Double overlap questions

[tzohrabyan]

I have stumbled upon this problem:

"adrian owns 48 neckties, each of which is either 100% silk or 100% polyester. Forty percent of his ties are striped, and 13 of his ties are silk. How many ties does adrian own that are polyester but are not striped?"
Source: 30 Days to the GMAT CAT (Macmillan)

Sure we can pick and choose numbers and see which one fits, but is there any approach to this? I know generally this type of questions are best to solve with charts having silk and polyester as columns (or rows) and Striped and not as rows (or columns) and try to solve. But The explanation in the book is really weird.

Can anyone help me decide the approach i need for this kind of problems?

Thanks!!!

[adiagr]

Just check....is the figure --48? or is it 40 %?? either of these two Nos. appear wrong.....

[JohnHarris]

Hi tzohrabyan,

Actually, as posed, the question doesn't have an answer in the sense of a single number of polyester but not striped ties. But it does have a minimum and maximum number of those. Anyway, to 'a solution'

First, as mentioned previously the numbers seem wrong but we can go through the problem to show a method assuming 40% was a round number and that it was actually 39.583333...%.

13 ties are silk - given
35 ties are polyester - 48 minus 13
19 ties are stripped - 39.583333...% of 48

Given these numbers we see that either all or none of the silk ties could be stripped but at least some of the polyester ties must be stripped. To satisfy the above conditions there could only be
13 silk stripped (ss) ties and 6 polyester stripped (ps) ties or
12 ss and 7 ps or
11 ss and 8 ps or
...
1 ss and 18 ps or
0 ss and 19 ps

Thus there are at least 6 ps and no more than 19 ps ties or at least 16 but no more than 29 polyester ties are not stripped.

[tim]

Be careful with problems you "stumbled upon" - if they aren’t from a trusted source, you may end up with nonsense like this. :) Our instructors will not be able to help with this problem until we see a corrected version of it..