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

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Intern
Joined: 11 Nov 2013
Posts: 16
GMAT Date: 12-26-2013
GPA: 3.6
WE: Consulting (Computer Software)
\$150 in prize money is going to be split among 6 contestants  [#permalink]

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26 Nov 2013, 17:02
2
6
00:00

Difficulty:

65% (hard)

Question Stats:

63% (02:30) correct 37% (02:51) wrong based on 138 sessions

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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.
Director
Joined: 25 Apr 2012
Posts: 676
Location: India
GPA: 3.21
Re: \$150 in prize money is going to be split among 6 contestants  [#permalink]

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26 Nov 2013, 23:36
6
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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##### General Discussion
Intern
Joined: 11 Nov 2013
Posts: 16
GMAT Date: 12-26-2013
GPA: 3.6
WE: Consulting (Computer Software)
Re: \$150 in prize money is going to be split among 6 contestants  [#permalink]

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26 Nov 2013, 17:04
2
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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26 Nov 2013, 23:55
1
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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\$150 in prize money is going to be split among 6 contestants  [#permalink]

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

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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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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?
Intern
Joined: 27 Sep 2017
Posts: 10
Re: \$150 in prize money is going to be split among 6 contestants  [#permalink]

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05 Mar 2018, 08:17
1
I don't like this question because it is very wordy. However here is my solution;

Statement 2 means that the difference between any two values in the set must be greater than or equal to 10. Assume that the values are A,B,C,D,E & F "where A is the greatest value and F is the least value"

1. A-B>=10
2. B-C>=10
3. C-D>=10
4. D-E>=10
5. E-F>=10

Take the Sum of Inequalities from 2 through 5 , you will end up with B-F>=40 -------> B>=F+40 . So "B" must be at least 40

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

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11 Apr 2019, 07:05
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Re: \$150 in prize money is going to be split among 6 contestants   [#permalink] 11 Apr 2019, 07:05
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