Data Sufficiency

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

Answer: E

Cheers,
Brent