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If the average (arithmetic mean) of n consecutive odd intege

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If the average (arithmetic mean) of n consecutive odd intege [#permalink] New post 30 Jan 2014, 22:40
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

If the average (arithmetic mean) of n consecutive odd integers is 10, what is the least of the integers?

(1) The range of the n integers is 14.
(2) The greatest of the n integers is 17.

Data Sufficiency
Question: 66
Category: Arithmetic Statistics
Page: 157
Difficulty: 600


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Re: If the average (arithmetic mean) of n consecutive odd intege [#permalink] New post 30 Jan 2014, 22:40
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SOLUTION

If the average (arithmetic mean) of n consecutive odd integers is 10, what is the least of the integers?

Odd consecutive integers is an evenly spaced set. For any evenly spaced set the mean equals to the average of the first and the last terms, so in our case mean=10=\frac{x_1+x_{n}}{2} --> x_1+x_{n}=20. Question: x_1=?

(1) The range of the n integers is 14 --> the range of a set is the difference between the largest and smallest elements of a set, so x_{n}-x_1=14 --> solving for x_1 --> x_1=3. Sufficient.

(2) The greatest of the n integers is 17 --> x_n=17 --> x_1+17=20 --> x_1=3. Sufficient.

Answer: D.

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Re: If the average (arithmetic mean) of n consecutive odd intege [#permalink] New post 30 Jan 2014, 23:35
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What we know:
If n consecutive integers have arithmetic mean of 10; those numbers are distributed either side of 10 perfectly symmetrically.


Statement (1)


Range is the difference between the greatest and the least numbers in the series.
If the range is known the least of these integers must be less than the mean, i.e. 10 - (14/2) = 3 (Note we don't really need to calculate this... to know we can is sufficient.)


Statement (2)


Similarly, the distance from the greatest number to mean equals to the distance from mean to the least number. So knowing the greatest number also sufficient to calculate the least number. (in this case 10 - (17 - 10) = 3)


The answer is D : Both Statement 1 and Statement 2 are sufficient ALONE .

Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If the average (arithmetic mean) of n consecutive odd integers is 10, what is the least of the integers?

(1) The range of the n integers is 14.
(2) The greatest of the n integers is 17.

Data Sufficiency
Question: 66
Category: Arithmetic Statistics
Page: 157
Difficulty: 600


GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

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2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
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Re: If the average (arithmetic mean) of n consecutive odd intege [#permalink] New post 31 Jan 2014, 01:34
Ans. D
Let the series start from x=>x,(x+2),(x+4),...(x+k) id the series.
Average=[x+(x+k)]/2=10(1)
x+(x+k)=20=>2x+k=20

Given in S1, x+k-x=14=>k=14.We can find out x,the smallest integer.Sufficient

From S2: x+k=17
By putting this value in (1),we can get x,the answer.
Sufficient.
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Re: If the average (arithmetic mean) of n consecutive odd intege [#permalink] New post 01 Feb 2014, 09:14
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SOLUTION

If the average (arithmetic mean) of n consecutive odd integers is 10, what is the least of the integers?

Odd consecutive integers is an evenly spaced set. For any evenly spaced set the mean equals to the average of the first and the last terms, so in our case mean=10=\frac{x_1+x_{n}}{2} --> x_1+x_{n}=20. Question: x_1=?

(1) The range of the n integers is 14 --> the range of a set is the difference between the largest and smallest elements of a set, so x_{n}-x_1=14 --> solving for x_1 --> x_1=3. Sufficient.

(2) The greatest of the n integers is 17 --> x_n=17 --> x_1+17=20 --> x_1=3. Sufficient.

Answer: D.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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.


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Re: If the average (arithmetic mean) of n consecutive odd intege   [#permalink] 01 Feb 2014, 09:14
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