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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
1
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A
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C
D
E

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  55% (hard)

Question Stats:

64% (01:55) correct 36% (02:01) wrong based on 83 sessions

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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.

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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
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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
1
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]

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New post 22 Jun 2018, 00:21
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.



Given there are 6 children & 21 pieces of candy.

Statement 1: Each child can receive any number of candies, including 0.

Hence statement 1 is not sufficient.

Statement 2: 6xxxxx the 'x' can be any number again including 0.

Hence statement 2 is not sufficient.

Combining, we get 6abcde, we have a+b+c+d+e = 15, hence {a,b,c,d,e} = {5,4,3,2,1}

We cannot consider 0, since then statement 1 won't be true.

We can say that each child received at least 1 piece of candy.

Combining is Sufficient.

Hence C.

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GyM
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Re: A child had 5 friends at her birthday party. The children opened a box &nbs [#permalink] 22 Jun 2018, 00:21
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