x 5 = 20. Thus, the greatest number of employees at the company is 20.

Answer: C

Scott Woodbury-Stewart
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