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D
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Difficulty:
5%
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Question Stats:
91% (02:04) correct
9%
(02:27)
wrong
based on 393
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Of the 400 employees in a certain office, 260 have been given a watch and 80 have been given a cell phone. If the number of employees who have been given both a watch and a cell phone is 1/2 the number who have been given neither a watch nor a cell phone, how many employees have been give a watch but not a cell phone?
A. 90
B. 170
C. 180
D. 200
E. 220
A. 90
B. 170
C. 180
D. 200
E. 220
21 Jul 2023, 21:30
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Given: Of the 400 employees in a certain office, 260 have been given a watch and 80 have been give a cell phone.
Asked: If the number of the employees have been given both a watch and a cell phone is 1/2 the number who have been given neither a watch nor a cell phone. How many employees have been give a watch but not a cell phone?
Since 320-2x = 260 - x
x = 60
IMO D
Asked: If the number of the employees have been given both a watch and a cell phone is 1/2 the number who have been given neither a watch nor a cell phone. How many employees have been give a watch but not a cell phone?
| Number of employees given a watch | Number of employees not given a watch | Total number of employees | |
| Number of employees given a cell phone | x | 80-x=140-2x | 80 |
| Number of employees not given a cell phone | 320-2x=260-x | 2x | 320 |
| Total number of employees | 260 | 140 | 400 |
Since 320-2x = 260 - x
x = 60
| Number of employees given a watch | Number of employees not given a watch | Total number of employees | |
| Number of employees given a cell phone | 60 | 20 | 80 |
| Number of employees not given a cell phone | 200 | 120 | 320 |
| Total number of employees | 260 | 140 | 400 |
IMO D
20 Jul 2023, 09:27
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TinaHo
Of the 400 employees in a certain office, 260 have been given a watch and 80 have been give a cell phone. If the number of the employees have been given both a watch and a cell phone is 1/2 the number who have been given neither a watch nor a cell phone. How many employees have been give a watch but not a cell phone?
A. 90
B. 170
C. 180
D. 200
E. 220
A. 90
B. 170
C. 180
D. 200
E. 220
#W + #C - #W&C + Neither = Total
260 + 80 – (1/2)Neither + Neither = 400
(1/2)Neither = 60
Neither = 120
#W&C = (1/2)120 = 60
#W&NC = #W - #W&C = 260 – 60 = 200
Therefore, 200 employees have been given a watch but not a cell phone.
Answer: D
