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Two sets of 4

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by sanju09 » Mon Mar 05, 2012 1:55 am
Two sets of 4 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?
A. 4
B. 7
C. 8
D. 12
E. 15
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by krusta80 » Mon Mar 05, 2012 4:28 am
sanju09 wrote:Two sets of 4 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?
A. 4
B. 7
C. 8
D. 12
E. 15
The only way that the overlap can be exactly one is if the last integer of one set is the first of the other...

x+(x+1)+(x+2)+(x+3) = (x+3)+(x+4)+(x+5)+(x+6) - y

4x+6 = 4x+18-y

y=12

D
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by Brent@GMATPrepNow » Mon Mar 05, 2012 5:40 am
sanju09 wrote:Two sets of 4 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?
A. 4
B. 7
C. 8
D. 12
E. 15
Another approach is to find 2 sets that meet the given criteria.
For example:
Set A = {1, 2, 3, 4}
Set B = {4, 5, 6, 7}

Sum of set A = 10
Sum of set B = 22

Difference = 12 = D

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Brent
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