Sufficient & Necessary Questions - - Question 26

If a country's manufacturing capacity is fully utilized, there can be no industrial growth without new capital invest...

Molly-Prendes January 22, 2022

Modifier words!

Hello! I am so confused on the diagramming for the first sentence. I thought when there is a "without" modifier, it becomes the necessary condition and the remaining term is negated and becomes the sufficient condition. First sentence: manufacturing capacity fully utilized->industrial growth-> new capital investment. Second, reduction in interest rates->new capital investment. Please help! Thank you!

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Jay-Etter January 22, 2022

Hi Molly,
Good job breaking this one down, you're almost exactly right! The only thing I would change is for our first sentence, we would map this as

fully utilized -> (growth -> capital investment)

This is because our sentence is "if a country's manufacturing capacity is fully utilized, there can be no industrial growth without new capital investment." In other words, If UTILIZED, then this specific relationship between growth and investment has to hold.

The difference between
What we want: fully utilized -> (growth -> capital investment)
and what we don't want: fully utilized -> growth -> capital investment

is that the first one is just telling us when we have fully utilized, then the second conditional must be true. When we have fully utilized, then growth->capital investment. With the first one, just knowing fully utilized is sufficient to know the relationship between growth and investment holds, but we don't actually know we HAVE growth.

In the second one, if we have fully utilized we have to have growth and also capital investment.

You diagrammed the second sentence correctly as:
reduction in interest -> capital investment

Hope this helps, feel free to follow up.

Molly-Prendes January 23, 2022

Thank you very much! I do understand the difference and the answer choice now. I didn't realize that the correct answer (because of how it was phrased or I am reading too fast) was actually a simple restatement of the second sentence... reduction in interest->capital investment which creates a "precondition" for industrial growth of the first sentence. New investment is necessary for industrial growth and therefore a precondition is met for industrial growth. ugh! Thank you Jay!