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.
Statement 1: The numbers of pens, pencils, and pads that each staff member received were in the ratio 2:3:4, respectively.
Since 2+3+4 = 9, the total number of pens + pencils + pads must be a multiple of 9.
No way to determine the exact number of staff members.
Insufficient.
Statement 2: The manager distributed a total of 18 pens, 27 pencils, and 36 pads.
The given values are divisible both by 3 and by 9. Thus:
There could be 3 staff members, each receiving 6 pens, 9 pencils, and 12 pads.
There could be 9 staff members, each receiving 2 pens, 3 pencils, and 4 pads.
Since the number of staff members could be 3 or 9, insufficient.
Statements 1 and 2 combined:
In statement 2, pens:pencils:pads = 18:27:36 = 2:3:4, the same ratio given in statement 1. Thus, statement 1 offers no information beyond what is given in statement 2:
There could be 3 staff members, each receiving 6 pens, 9 pencils, and 12 pads.
There could be 9 staff members, each receiving 2 pens, 3 pencils, and 4 pads.
Since the number of staff members could be 3 or 9, insufficient.
The correct answer is
E.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
