A department manager distributed a number of pens, pencils, and pads among the staff in the department, with each staff member receiving \(x\) pens, \(y\) pencils, and \(z\) pads. How many staff members were in the department?
(1) The numbers of pens, pencils, and pads that each staff member received were in the ratio \(2:3:4,\) respectively.
(2) The manager distributed a total of \(18\) pens, \(27\) pencils, and \(36\) pads.
Answer: E
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A department manager distributed a number of pens, pencils, and pads among the staff in the department, with each staff
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deloitte247
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Each staff receiving x pens, y pencils, and z pads
Target question: How many staff members were in the department?
Statement 1: The numbers of pens, pencils, and pads that each staff member received were in the ratio 2:3:4 respectively.
This gives us the ratio of distribution but not the total number of staff or items distributed. So, statement 1 is NOT SUFFICIENT.
Statement 2: The manager distributed a total of 18 pens, 27 pencils, and 36 pads.
This gives the total number of items distributed but not the total number of staff they were distributed to.
No of staff = factor of 18, 27 and 36 = 3 or 9. So, therefore, statement 2 is NOT SUFFICIENT.
Combining both statements together:
Number of staff = 3 or 9
Items will be distributed as 6 pens, 9 pencils, and 12 pads; all in the ratio 2:3:4.
Therefore, the answer is not definite and the total number of staff remains unknown. Hence, both statements combined together are NOT SUFFICIENT.
Answer = option E
Target question: How many staff members were in the department?
Statement 1: The numbers of pens, pencils, and pads that each staff member received were in the ratio 2:3:4 respectively.
This gives us the ratio of distribution but not the total number of staff or items distributed. So, statement 1 is NOT SUFFICIENT.
Statement 2: The manager distributed a total of 18 pens, 27 pencils, and 36 pads.
This gives the total number of items distributed but not the total number of staff they were distributed to.
No of staff = factor of 18, 27 and 36 = 3 or 9. So, therefore, statement 2 is NOT SUFFICIENT.
Combining both statements together:
Number of staff = 3 or 9
Items will be distributed as 6 pens, 9 pencils, and 12 pads; all in the ratio 2:3:4.
Therefore, the answer is not definite and the total number of staff remains unknown. Hence, both statements combined together are NOT SUFFICIENT.
Answer = option E
