M7MBA wrote: ↑

Thu Jan 07, 2021 10:20 am

A certain mixture of paint requires blue, yellow, and red paints in ratios of 2:3:1, respectively, and no other ingredients. If there are ample quantities of the blue and red paints available, is there enough of the yellow paint to make the desired amount of the mixture?

(1) Exactly 20 quarts of the mixture are needed.
(2) Exactly 10 quarts of yellow paint are available.

Answer: C

Source: Official Guide

Target question: Is there enough of the yellow paint to make the desired amount of the mixture?

Statement 1: Exactly 20 quarts of the mixture are needed.
Since the ratio of blue : yellow : red = 2 : 3 : 1, we can conclude that we need:
20/3 quarts of blue paint
10 quarts of yellow paint
20/6 quarts of red paint
Since we don't know how much yellow paint is available, we cannot answer the target question with certainty.
So, statement 1 is NOT SUFFICIENT

Statement 2: Exactly 10 quarts of the yellow paint are available.
In this case, we don't know the VOLUME of mixed paint are needed. Consider these two cases:
Case a: we need 6 quarts of the mixed paint, which means we need 2 quarts of blue paint, 3 quarts of yellow paint and 1 quarts of red paint. In this case, there IS enough yellow paint
Case b: we need 600 quarts of the mixed paint, which means we need 200 quarts of blue paint, 300 quarts of yellow paint and 100 quarts of red paint. In this case, there is NOT enough yellow paint
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that we NEED 10 quarts of yellow paint
Statement 2 tells us that we HAVE 20 quarts of yellow paint
So, YES, there IS enough yellow paint
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C