duahsolo wrote:

Of the 350 members in the local carpenters union, 190 of the members have more than 10 years experience and 110 of the members with 10 or fewer years experience are not master craftsmen. If ten elevenths of the master craftsmen own their own shops and there are 110 master craftsmen who own their own shops, which could be the number of master craftsmen with more than 10 years experience who own their own shops?

A) 125

B) 115

C) 100

D) 75

E) 40

Dear

duahsolo,

I'm happy to respond.

I don't know the source of this question, but I would say that the wording is very poor. That first sentence is a train wreck that needs to be broken up for clarity.

I believe what the problem is saying is:

Of the 350 members in the local carpenters union, 190 of the members have more than 10 years experience. One hundred and ten of the members with 10 or fewer years experience are not master craftsmen.

This is the interpretation I will take.

total number of members = 350

total members with 10+ years = 190

so

total members with <10 years = 160

Of that latter set, 110 are not master craftsmen (MC), so 50 are MC.

Then we are told: "

ten elevenths of the master craftsmen own their own shops and there are 110 master craftsmen who own their own shops." Let the total number of MC be X. This says:

(10/11)X = 110

X = 110(11/10) = 121

That's the total number of MC. If 50 MC come from the group with <10 years, then 61 must come from the group with 10+ years.

How many MC with 10+ years owns their own shop? Well, now we have a problem. The number has to be 61 or fewer, so the only choice is (E), but that creates a problem with the scenario.

61 MC with 10+ years --> 40 own their own shop

50 MC with <10 years --> suppose all 50 own their own shops

That's only 90 owning their own shops, but there have to be a total of 110 who own their own shops.

Either there is more ambiguity in the question stem which I missed, or the author of the question did not think this thing through very carefully. In more ways than one, this is a poorly designed question.

Here's a much better PS practice question:

In Dewey Elementary SchoolDoes all this make sense?

Mike

_________________

Mike McGarry

Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)