Data Sufficiency

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