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A child had 5 friends at her birthday party. The children opened a box

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A child had 5 friends at her birthday party. The children opened a box [#permalink]

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New post 31 Oct 2017, 22:13
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A child had 5 friends at her birthday party. The children opened a box containing 21 pieces of candy. Each piece of candy was received by a child. There were no other pieces of candy received by the children at the party. Did each child at the party receive at least 1 piece of candy from the box?

(1) Each child received a different number of candies.

(2) The birthday girl received 6 pieces of candy, which was more than any other child.
[Reveal] Spoiler: OA

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A child had 5 friends at her birthday party. The children opened a box [#permalink]

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New post 31 Oct 2017, 23:11
Bunuel wrote:
A child had 5 friends at her birthday party. The children opened a box containing 21 pieces of candy. Each piece of candy was received by a child. There were no other pieces of candy received by the children at the party. Did each child at the party receive at least 1 piece of candy from the box?

(1) Each child received a different number of candies.

(2) The birthday girl received 6 pieces of candy, which was more than any other child.


5 friends + 1 bday girl = 6 children
A B C D E F

1) suppose A didn't receive any candy

x 2 3 4 5 7 - A did not receive any candy
or
1 2 3 4 5 6 - everyone receives one candy at least
Not sufficient

2)highest is 6
_ _ _ _ _ 6
let A not receive any candy and we will check if that''s possible
X _ _ _ _ 6 --> X 3 3 4 5 6 -------> equals 21 ---possible for one to not receive any candy
and of course everyone can receive one candy at least
Not sufficient

1 & 2
we can't repeat this pattern with one not receiving any candy
X _ _ _ _ 6 --> X 3 2 3 4 5 6 -------> equals 21 - one place short to accommodate the extra 1 candy with the restriction of all numbers being different.
so C will give us a definite answer that yes everyone has to receive at least one candy if statement 1 & 2 are to be true.
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Re: A child had 5 friends at her birthday party. The children opened a box [#permalink]

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New post 31 Oct 2017, 23:18
Bunuel wrote:
A child had 5 friends at her birthday party. The children opened a box containing 21 pieces of candy. Each piece of candy was received by a child. There were no other pieces of candy received by the children at the party. Did each child at the party receive at least 1 piece of candy from the box?

(1) Each child received a different number of candies.

(2) The birthday girl received 6 pieces of candy, which was more than any other child.


6 children = 21 candies

(1) 1,2,3,4,5,6 or 0,1,2,3,4,11 not sufficient

(2) 1,2,3,4,5,6 or 0,3,3,4,5,6 not sufficient

on combining only 1,2,3,4,5,6 possible
suffficient
yes
C
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Re: A child had 5 friends at her birthday party. The children opened a box   [#permalink] 31 Oct 2017, 23:18
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