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A gymnast's score for a routine is the average of the scores awarded

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A gymnast's score for a routine is the average of the scores awarded  [#permalink]

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New post 07 Feb 2018, 05:41
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A gymnast's score for a routine is the average of the scores awarded by ten judges on a scale ranging from 0 to 10. If the first seven judges have awarded the gymnast scores of 7, 8, 7.5, 9, 8.2, 8.5, and 7.8, and she does not receive a score lower than 6 from any of the other judges, then her final score for the routine will be

(A) greater than 8.0

(B) greater than 7.8

(C) greater than or equal to 7.8

(D) between 7.0 and 7.4

(E) greater than or equal to 7.4

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Re: A gymnast's score for a routine is the average of the scores awarded  [#permalink]

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New post 07 Feb 2018, 06:24
Bunuel wrote:
A gymnast's score for a routine is the average of the scores awarded by ten judges on a scale ranging from 0 to 10. If the first seven judges have awarded the gymnast scores of 7, 8, 7.5, 9, 8.2, 8.5, and 7.8, and she does not receive a score lower than 6 from any of the other judges, then her final score for the routine will be

(A) greater than 8.0

(B) greater than 7.8

(C) greater than or equal to 7.8

(D) between 7.0 and 7.4

(E) greater than or equal to 7.4


We'll show two approaches to solution.

The first is the standard, Precise, calculation.
If the minimum is 6 then the minimal sum of all scores is 7+8 = 15 + 7.5 = 22.5 + 9 = 31.5 + 8.2 = 39.7 +8.5 = 48.2 + 7.8 = 56 + 6*3 = 74
Then her average is at least 7.4.
(E) is our answer.

The Alternative approach relies on the fact that the answers all involve overlapping ranges:
If (A) were true then (B), (C) and (E) would also be true.
Since there is only one correct answer, (A) is impossible.
Similarly, (B) and (C) are also impossible
We are left with (D) and (E), both of which have 7.4 in common.
Looking at our numbers, almost all of them are above 7.4.
Even without calculating, we can SEE that if the 3 judges gave a maximal score of 10, the average would definitely be above 7.4
(D) is also eliminated.

(E) is our answer.
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Re: A gymnast's score for a routine is the average of the scores awarded  [#permalink]

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New post 07 Feb 2018, 11:14
Bunuel wrote:
A gymnast's score for a routine is the average of the scores awarded by ten judges on a scale ranging from 0 to 10. If the first seven judges have awarded the gymnast scores of 7, 8, 7.5, 9, 8.2, 8.5, and 7.8, and she does not receive a score lower than 6 from any of the other judges, then her final score for the routine will be

(A) greater than 8.0

(B) greater than 7.8

(C) greater than or equal to 7.8

(D) between 7.0 and 7.4

(E) greater than or equal to 7.4
Attachment:
Capture.PNG
Capture.PNG [ 5.11 KiB | Viewed 241 times ]

Answer must be (E)
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Re: A gymnast's score for a routine is the average of the scores awarded  [#permalink]

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New post 09 Feb 2018, 10:55
Bunuel wrote:
A gymnast's score for a routine is the average of the scores awarded by ten judges on a scale ranging from 0 to 10. If the first seven judges have awarded the gymnast scores of 7, 8, 7.5, 9, 8.2, 8.5, and 7.8, and she does not receive a score lower than 6 from any of the other judges, then her final score for the routine will be

(A) greater than 8.0

(B) greater than 7.8

(C) greater than or equal to 7.8

(D) between 7.0 and 7.4

(E) greater than or equal to 7.4


We are given the scores of 7, 8, 7.5, 9, 8.2, 8.5, and 7.8, and let’s say the last 3 judges all award her scores of 6.

The sum of all the scores would be:

7 + 8 + 7.5 + 9 + 8.2 + 8.5 + 7.8 + 6 + 6 + 6

56 + 18 = 74

Average = 74/10 = 7.4

Thus the average would be greater than or equal to 7.4.

Answer: E
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Re: A gymnast's score for a routine is the average of the scores awarded &nbs [#permalink] 09 Feb 2018, 10:55
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