Double overlap questions

tzohrabyan wrote: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!!!

hi

% 40 percent of 48 is not a full number? and i think some info is missing to arrive to a conclusion?
could you supply the answer options pls?
may be we can use backsolve technique to get a number?

Here is the full explanation which totally doesn't make sense to me. Even when i pick and choose numbers, there are lots and lots of them that fit to this problem. Here is their "official" explanation:

"Given that 13 ties are silk, 35 ties must be polyester. Also, given that 40% of the ties are striped, 60% must be nonstriped. Thus 60% of 35 ties, or 19 ties, are polyester and nonstriped. "

Note, even the calculation is wrong. It is not just me, right? It is plain wrong question - i think.

Thanks

I feel something is missed out/taken for granted. Confused! is this a valid GMAT question?