1/3 of the cookies in a jar are chocolate chip, 2/3 of the remaining : Problem Solving (PS)

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1/3 of the cookies in a jar are chocolate chip, 2/3 of the remaining

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Math Expert

Joined: 02 Sep 2009

Posts: 53061

1/3 of the cookies in a jar are chocolate chip, 2/3 of the remaining [#permalink]

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22 Jan 2019, 23:54

00:00

Difficulty:

25% (medium)

Question Stats:

73% (01:45) correct

27% (02:29) wrong

based on 40 sessions

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1/3 of the cookies in a jar are chocolate chip, 2/3 of the remaining cookies are peanut butter, and the rest of the cookies are white chocolate. If 20 cookies are white chocolate, how many cookies are in the jar?

A 40

B 60

C 70

D 90

E 100

Spoiler: OA

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Re: 1/3 of the cookies in a jar are chocolate chip, 2/3 of the remaining [#permalink]

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23 Jan 2019, 00:15

Bunuel wrote:

let there are x cookies in the jar.

chocolate chip = 1/3*x = x/3.

Remaining cookies = 2x/3.

PB = 2x/3 * 2/3 = 4x/9.

Remaining cookies = 2x/3 - 4x/9 = 2x /9.

2x/9 = white chips.

2x/9 = 20

x = 90.

D is the correct answer.

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1/3 of the cookies in a jar are chocolate chip, 2/3 of the remaining [#permalink]

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23 Jan 2019, 00:58

IMO D ie 90 cookies in the jar

chocolate chip cookies = 1/3
So remaining cookies =2/3

Peanut butter cookies=2/3 of remaining
ie 2/3*2/3=4/9 of total is PB

Remaining cookies= 1-(1/3+4/9)=1-7/9= 2/9 of total cookies

2/9 of total cookies = 20

Therefore Total cookies = 90.

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Re: 1/3 of the cookies in a jar are chocolate chip, 2/3 of the remaining [#permalink]

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23 Jan 2019, 07:08

Bunuel wrote:

we can solve < 30 seconds this quesiton
given x/3 are chocolate cookies
so all options except b & d are valid

further we can notice that option b ends up being a fraction where as d stands as an integer

so IMO D is correct..
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Re: 1/3 of the cookies in a jar are chocolate chip, 2/3 of the remaining [#permalink]

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27 Jan 2019, 18:23

Bunuel wrote:

We can let the total number of cookies = n. We see that n/3 cookies are chocolate chip. The remaining number of cookies is (2/3) x n = 2n/3. We know that 2/3 of these 2n/3 cookies are peanut butter, so (2/3)x(2n/3) are peanut butter. We can now create the equation:

n/3 + 2/3(2n/3) + 20 = n

n/3 + 4n/9 + 20 = n

Multiplying by 9, we have:

3n + 4n + 180 = 9n

180 = 2n

90 = n

Answer: D
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