Of the students in Tanner's class, 8 wore a hat to school, 1

[anik1989]

Of the students in Tanner's class, 8 wore a hat to school, 15 students wore gloves, and 10 wore scarves. None of the students wore a scarf without gloves. Four students wore a hat, gloves, and a scarf. Half of the students who wore a hat also wore gloves. How many students are in Tanner's class?

ans -19

I can not find out how to solve. its from from kaplan MST

[n00bpron00bpron00b]

I got 17

[pelin.akar]

I think drawing a venn diagram would make it much easier to clarify the question. Let's say you draw 3 circle intersects each other. So you have 3 circle: H, G and S. H will have only 4 members including only hat people. G has 5 members only Gloves people. S has 6 people common with G+S, and 4 people will be in H+G+S. If you add all these numbers (4+5+6+4=19)

[tommywallach]

Let's take it step by step:

8 wore a hat to school, 15 students wore gloves, and 10 wore scarves.

8 + 15 + 10 = 33

So we're at 33 before we think about overlap.

None of the students wore a scarf without gloves. That means that of the 15 we counted in gloves, 10 had already been counted in scarves, so we should subtract 10:

33 - 10 = 23

Now, let's jump to half of the students who wore a hat also wore gloves. That means 4 of the hat people were double counted:

23 - 4 = 19

Finally, four students wore all three. These people were double counted, but we already covered them (because we already had 4 people who wore a hat and gloves, so now we know these students wore all three, and we already had MORE than 4 people who wore a scarf and gloves). So we finish at 19.

In the final Venn, you have 4 in the hat only, 4 in the all 3 category, 5 in the gloves only category, and 6 in the gloves and scarf category.

19 is the answer. (Unless I missed something, Noob!)

[anik1989]

Thank you tomy, i always like your approach of answering

[anik1989]

What is your personal opinion about kaplan MST? I found some questions are atypical. Is there any review about this?

[tommywallach]

Hey Anik,

Sadly, I know nothing about Kaplan's materials. I'm sure there's discussion of it somewhere though!

-t