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If a jar of candies is divided among 3 children, how many candies did

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If a jar of candies is divided among 3 children, how many candies did the child that received the fewest pieces receive?

(1) The two children that received the greatest number of pieces received a total of 13 pieces.
(2) The two children that received the fewest number of pieces received a total of 11 pieces.
[Reveal] Spoiler: OA

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If a jar of candies is divided among 3 children, how many candies did [#permalink]

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New post 26 Nov 2016, 04:25
duahsolo wrote:
If a jar of candies is divided among 3 children, how many candies did the child that received the fewest pieces receive?

(1) The two children that received the greatest number of pieces received a total of 13 pieces.
(2) The two children that received the fewest number of pieces received a total of 11 pieces.


Let x be the number of candies with child who received least candies, y who received 2nd highest and z be the highest so from question x<y<Z

(1) y+z =13 no information of x so z can be 11, y can be 2 and x can be 1 or z can be 10 y can be 3 and x can be 1 or 2, SO not Sufficient
(2) x+y=11 again x can be 1 and y 10 or x can be 2 and y 9 so not sufficient

Subtracting 2 from 1 (z-x=2) so x,y,z are consecutive integers so only one possible solution x=5,y=6,z=7

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If a jar of candies is divided among 3 children, how many candies did [#permalink]

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New post 25 Sep 2017, 10:08
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Bunuel wrote:
If a jar of candies is divided among 3 children, how many candies did the child that received the fewest pieces receive?

(1) The two children that received the greatest number of pieces received a total of 13 pieces.
(2) The two children that received the fewest number of pieces received a total of 11 pieces.


Let the three children be \(A\), \(B\) & \(C\) where candy distribution is \(A>B>C\). we need to find \(C\) the lowest

Statement 1: implies that \(A+B = 13\). or \(A=13-B\).
Hence \((A,B)\) can be: (12,1), (11,2), (10,3), (9,4), (8,5), (7,6). No information given about the lowest distribution Hence Insufficient,

Statement 2: implies that \(B+C=11\). or \(C=11-B\)
Hence \((B,C)\) can be: (10,1), (9,2), (8,3), (7,4), (6,5). There are multiple values of C possible. Hence Insufficient

Combining 1 & 2, we know that \(A>B>C\) and \(A+B=13\) and \(B+C=11\), from the given pair of possible values for \((A,B)\) and \((B,C)\), only one value satisfies the given conditions simultaneously

\(A=7\), \(B=6\) and \(C=5\). Hence Sufficient

Option C

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If a jar of candies is divided among 3 children, how many candies did [#permalink]

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Responding to a pm:

If a jar of candies is divided among 3 children, how many candies did the child that received the fewest pieces receive?

(1) The two children that received the greatest number of pieces received a total of 13 pieces.
(2) The two children that received the fewest number of pieces received a total of 11 pieces.

Solution:

Child that received the greatest number of pieces got - G
Child that received the next smaller number of pieces got - M
Child that received the smallest number of pieces got - S

We need to find the value of S.

(1) The two children that received the greatest number of pieces received a total of 13 pieces.
G + M = 13 ......(I)
Not sufficient

(2) The two children that received the fewest number of pieces received a total of 11 pieces.
M + S = 11.......(II)
Not sufficient

Using both statements, (I) - (II)
G - S = 2

So greatest and smallest have a difference of 2. So M would be right in the middle (so that we have 2 greatest and 2 least).
So G, M and S are consecutive integers. G = 7, M = 6, S = 5
Answer(C)
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If a jar of candies is divided among 3 children, how many candies did   [#permalink] 07 Oct 2017, 00:10
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