BTGmoderatorLU wrote: ↑Wed Nov 10, 2021 2:10 pm

**Source: Official Guide**
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 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

The OA is

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

Answer: E

Cheers,

Brent