A bit confused with the wording of this question [Manhattan 5lb c11 q32]

GRE Quant Problem Solving
1

So the question is -

If 3/4 of all the cookies have nuts and 1/3 of all the cookies have both nuts and fruit, what fraction of all the
cookies have nuts but no fruit?

3/4 of all the cookies have nuts?
So, 3/4 of all the cookies have only? nuts (but no fruit or might have fruit?)
1/4 of them have both nuts and fruits (this is clear)

So if we have 60 cookies
3/4 of them i.e, 45 have nuts (only nuts?)
1/3 of them i.e, 20 have both nuts and fruits

I searched for this problem in gmatclub forum, deduction for cookies with only nuts and no fruits
is to subtract 45 - 20 (I didn’t get this part)

2

Hi misnomerguy,
Lets say we gave 60 Cookies in total.
3/4 of all cookies have nuts=45
Now we have 45 cookies which include cookies with nuts only and nut+fruit as well.
1/3 of all cookies have both hence its 20.
So Cookies with only Nuts= 45-20=15
And cookies with Only Fruits(No Nuts)=60-15=45

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3

Thanks,

Now we have 45 cookies which include cookies with nuts only and nut+fruit as well.

this sentence made it very clear.

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