In country Z, 10% of the people do not have a university

[I_need_a_700plus]

The following question can be found on Question Bank: Word Translations.

In country Z, 10% of the people do not have a university diploma but have the job of their choice, and 25% of the people who do not have the job of their choice have a university diploma. If 40% of the people have the job of their choice, what percent of the people have a university diploma?

- 35%
- 45%
- 55%
- 65%
- 75%

I understand that in order to resolve the problem, you can use the double set matrix. However, I am constantly having the same problem identifying "25% of the people who do not have the job of their choice have a university diploma" as "0.25x" vs just entering in "25" for the box "University Diploma" & "Not a Job Choice."

Can someone explain to me why it is "0.25x" and not "25"? Also, any advice on how I can identify this going forward so I can eliminate repeat errors!

Thanks!

[RonPurewal]

The "best way to identify this going forward" is to read these things the way you'd read them in the real world, and NOT to read them in a way that's "academic".

E.g., here are 2 statements that you will almost certainly have no trouble with.

1/
20% of my friends are married and live in Florida.

2/
20% of my friends who live in Florida are married.

You shouldn't need very much (if any) conscious processing to understand these: #1 is 20% of all my friends, but #2 is 20% of my Florida friends.
You may have to read these sentences somewhat more slowly than you'd read most things -- but you certainly shouldn't need to make a Venn diagram to understand them, nor should you have to think about modifiers and suchlike.

Try to adopt a real-world reading outlook -- i.e., ridding yourself of "classroom thinking" -- and then looking at those statements again. The difference should be much more clear.

[I_need_a_700plus]

Hi Ron, thanks for clarifying. I can see the distinction between your example, but I am still having some difficulty trying to find the distinction within the problem.

So if the problem stated, "25% of the people do not have the job of their choice but have a university diploma"...this will then result to just "25" within the box of "no job" & "diploma"?

[RonPurewal]

Yeah, that's a correct interpretation. Trust your real-world brain on this stuff -- it's much, much smarter than your "classroom" brain could ever hope to be.

[RonPurewal]

Maybe you're asking about the "but" vs. the "and". (If you aren't, then ignore.)

In terms of pure logic, there's no difference between "and" and "but". The only difference is in how the two things are perceived in relation to each other.

E.g., "I left home early and arrived at work late" is, in terms of pure facts, exactly the same statement as "I left home early but arrived at work late". A computer wouldn't even understand that there was a difference.
The difference is that, in the second case, the late arrival is perceived as "unexpected" given the early departure; in the first case, it's considered normal (say, in Los Angeles traffic). This difference will have no effect on the logical/mathematical interpretation of the statements.

Similarly, using your sample statement,
25% of the people have a university diploma but do not have the job of their choice
is exactly the same thing as
25% of the people have a university diploma but do not have the job of their choice

If this were a sentence correction problem, then those wouldn't be the same (and, in fact, that difference might be a focal point of the problem). In a math problem -- in which "intention" and "perceived relationship" are not things -- they're the same.