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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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New post 25 Oct 2009, 01:13
2
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A
B
C
D
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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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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
2
1
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
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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: Set K consists of a finite number of consecutive odd  [#permalink]

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New post 08 Feb 2018, 11:17
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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.


Target question: What is the value of y - x?

Given: Set K consists of a finite number of consecutive odd integers

Statement 1: The average (arithmetic mean) of set K is –36
There's a nice rule that says, "In a set where the numbers are equally spaced, the mean will equal the median."
For example, in each of the following sets, the mean and median are equal:
{7, 9, 11, 13, 15}
{-1, 4, 9, 14}
{3, 4, 5, 6}

Set K consists of consecutive odd integers, so the values are EQUALLY SPACED.
Since the mean of set K is –36, we know that the MEDIAN is -36 as well.
HOWEVER, we don't know the number of elements in set K.
So, consider these two possible sets that yield conflicting answers to the target question:
Case a: set K = {-37, -35}, so the average is -36. In this case y - x = -35 - (-37) = 2
Case b: set K = {-39, -37, -35, -33}, so the average is -36. In this case y - x = -33 - (-39) = 6
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: There are 8 numbers in set K.
We already know that the numbers are consecutive ODD integers.
This means that each number in the set is 2 GREATER than the one before it.
So, if we let x = the smallest (1st) value in set K
Then x + 2 = the 2nd value in set K
And x + 4 = the 3rd value in set K
And x + 6 = the 4th value in set K
And x + 8 = the 5th value in set K
And x + 10 = the 6th value in set K
And x + 12 = the 7th value in set K
And x + 14 = the 8th value in set K
In other words, x + 14 = y, the largest value in set K

So, y - x = (x + 14) - x = 14
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent
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Re: Set K consists of a finite number of consecutive odd &nbs [#permalink] 08 Feb 2018, 11:17
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