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# If each member of a 10 person class earned an integer score between 1

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Math Expert
Joined: 02 Sep 2009
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If each member of a 10 person class earned an integer score between 1  [#permalink]

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19 Jun 2018, 23:52
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15% (low)

Question Stats:

74% (01:27) correct 26% (01:39) wrong based on 113 sessions

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If each member of a 10 person class earned an integer score between 1 and 10, inclusive, on a recent quiz and the range between the highest and lowest scores was 8, what is the lowest average score possible for the class?

A. 1.2
B. 1.8
C. 2
D. 2.6
E. 4.5

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Re: If each member of a 10 person class earned an integer score between 1  [#permalink]

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20 Jun 2018, 00:01
Bunuel wrote:
If each member of a 10 person class earned an integer score between 1 and 10, inclusive, on a recent quiz and the range between the highest and lowest scores was 8, what is the lowest average score possible for the class?

A. 1.2
B. 1.8
C. 2
D. 2.6
E. 4.5

As we're asked about 'the lowest possible value' we'll look at the extremes.

We're looking for the lowest possible average so we want as many students as possible to have the minimum value - 1.
Since 1 studnet must have a score of 1 + 8 = 9, this means that we can give 9 students a score of 1 and 1 a score of 9.
This sums to 1*9 +9*1 = 18.
Dividing by the number of students gives the average: 18/10 = 1.8

(B) is our answer.
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If each member of a 10 person class earned an integer score between 1  [#permalink]

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20 Jun 2018, 02:59

Solution

Given:
$$• There are 10 persons in a class. • The score of each person of the class is between 1 and 10, inclusive. • The range of the score earned by the all the 10 persons is 8. To find: • We need to find the the lowest averagSe score possible for the class.$$

Approach and Working:

We will get the lowest average of the class if all the persons score the lowest possible score.
Between 1 to 10, the lowest score is 1."]"

Hence, nine students of the class scores 1 and one student scores 9 as range must be 9.
• Thus, average= 9*1+1*9/10= 18/10= 1.8
Hence, option B is the correct answer."
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If each member of a 10 person class earned an integer score between 1  [#permalink]

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21 Jul 2018, 09:30
EgmatQuantExpert wrote:

Solution

Given:
$$• There are 10 persons in a class. • The score of each person of the class is between 1 and 10, inclusive. • The range of the score earned by the all the 10 persons is 8. To find: • We need to find the the lowest averagSe score possible for the class.$$

Approach and Working:

We will get the lowest average of the class if all the persons score the lowest possible score.
Between 1 to 10, the lowest score is 1."]"

Hence, nine students of the class scores 1 and one student scores 9 as range must be 9.
• Thus, average= 9*1+1*9/10= 18/10= 1.8
Hence, option B is the correct answer."

Thanks for the explanation but the question says that each student in the class earned an INTEGER score... From this line I expected that even the extremes of the scores should be integers. Or am I wrong?
Please Bunuel, help me out.
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If each member of a 10 person class earned an integer score between 1  [#permalink]

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21 Jul 2018, 10:13
1
Kem12 wrote:

Thanks for the explanation but the question says that each student in the class earned an INTEGER score... From this line I expected that even the extremes of the scores should be integers. Or am I wrong?
Please Bunuel, help me out.
Posted from my mobile device

Hi Kem12,

I think that you are confused by this: average= 9*1+1*9/10= 18/10= 1.8. Indeed it should be average= (9*1+1*9)/10= 18/10= 1.8. The second extreme is not a fraction.
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Re: If each member of a 10 person class earned an integer score between 1  [#permalink]

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22 Jul 2018, 00:56
Hero8888 wrote:
Kem12 wrote:

Thanks for the explanation but the question says that each student in the class earned an INTEGER score... From this line I expected that even the extremes of the scores should be integers. Or am I wrong?
Please Bunuel, help me out.
Posted from my mobile device

Hi Kem12,

I think that you are confused by this: average= 9*1+1*9/10= 18/10= 1.8. Indeed it should be average= (9*1+1*9)/10= 18/10= 1.8. The second extreme is not a fraction.

Thanks. I now understand.
Re: If each member of a 10 person class earned an integer score between 1   [#permalink] 22 Jul 2018, 00:56
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