BTGModeratorVI wrote: ↑

Tue Dec 15, 2020 7:04 am

A factory has three types of machines – A, B, and C – each of which works at its own constant rate. How many widgets could one machine A, one Machine B, and one Machine C produce in one 8-hour day?

(1) 7 Machine As and 11 Machine Bs can produce 250 widgets per hour
(2) 8 Machine As and 22 Machine Cs can produce 600 widgets per hour

Answer: C
Source: Veritas Prep

Target question: How many widgets could one machine A, one Machine B, and one Machine C produce in one 8-hour day?

Statement 1: 7 Machine A's and 11 Machine B's can produce 250 widgets per hour
No information about Machine C
NOT SUFFICIENT

Statement 2: 8 Machine A's and 22 Machine C's can produce 600 widgets per hour
No information about Machine B
NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1: 7 Machine A's and 11 Machine B's can produce 250 widgets per hour
Statement 2: 8 Machine A's and 22 Machine C's can produce 600 widgets per hour

Hmmm, I see that we're given info about 11 Machine Bs and 22 Machine Cs. Perhaps we might gain some useful information, if we create an EQUIVALENT statement such that Machines B and C produce the SAME number of widgets.

Take statement 2 and HALVE everything to get: 4 Machine As and 11 Machine Cs can produce 300 widgets per hour
Combine this new (equivalent) info with statement 1 to see we have two useful pieces of info:

7 Machine A's and 11 Machine B's can produce 250 widgets per hour
4 Machine As and 11 Machine Cs can produce 300 widgets per hour

So, if we ADD all of the machines we get:
11 Machine A's, 11 Machine B's and 11 Machine C's can produce 550 widgets per hour

Now divide everything by 11 to get: 1 Machine A, 1 Machine B and 1 Machine C can produce 50 widgets per hour
So, 1 Machine A, 1 Machine B and 1 Machine C can produce 400 widgets in 8 hours
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C