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07 Jun 2021, 07:15
Kudos
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
85% (01:26) correct
15%
(01:55)
wrong
based on 81
sessions
History
Date
Time
Result
Not Attempted Yet
In a certain store, the ratio of part-time workers to full-time workers is 2 to 5. If 4 part-time workers were hired, then the ratio would be 3 to 5. How many workers does the store have?
(A) 11
(B) 12
(C) 21
(D) 28
(E) 35
(A) 11
(B) 12
(C) 21
(D) 28
(E) 35
07 Jun 2021, 08:21
Kudos
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Three ways to solve:
-- If adding 4 part-time workers changes the ratio from "2 to 5" to "3 to 5", then 4 must represent one part of the ratio, and since we have 7 parts in the original ratio, we have 28 workers.
-- If the original ratio is 2 to 5, the total must be divisible by 2 + 5 = 7, so C, D or E is right. If we get a 3 to 5 ratio by hiring 4 workers, then we must get a multiple of 3 + 5 = 8 when we add 4 to the right answer, and D must be right.
-- If the ratio of part-time to full-time workers is initially 2 to 5, we must have 2x part-time workers, and 5x full-time workers, for some integer x, and the question asks us to find 2x + 5x = 7x. When we hire 4 new part-time workers, we have 2x + 4 part time workers, and we still have 5x full-time workers. These are in a 3 to 5 ratio, so
(2x + 4)/5x = 3/5
10x + 20 = 15x
x = 4
and 7x, which we wanted to find, is 28.
Posted from my mobile device
-- If adding 4 part-time workers changes the ratio from "2 to 5" to "3 to 5", then 4 must represent one part of the ratio, and since we have 7 parts in the original ratio, we have 28 workers.
-- If the original ratio is 2 to 5, the total must be divisible by 2 + 5 = 7, so C, D or E is right. If we get a 3 to 5 ratio by hiring 4 workers, then we must get a multiple of 3 + 5 = 8 when we add 4 to the right answer, and D must be right.
-- If the ratio of part-time to full-time workers is initially 2 to 5, we must have 2x part-time workers, and 5x full-time workers, for some integer x, and the question asks us to find 2x + 5x = 7x. When we hire 4 new part-time workers, we have 2x + 4 part time workers, and we still have 5x full-time workers. These are in a 3 to 5 ratio, so
(2x + 4)/5x = 3/5
10x + 20 = 15x
x = 4
and 7x, which we wanted to find, is 28.
Posted from my mobile device
09 Jun 2024, 15:16
Kudos
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A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.
This post was generated automatically.
