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$150 in prize money is going to be split among 6 contestants

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$150 in prize money is going to be split among 6 contestants [#permalink]

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$150 in prize money is going to be split among 6 contestants in a competition at a charity event. The person in first place receives the most money, the person in second place receives the second most, the person in third place receives the third most, and so on. Did the person in second place receive at least $40 of the prize money?

(1) The person in first place won $50

(2) No individual prize was within $10 of another prize.
[Reveal] Spoiler: OA

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Re: $150 in prize money is going to be split among 6 contestants [#permalink]

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New post 26 Nov 2013, 17:04
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A4G wrote:
$150 in prize money is going to be split among 6 contestants in a competition at a charity event. The person in first place receives the most money, the person in second place receives the second most, the person in third place receives the third most, and so on. Did the person in second place receive at least $40 of the prize money?

(1) The person in first place won $50

(2) No individual prize was within $10 of another prize.


Statement 1:
If the person in first place received $50, then the remaining 5 contestants need to account for $100 of prize money. This can be done with the 2nd person getting at least $40 (say 40, 35, 10, 8, 7) or getting less than $40 (say 35, 25, 20, 12, 8). Statement (1) is not sufficient.

Statement 2:
If no individual prize was within $10 of another prize then the only possibility is 0,10,20,30,40,and 50 and statement (2) is sufficient by itself.

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Re: $150 in prize money is going to be split among 6 contestants [#permalink]

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New post 26 Nov 2013, 23:36
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A4G wrote:
$150 in prize money is going to be split among 6 contestants in a competition at a charity event. The person in first place receives the most money, the person in second place receives the second most, the person in third place receives the third most, and so on. Did the person in second place receive at least $40 of the prize money?

(1) The person in first place won $50

(2) No individual prize was within $10 of another prize.



Let the 6 contestants be S1,S2,S3,S4,S5 and S6. We need to find if S2 greater then or equal to 40

From St 1 we have S1 = 50
Then S2 +S3+S4+S5+S6 = 100

If S2 = 40, S3 = 20, S4 =15, S5= 13, S6= 12
If S2= 35 , S3 = 25,S4= 20, S5=11,S6 =9

Since 2 cases are possible A and D can be ruled out

From St 2, we have that S1-S2>10, S2-S3>10 ,S3-S4>10, S4-S5>10 and S5-S6>10

-----> S5>10+ S6
S4>20+ S6
S3>30+S6
S2>40+S6
S1>50+S6

Now S6 can be greater than or equal to 0 that means S2 =40 +S6 or greater then equal to 40.

Hence B Sufficient
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Re: $150 in prize money is going to be split among 6 contestants [#permalink]

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New post 26 Nov 2013, 23:55
Actually with statement 2 there are several possibilities... According to statement 2, it is not required that the first place person receive $50 (which is a condition given by statement 1). This a common ploy that the GMAT uses. Although in this case, it does not lead to an erroneous answer, it very well can in some other case.

The reasoning behind statement 2 is:

The amount received by each contestant is different as stated by the question prompt.

If second place receives less than 40, let's say 39, third place will receive at most 29, fourth place will receive at most 19, fifth place will receive at most 9 but sixth place cannot receive 0 since the difference between 0 and 9 is less than 10.

So second place has to receive at least 40.
A4G wrote:
A4G wrote:
$150 in prize money is going to be split among 6 contestants in a competition at a charity event. The person in first place receives the most money, the person in second place receives the second most, the person in third place receives the third most, and so on. Did the person in second place receive at least $40 of the prize money?

(1) The person in first place won $50

(2) No individual prize was within $10 of another prize.


Statement 1:
If the person in first place received $50, then the remaining 5 contestants need to account for $100 of prize money. This can be done with the 2nd person getting at least $40 (say 40, 35, 10, 8, 7) or getting less than $40 (say 35, 25, 20, 12, 8). Statement (1) is not sufficient.

Statement 2:
If no individual prize was within $10 of another prize then the only possibility is 0,10,20,30,40,and 50 and statement (2) is sufficient by itself.

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Re: $150 in prize money is going to be split among 6 contestants [#permalink]

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$150 in prize money is going to be split among 6 contestants [#permalink]

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New post 19 Apr 2016, 19:00
A4G wrote:
$150 in prize money is going to be split among 6 contestants in a competition at a charity event. The person in first place receives the most money, the person in second place receives the second most, the person in third place receives the third most, and so on. Did the person in second place receive at least $40 of the prize money?

(1) The person in first place won $50

(2) No individual prize was within $10 of another prize.


1. A: 1-50, 2-30, 3-29, 4-28, 5-10, 6-3 - no or B: 1-50, 2-45, 3-40, 4-9, 5-6, 6-3. Yes. - 1 alone not sufficient AD out.

2. difference between prizes is more than 10$.
suppose 6th got 1$. 5th must have received at least 12$, 4th must have received at least 23$, 3rd must have received at least 34$, and second must have received at least 45$. so 2 alone is sufficient.

B.

on the other hand..statements "if taken together" gets us conflicting results.
if 1st received 50, then second must have received less than 40...i know we are not supposed to mix the two statements if at least one is sufficient, but the statements MUST NOT CONTRADICT each other!!!

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Re: $150 in prize money is going to be split among 6 contestants [#permalink]

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New post 19 Apr 2016, 20:49
The question is really badly worded and wrong

According to "b" part of the question "No individual prize was within $10 of another prize".
Let's assume that the lowest prize is X, then second prize is more than X+10, the third is more than X+20 and so on. The Sum of all prizes must be more than 6X+150 or we can put it in this way:
6X+150<150
6X<0
x<0

But X cannot be less than zero.

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Re: $150 in prize money is going to be split among 6 contestants [#permalink]

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New post 20 Apr 2016, 12:20
MacFauz wrote:
Actually with statement 2 there are several possibilities... According to statement 2, it is not required that the first place person receive $50 (which is a condition given by statement 1). This a common ploy that the GMAT uses. Although in this case, it does not lead to an erroneous answer, it very well can in some other case.

The reasoning behind statement 2 is:

The amount received by each contestant is different as stated by the question prompt.

If second place receives less than 40, let's say 39, third place will receive at most 29, fourth place will receive at most 19, fifth place will receive at most 9 but sixth place cannot receive 0 since the difference between 0 and 9 is less than 10.

So second place has to receive at least 40.
A4G wrote:
A4G wrote:
$150 in prize money is going to be split among 6 contestants in a competition at a charity event. The person in first place receives the most money, the person in second place receives the second most, the person in third place receives the third most, and so on. Did the person in second place receive at least $40 of the prize money?

(1) The person in first place won $50

(2) No individual prize was within $10 of another prize.


Statement 1:
If the person in first place received $50, then the remaining 5 contestants need to account for $100 of prize money. This can be done with the 2nd person getting at least $40 (say 40, 35, 10, 8, 7) or getting less than $40 (say 35, 25, 20, 12, 8). Statement (1) is not sufficient.

Statement 2:
If no individual prize was within $10 of another prize then the only possibility is 0,10,20,30,40,and 50 and statement (2) is sufficient by itself.



$150 has to be split among 6 contestants, how can we assume the 6th contestant gets 0.?? Does this not mean that the 6th contestant gets at least $1?

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Re: $150 in prize money is going to be split among 6 contestants [#permalink]

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New post 25 Sep 2017, 07:44
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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Re: $150 in prize money is going to be split among 6 contestants   [#permalink] 25 Sep 2017, 07:44
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$150 in prize money is going to be split among 6 contestants

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