PrepTest 132, Section 4, Question 16
All etching tools are either pin-tipped or bladed.(46 more words not shown)
The conclusion of the argument(10 more words not shown)
- AAll tools used(7 more words not shown)
- BThere are as(10 more words not shown)
- CNo etching tool(5 more words not shown)
- DThe majority of(8 more words not shown)
- EAll etching tools(8 more words not shown)
Reading the argument
How many tools are in each group? That's what we need before comparing the totals.
All pin-tipped etching tools engrave. Some bladed etching tools engrave and some don't. But those descriptions don't tell us whether pin-tipped tools make up most of the collection or only a tiny part. If the collection has very few pin-tipped tools and lots of bladed tools that don't engrave, the conclusion could fail.
What we’re looking for
We need an assumption that guarantees more engravers than non-engravers. My first thought is to make most of the etching tools pin-tipped. Since every one of those engraves, that would immediately give us a majority. That is one way to fix the argument.
Working the answers
- A
This says every engraving tool is also an etching tool. It doesn't tell us what fraction of etching tools engrave. A small group of engravers could sit inside a much larger group of etching tools. We need the sizes, not another statement about which category contains which.
- BCorrect
Equal numbers are enough. Every pin-tipped tool engraves, so the number of engravers is at least the number of pin-tipped tools. All non-engravers are bladed, and some bladed tools do engrave, so the number of non-engravers is smaller than the number of bladed tools. If the two tool groups are equally large, engravers must outnumber non-engravers.
For a simple example with separate groups, imagine ten pin-tipped tools and ten bladed tools. All ten pin-tipped tools engrave, and at least one bladed tool does too. That's at least eleven engravers and at most nine non-engravers. The comparison above also works if some tools belong to both groups.
- C
Even if the groups don't overlap, we still don't know their sizes. There could be one pin-tipped tool and ninety-nine bladed tools, with only one of the bladed tools used for engraving. Separate categories alone don't establish a majority of engravers.
- D
This concerns a majority within the bladed group. We still don't know how large that group is relative to the pin-tipped group. Plenty of pin-tipped tools might offset those non-engraving blades, or very few might not. D doesn't guarantee the conclusion.
- E
We can already infer this. Every etching tool is pin-tipped or bladed, and all pin-tipped tools engrave, so a non-engraver must be bladed. That identifies its type without telling us how many non-engravers exist. The missing information is still the group sizes.
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