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# What is the mean of the exams taken by a group of students?

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Math Expert
Joined: 02 Sep 2009
Posts: 61283
What is the mean of the exams taken by a group of students?  [#permalink]

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05 Feb 2015, 08:13
00:00

Difficulty:

25% (medium)

Question Stats:

71% (00:52) correct 29% (01:09) wrong based on 110 sessions

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What is the mean of the exams taken by a group of students?

(1) The score 3 standard deviations above the mean is 95
(2) The score 2 standard deviations below the mean is 64

Kudos for a correct solution.

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Re: What is the mean of the exams taken by a group of students?  [#permalink]

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05 Feb 2015, 08:50
Bunuel wrote:
What is the mean of the exams taken by a group of students?

(1) The score 3 standard deviations above the mean is 95
(2) The score 2 standard deviations below the mean is 64

Kudos for a correct solution.

I'd pick C.

from st1: m+3SD=95 from st2: m-2SD=64 together we can determine m.
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Re: What is the mean of the exams taken by a group of students?  [#permalink]

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05 Feb 2015, 17:30
Bunuel wrote:
What is the mean of the exams taken by a group of students?

(1) The score 3 standard deviations above the mean is 95
(2) The score 2 standard deviations below the mean is 64

Kudos for a correct solution.

let std dev =x

Statement 1:
mean + 3x = 95
the mean or x could both change depending on the value of the other
Insufficient

Statement 1:
mean - 2x = 64
same as above
Insufficient

Combined, we have 2 equations 2 variables and we can eliminate x, resulting in a unique value for the mean.

Math Expert
Joined: 02 Sep 2009
Posts: 61283
Re: What is the mean of the exams taken by a group of students?  [#permalink]

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09 Feb 2015, 04:37
Bunuel wrote:
What is the mean of the exams taken by a group of students?

(1) The score 3 standard deviations above the mean is 95
(2) The score 2 standard deviations below the mean is 64

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

The correct response is (C).

While this data sufficiency employs statistical terms, it is an algebra question that can be solved using the technique of simultaneous equations.

Statement (1) can be expressed as: Mean + 3 Standard Deviations = 95. Since this one equation has two unknowns it is insufficient to determine the mean.
Statement (2) can be expressed as: Mean – 2 Standard Deviations = 60. Since this one equation has two unknowns it is insufficient to determine the mean.
If you combine the two, you have two equations with two unknowns:

Mean + 3 Standard Deviations = 95
Mean – 2 Standard Deviations = 60 By subtracting the second equation from the first one, you get:

5 Standard Deviations = 35

By dividing both sides by 5, you get:

1 Standard Deviation = 7

By substituting this value into either equation you get the mean.

The mean is 74, making (C) the correct response.
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Re: What is the mean of the exams taken by a group of students?  [#permalink]

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07 Mar 2019, 09:33
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Re: What is the mean of the exams taken by a group of students?   [#permalink] 07 Mar 2019, 09:33
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