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

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

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New post 05 Feb 2015, 09:13
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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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New post 05 Feb 2015, 09:50
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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New post 05 Feb 2015, 18:30
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.

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

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New post 09 Feb 2015, 05:37
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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New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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Re: What is the mean of the exams taken by a group of students?   [#permalink] 07 Mar 2019, 10:33
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