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# Al, Bert, and Carl are the winners of a school drawing for a pile of

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Intern
Status: students
Joined: 08 Mar 2019
Posts: 34
GPA: 3.9
WE: Account Management (Accounting)
Al, Bert, and Carl are the winners of a school drawing for a pile of  [#permalink]

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17 Mar 2019, 09:48
2
00:00

Difficulty:

65% (hard)

Question Stats:

38% (03:16) correct 63% (03:02) wrong based on 8 sessions

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Al, Bert, and Carl are the winners of a school drawing for a pile of Halloween candy, which they are to divide in a ratio of 3 : 2 : 1, respectively. Due to some confusion they come at different times to claim their prizes, and each assumes he is the first to arrive. If each takes what he believes to be his correct share of candy, what fraction of the candy goes unclaimed?

(A)$$\frac{1}{18}$$

(B)$$\frac{1}{6}$$

(C)$$\frac{2}{9}$$

(D)$$\frac{5}{18}$$

(E)$$\frac{5}{12}$$
Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 969
WE: Supply Chain Management (Energy and Utilities)
Al, Bert, and Carl are the winners of a school drawing for a pile of  [#permalink]

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17 Mar 2019, 10:42
Rubina11 wrote:
Al, Bert, and Carl are the winners of a school drawing for a pile of Halloween candy, which they are to divide in a ratio of 3 : 2 : 1, respectively. Due to some confusion they come at different times to claim their prizes, and each assumes he is the first to arrive. If each takes what he believes to be his correct share of candy, what fraction of the candy goes unclaimed?

(A)$$\frac{1}{18}$$

(B)$$\frac{1}{6}$$

(C)$$\frac{2}{9}$$

(D)$$\frac{5}{18}$$

(E)$$\frac{5}{12}$$

Al's share=$$\frac{3x}{(3x+2x+x)}=\frac{1}{2}$$
Bert's share=$$\frac{2x}{(3x+2x+x)}=\frac{1}{3}$$
Carl's share=$$\frac{x}{(3x+2x+x)}=\frac{1}{6}$$

Suppose Al came first to claim his share, he would take=1-1/2=1/2 pile of candy
Suppose Carl came next, his share would be 1/2-1/12=5/12 pile of candy
Suppose Bertl came next, his share would be 1/12-5/36=10/36= $$\frac{5}{18}$$pile of candy

Here order doesn't matter since their shares are dependent on each other and the total quantity is fixed.

Ans. (D)
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PKN

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Al, Bert, and Carl are the winners of a school drawing for a pile of   [#permalink] 17 Mar 2019, 10:42
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