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# Melissa enters a charity raffle in which bags of candy are being given

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Intern
Joined: 28 Feb 2011
Posts: 33
Melissa enters a charity raffle in which bags of candy are being given  [#permalink]

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03 Nov 2011, 17:37
1
00:00

Difficulty:

95% (hard)

Question Stats:

37% (03:37) correct 63% (03:00) wrong based on 24 sessions

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Melissa enters a charity raffle in which bags of candy are being given away as prizes. She will be randomly assigned a number from the set of positive integers from 1 to 500 and receive a bag filled with that many pieces of candy. She decides that if the number of pieces of candy she receives is such that she can distribute the candy equally among her three children OR such that she can distribute the candy equally among her children, herself, and her husband, then she will keep it. In all other cases, she will give the candy to her neighbor if only if it can be distributed equally among the seven members of her neighbor’s family. What is the probability that Melissa gives the bag of candy to her neighbor?

A. 0.068
B. 0.076
C. 0.096
D. 0.114
E. 0.142
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Joined: 24 Jul 2011
Posts: 1672
GMAT 1: 780 Q51 V48
GRE 1: Q800 V740
Re: Melissa enters a charity raffle in which bags of candy are being given  [#permalink]

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03 Nov 2011, 21:51
1
The way to solve this question is as follows:

Melissa will give the candy to her neighbor if the number of pieces of candy she receives is a multiple of 7. However, she will not give her neighbor the candy if the number of pieces she receives is a multiple of 3 or a multiple of 5. Therefore cases in which she will give the candy to her neighbor = cases in which the number of candies she gets is a multiple of 7 but not a multiple of 3 or a multiple of 5.

Number of multiples of 7 from 1 to 500 = 71
LCM of 3 and 7 = 21. Total multiples of 21 from 1 to 500 = 23
LCM of 5 and 7 = 35. Total multiples of 35 from 1 to 500 = 14
LCM of 3, 5, and 7 = 105. Total multiples of 105 from 1 to 500 = 4
So multiples of 7 from 1 to 500 that are not multiples of 3 or 5 = 71 - 23 - 14 + 4 = 38

Therefore the required probability = 38/500 = 0.076

Option (E)
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Joined: 31 Oct 2011
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Location: India
Re: Melissa enters a charity raffle in which bags of candy are being given  [#permalink]

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18 Dec 2011, 02:17
Nice explanation GyanOne
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Re: Melissa enters a charity raffle in which bags of candy are being given  [#permalink]

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13 Sep 2018, 06:36
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Melissa enters a charity raffle in which bags of candy are being given   [#permalink] 13 Sep 2018, 06:36
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