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Set K consists of a finite number of consecutive odd

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Set K consists of a finite number of consecutive odd [#permalink]

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Set K consists of a finite number of consecutive odd integers. If x is the smallest number in K and y is the greatest, then y - x =

(1) The average (arithmetic mean) of set K is –36.

(2) There are 8 numbers in set K.
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Re: stats [#permalink]

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New post 25 Oct 2009, 01:57
Economist wrote:
Set K consists of a finite number of consecutive odd integers. If x is the smallest number in K and y is the greatest, then y - x =

(1) The average (arithmetic mean) of set K is –36.

(2) There are 8 numbers in set K.


(1) Insufficient. It could be (-37,-35), (-39,-37,-35,-33), etc.
(2) Insufficient. It could be any 8 (consecutive odd) numbers.

Combining information the set must be (-43,-41,-39,-37,-35,-33,-31,-29). The trick here is that they are consecutive odd numbers.

y-x is -29-(-43) = 14 and the answer is C.

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Set K consists of a finite number of consecutive odd [#permalink]

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New post 25 Oct 2009, 14:12
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Economist wrote:
Set K consists of a finite number of consecutive odd integers. If x is the smallest number in K and y is the greatest, then y - x =

(1) The average (arithmetic mean) of set K is –36.

(2) There are 8 numbers in set K.


Set K consists of a finite number of consecutive odd integers. If x is the smallest number in K and y is the greatest, then y - x =

From the stem: first term x, las t term y --> as we have consecutive odd integers then y=x+2(n-1), where n is the number of terms in the set. --> y-x=x+2(n-1)-x=2(n-1)

Basically we should find the number of terms to calculate y-x.

(1) The average=-36, --> (x+y)/2=-36 --> (2x+2(n-1))=-36 --> x+n-1=-36. Multiple choices for x and n. Not sufficient.

The mean of consecutive ODD integers is ODD, when # of terms is ODD.
The mean of consecutive ODD integers is EVEN, when # of terms is EVEN.
So, as -36 is even, that is why the mean =(first term+last term)/2=-36

(2) n=8. --> y-x=2(n-1)=14. Sufficient

Answer: B.
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Re: stats [#permalink]

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New post 25 Oct 2009, 15:23
D'oh!

I keep falling into these traps. Hopefully, practice will allow me to master them eventually...

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Re: Set K consists of a finite number of consecutive odd [#permalink]

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New post 30 Mar 2017, 15:22
What about this set: (-5,-3,-1,1,3,5,7). Y-X = 12 in this case.

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Set K consists of a finite number of consecutive odd [#permalink]

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New post 30 Mar 2017, 21:46

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Set K consists of a finite number of consecutive odd [#permalink]

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New post 30 Mar 2017, 23:26
Bunuel wrote:
Economist wrote:
Set K consists of a finite number of consecutive odd integers. If x is the smallest number in K and y is the greatest, then y - x =

(1) The average (arithmetic mean) of set K is –36.

(2) There are 8 numbers in set K.


From the stem: first term x, las t term y --> as we have consecutive odd integers then y=x+2(n-1), where n is the number of terms in the set. --> y-x=x+2(n-1)-x=2(n-1)

Basically we should find the number of terms to calculate y-x.

(1) The average=-36, --> (x+y)/2=-36 --> (2x+2(n-1))=-36 --> x+n-1=-36. Multiple choices for x and n. Not sufficient.

The mean of consecutive ODD integers is ODD, when # of terms is ODD.
The mean of consecutive ODD integers is EVEN, when # of terms is EVEN.
So, as -36 is even, that is why the mean =(first term+last term)/2=-36

(2) n=8. --> y-x=2(n-1)=14. Sufficient

Answer: B.


Bunuel, Could you please help to explain or elaborate the statement as highlighted in red? y=x+2(n-1)

Source : Magoosh
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Re: Set K consists of a finite number of consecutive odd [#permalink]

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New post 30 Mar 2017, 23:34
ziyuen wrote:
Bunuel wrote:
Economist wrote:
Set K consists of a finite number of consecutive odd integers. If x is the smallest number in K and y is the greatest, then y - x =

(1) The average (arithmetic mean) of set K is –36.

(2) There are 8 numbers in set K.


From the stem: first term x, las t term y --> as we have consecutive odd integers then y=x+2(n-1), where n is the number of terms in the set. --> y-x=x+2(n-1)-x=2(n-1)

Basically we should find the number of terms to calculate y-x.

(1) The average=-36, --> (x+y)/2=-36 --> (2x+2(n-1))=-36 --> x+n-1=-36. Multiple choices for x and n. Not sufficient.

The mean of consecutive ODD integers is ODD, when # of terms is ODD.
The mean of consecutive ODD integers is EVEN, when # of terms is EVEN.
So, as -36 is even, that is why the mean =(first term+last term)/2=-36

(2) n=8. --> y-x=2(n-1)=14. Sufficient

Answer: B.


Bunuel, Could you please help to explain or elaborate the statement as highlighted in red? y=x+2(n-1)

Source : Magoosh


It's the formula of nth term of arithmetic progression. Check here: https://gmatclub.com/forum/math-sequenc ... 01891.html
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 133146 [0], given: 12415

Re: Set K consists of a finite number of consecutive odd   [#permalink] 30 Mar 2017, 23:34
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Set K consists of a finite number of consecutive odd

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