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

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

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25 Oct 2016, 16:13
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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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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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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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07 Oct 2017, 00:10
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Expert's post
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
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