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Jan and 5 of his friends sold candy bars to raise money for their scho

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saxenarahul021
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Jan and 5 of his friends sold candy bars to raise money for their scho [#permalink] New post   Updated on: 05 Apr 2019, 00:38
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Jan and 5 of his friends sold candy bars to raise money for their school trip. Jan sold 20 bars and each of his 5 friends sold at least one bar. Did Jan sell more candy bars than each of at least 3 of his friends?

(1) The median of the number of bars sold by Jan's 5 friends is 18.
(2) The average (arithmetic mean) of the number of bars sold by Jan's 5 friends is 12.
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Originally posted by saxenarahul021 on 27 Nov 2012, 01:03.
Last edited by Bunuel on 05 Apr 2019, 00:38, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
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Jan and 5 of his friends sold candy bars to raise money for their scho [#permalink] New post   27 Nov 2012, 06:21
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Jan and 5 of his friends sold candy bars to raise money for their school trip. Jan sold 20 bars and each of his 5 friends sold at least one bar. Did Jan sell more candy bars than each of at least 3 of his friends?

(1) The median of the number of bars sold by Jan's 5 friends is 18.

{a, b, 18, c, d}, so at least 3 friends sold less than 20 bars (a, b and 18). Sufficient.

(2) The average (arithmetic mean) of the number of bars sold by Jan's 5 friends is 12.

The total number of bars sold by Jan's 5 friends is 5*12=60. Can there be a case where at least 3 of Jan's friends sold 20 or more bars? No, since in this case the total number of bars sold by his friends would be more than 60 (20+20+20+1+1=62). Sufficient.

Answer: D.­
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Re: Jan and 5 of his friends sold candy bars to raise money for their scho [#permalink] New post   26 Feb 2024, 09:36
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Bunuel wrote:
Jan and 5 of his friends sold candy bars to raise money for their school trip. Jan sold 20 bars and each of his 5 friends sold at least one bar. Did Jan sell more candy bars than each of at least 3 of his friends?

(1) The median of the number of bars sold by Jan's 5 friends is 18 --> {a, b, 18, c, d}, so at least 3 friends sold less than 20 bars (a, b and 18). Sufficient.

(2) The average (arithmetic mean) of the number of bars sold by Jan's 5 friends is 12 --> total number of bars sold by Jan's 5 friends is 5*12=60. Can there be a case where at least 3 of Jan's friends sold 20 or more bars? No, since in this case the total number of bars sold by his friends would be more than 60 (20+20+20+1+1=62). Sufficient.

Answer: D.


Hi Bunuel,
The question asked is if Jan sold more candy bars than each of at least 3 of his friends:
In statement 2.  I analyzed the following situations:
12+12+12+12+12=60 which would render a NO answer; and
1+1+12+23+23=60 which would render a YES answer.

Why is this wrong?
How come you negated the question asked to get to the right answer?
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Re: Jan and 5 of his friends sold candy bars to raise money for their scho [#permalink] New post   27 Feb 2024, 01:50
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Amobnc wrote:
Bunuel wrote:
Jan and 5 of his friends sold candy bars to raise money for their school trip. Jan sold 20 bars and each of his 5 friends sold at least one bar. Did Jan sell more candy bars than each of at least 3 of his friends?

(1) The median of the number of bars sold by Jan's 5 friends is 18 --> {a, b, 18, c, d}, so at least 3 friends sold less than 20 bars (a, b and 18). Sufficient.

(2) The average (arithmetic mean) of the number of bars sold by Jan's 5 friends is 12 --> total number of bars sold by Jan's 5 friends is 5*12=60. Can there be a case where at least 3 of Jan's friends sold 20 or more bars? No, since in this case the total number of bars sold by his friends would be more than 60 (20+20+20+1+1=62). Sufficient.

Answer: D.


Hi Bunuel,
The question asked is if Jan sold more candy bars than each of at least 3 of his friends:
In statement 2.  I analyzed the following situations:
12+12+12+12+12=60 which would render a NO answer; and
1+1+12+23+23=60 which would render a YES answer.

Why is this wrong?
How come you negated the question asked to get to the right answer?

­
{12, 12, 12, 12, 12} also gives a YES answer to the question: Jan sold more candy bars than each of at least 3 of his friend.­
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Re: Jan and 5 of his friends sold candy bars to raise money for their scho [#permalink] New post   28 Feb 2024, 07:38
Bunuel wrote:
Amobnc wrote:
Bunuel wrote:
Jan and 5 of his friends sold candy bars to raise money for their school trip. Jan sold 20 bars and each of his 5 friends sold at least one bar. Did Jan sell more candy bars than each of at least 3 of his friends?

(1) The median of the number of bars sold by Jan's 5 friends is 18 --> {a, b, 18, c, d}, so at least 3 friends sold less than 20 bars (a, b and 18). Sufficient.

(2) The average (arithmetic mean) of the number of bars sold by Jan's 5 friends is 12 --> total number of bars sold by Jan's 5 friends is 5*12=60. Can there be a case where at least 3 of Jan's friends sold 20 or more bars? No, since in this case the total number of bars sold by his friends would be more than 60 (20+20+20+1+1=62). Sufficient.

Answer: D.


Hi Bunuel,
The question asked is if Jan sold more candy bars than each of at least 3 of his friends:
In statement 2.  I analyzed the following situations:
12+12+12+12+12=60 which would render a NO answer; and
1+1+12+23+23=60 which would render a YES answer.

Why is this wrong?
How come you negated the question asked to get to the right answer?

­
{12, 12, 12, 12, 12} also gives a YES answer to the question: Jan sold more candy bars than each of at least 3 of his friend.­

­Thanks @Bunuel. 
For some reason I interpreted 'than each of at least 3 of his friends' as the sum of the number of candy bars that each of at least 3 of his friends had..
Twist in the brain..! 
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Re: Jan and 5 of his friends sold candy bars to raise money for their scho [#permalink]
28 Feb 2024, 07:38
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