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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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### A department manager distributed a number of pens, pencils, and pads among the staff in the department, with each staff

by AAPL » Tue Aug 02, 2022 10:18 am

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## Global Stats

Official Guide

A department manager distributed 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 number 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

OA E

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### Re: A department manager distributed a number of pens, pencils, and pads among the staff in the department, with each st

by [email protected] » Wed Aug 03, 2022 12:38 pm

00:00

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## Global Stats

AAPL wrote:
Tue Aug 02, 2022 10:18 am
Official Guide

A department manager distributed 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 number 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

OA E
Given: 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.

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.
2 + 3 + 4 = 9
So, the TOTAL number of pens, pencils, and pads each worker receives is a multiple of 9.
There's no way we can use this information to determine the number of workers
Statement 1 is NOT SUFFICIENT

Statement 2: The manager distributed a total of 18 pens, 27 pencils, and 36 pads.
Important: Notice that 18 pens, 27 pencils, and 36 pads is in the same ratio as noted in statement 1. So, statement 2 doesn't seem to be adding a whole lot of new information. So I'm already thinking that statement 2 it's not sufficient. Let's see if we can find two conflicting cases that satisfy statement 2
Case a: It could be the case that there's 1 worker, and that worker receives 18 pens, 27 pencils, and 36 pads. In this case, the answer to the target question is the department has 1 staff member
Case b: It could be the case that there are 3 workers, and each worker receives 6 pens, 9 pencils, and 12 pads. In this case, the answer to the target question is the department has 3 staff members
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT: Notice that the same counter-examples I used to show that statement 2 is not sufficient also satisfy the conditions stated in statement 1. So, the same counter-examples will satisfy the two statements COMBINED.
In other words,
Case a: It could be the case that there's 1 worker, and that worker receives 18 pens, 27 pencils, and 36 pads. In this case, the answer to the target question is the department has 1 staff member
Case b: It could be the case that there are 3 workers, and each worker receives 6 pens, 9 pencils, and 12 pads. In this case, the answer to the target question is the department has 3 staff members
Since we can’t answer the target question with certainty, the combined statements are NOT SUFFICIENT