Set K consists of a finite number of consecutive odd

Question

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.

Bunuel · Accepted Answer

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.

Augustus · Answer

(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.

Augustus · Answer

D'oh!

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

gardnej369 · Answer

What about this set: (-5,-3,-1,1,3,5,7). Y-X = 12 in this case.

Bunuel · Answer

There are 7 numbers in your set, not 8.

BillyZ · Answer

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

Source : Magoosh

Bunuel · Answer

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

BrentGMATPrepNow · Answer

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

nick1816 · Answer

Statement 1= tells us there are even number of turns and middle two terms are -35 and -37. But there can be possibly infinite such sequences.
For Example- {-37,-35}, {-39,-37,-35.-33} and so on
y-x can have infinite values

Statement 2 - There are 8 terms
y=x+(k-1)2
y-x=7*2=14
Sufficient

TarunKumar1234 · Answer

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.
(x +y) = -36*2. or, x + x +2(n-1) =-36*2 or, 2x +2(n-1) = -72 Not Sufficient.

(2) There are 8 numbers in set K.
y = x +2(n-1) or, y-x = 2(n-1) = 2*7 =14. Sufficient

So, It is B.

Vivek1707 · Answer

DS Question Analysis

Set (K) consists of a finite number of consecutive odd integers
If (x) is the smallest number in (K) and (y) is the greatest, what is (y - x)?

Statement (1)

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

Insufficient

Knowing the average alone does not determine the number of terms in the set.
Different sets of consecutive odd integers can share the same average but have different ranges.

For example:
(-37, -35) → average = –36 → (y - x = 2)
(-39, -37, -35, -33) → average = –36 → (y - x = 6)

So statement (1) is not sufficient.

Statement (2)
There are 8 numbers in set (K).

Key observation:
For a set of consecutive odd integers, the difference between the largest and smallest values depends only on the number of terms, not on the actual values.

Consecutive odd integers differ by 2
With 8 numbers, there are 7 equal gaps

Therefore:
y - x = 7 and 7 times 2 = 14

No computation of actual numbers is required.

One-Line Intuition
> In any set of consecutive numbers, the range equals *(number of terms − 1) × common difference* — so once the count is known, the endpoints’ difference is fixed.

Set K consists of a finite number of consecutive odd

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GMAT Data Sufficiency (DS) Questions

Set K consists of a finite number of consecutive odd

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