# All etching tools are either pin-tipped or bladed. While some bladed etching tools are used for engraving, some are n...

tomgbean on November 18, 2019

C

Please explain why C is incorrect.

Irina on November 18, 2019

@tomgbean,

(C) is incorrect because the question requires us to identify the sufficient condition, whereas (C) leaves open the possibility that the conclusion could be false.

We have the following premises:

(1) All etching tools are either pin-tipped or bladed.
A -> B v C
(2) Some bladed tools are used for engraving.
C - some - D
(3) All pin-tipped tools are used for engraving
B ->D

The argument concludes that there are more etching tools that are used for engraving than there are etching tools not used for engraving.
B & C -some - D > C -some -~D

To reach this conclusion, we need to know the comparative number of pin-tipped versus bladed tools, and if these numbers differ, a proportion of bladed tools used for engraving. The correct answer (B) tells us that there are as many pin-tipped as there are bladed etching tools, meaning that even if a portion of bladed-tools are not used for etching, we could always conclude that there are more etching used for engraving than not.

(C) tells us that no etching tool is both pin-tipped and bladed. Even if this is true, it is still possible that there are more bladed tools overall, thus leaving open the possibility that there are more etching tools not used for engraving than there are used for engraving.
Let's say there are 100 pin-tipped tools and 500 bladed tools. 150 bladed tools are used for engraving, and 350 not. In this scenario, we have a total of 250 etching tools used for engraving, and 350 not, meaning our conclusion is no longer valid. Since (C) cannot guarantee the truth of the conclusion, it is incorrect.

Let me know if you have any other questions.