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The Sargon Corporation offers an optional stock-option buy i
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19 Nov 2020, 11:40
19 Nov 2020, 11:40
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Question Stats:
27% (02:04) correct
72% (02:36) wrong based on 69 sessions
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The Sargon Corporation offers an optional stock-option buy in program to its employees. Of the employees with salaries greater than or equal to $100K, 85% choose to participate in this plan. Of the employees with salaries less than $100K, 77% choose to participate in this plan. Which of the following could be the total number of employees? Answer choices below:
A) 100
B) 200
C) 350
D) 460
E) 525
F) 640
G) 750
H) 880
A) 100
B) 200
C) 350
D) 460
E) 525
F) 640
G) 750
H) 880
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Official Answer
B,D,F,H
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: The Sargon Corporation offers an optional stock-option buy i
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19 Nov 2020, 12:01
19 Nov 2020, 12:01
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GreenlightTestPrep wrote:
The Sargon Corporation offers an optional stock-option buy in program to its employees. Of the employees with salaries greater than or equal to $100K, 85% choose to participate in this plan. Of the employees with salaries less than $100K, 77% choose to participate in this plan. Which of the following could be the total number of employees? Answer choices below:
A) 100
B) 200
C) 350
D) 460
E) 525
F) 640
G) 750
H) 880
A) 100
B) 200
C) 350
D) 460
E) 525
F) 640
G) 750
H) 880
We can solve this using the Double Matrix method
Keep the word count down to a minimum, let's refer to the employees earning more than or equal to $100,000 a year as RICH employees, and refer to the other employees as POOR employees.
Let x = the total number of RICH employees
Let y = the total number of POOR employees
So, x+y = the TOTAL number of employees
This also means 0.85x = the number of RICH employees participating in the program
And 0.77y = the number of POOR employees participating in the program
We get the following:
Key concept: 0.85x and 0.77y must be POSITIVE INTEGERS
0.85x = (85/100)x = (17/20)x = 17x/20
If 17x/20 is a POSIIVE INTEGER, then x must be a multiple of 20
0.77y = (77/100)y = 77y/100
If 77y/100 is a POSIIVE INTEGER, then y must be a multiple of 100
Since x+y = the TOTAL number of employees, we're looking for answers choices such that the total number of employees can be expressed as (some positive multiple of 20) + (some positive multiple of 100)
A) 100 --> we can't rewrite 100 in the form (some positive multiple of 20) + (some positive multiple of 100)
B) 200 = (5)(20) + (1)(100) GREAT!
C) 350 --> we can't rewrite 350 in the form (some positive multiple of 20) + (some positive multiple of 100)
D) 460 = (3)(20) + (4)(100) GREAT!
E) 525 --> we can't rewrite 525 in the form (some positive multiple of 20) + (some positive multiple of 100)
F) 640 = (2)(20) + (6)(100) GREAT!
G) 750 --> we can't rewrite 750 in the form (some positive multiple of 20) + (some positive multiple of 100)
H) 880 = (4)(20) + (8)(100) GREAT!
Answer: B, D, F, H
Cheers,
Brent
General Discussion
Re: The Sargon Corporation offers an optional stock-option buy i
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19 Nov 2020, 12:15
19 Nov 2020, 12:15
Expert Reply
Wowwwwwwwwwwwwww 
