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01 Jan 2020, 03:08
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
66% (02:03) correct
34%
(02:48)
wrong
based on 177
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Consider the set S = {2, 3, 4, ...., 2n+1), where n is a positive integer larger than 2007. Define X as the average of the odd integers in S and Y as the average of the even integers in S. What is the value of X – Y?
(A) 0
(B) 1
(C) 2008
(D) n/2
(E) (n + 1)/(2n)
(A) 0
(B) 1
(C) 2008
(D) n/2
(E) (n + 1)/(2n)
firas92
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Joined: 16 Jan 2019
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Location: India
Concentration: General Management
Schools: Tepper '23 (M$) Foster '23 (D)
GMAT 1: 740 Q50 V40
WE:Sales (Other)
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01 Jan 2020, 06:41
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Even set = {2,4,6,8,...2n}
Odd set = {3,5,7,9,...2n+1}
By property, if a certain number x is added to all elements of a set, the average of the set increases by x
By this property, since the odd set is just the even set with 1 added to all elements, the average of the odd set must be 1 greater than the average of the even set
So X-Y=1
Answer is (B)
Posted from my mobile device
Odd set = {3,5,7,9,...2n+1}
By property, if a certain number x is added to all elements of a set, the average of the set increases by x
By this property, since the odd set is just the even set with 1 added to all elements, the average of the odd set must be 1 greater than the average of the even set
So X-Y=1
Answer is (B)
Posted from my mobile device
General Discussion
01 Jan 2020, 06:23
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Take smaller values of n, such as n=5 or n=6.
Notice that n=5 => X=7,Y=6
n=6 => X=8, Y=7.
As we can see, X=n+2 and Y=n+1.
Hence, X-Y = 1.
Option B
Notice that n=5 => X=7,Y=6
n=6 => X=8, Y=7.
As we can see, X=n+2 and Y=n+1.
Hence, X-Y = 1.
Option B
