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10 Feb 2020, 02:25
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A, B, C, D, and E are five friends. The sums of the weights of each group of four of them are 132, 138, 113, 131, and 126. What is the positive difference of the weights of the heaviest and lightest among them?
A. 25
B. 26
C. 27
D. 28
E. 29
Are You Up For the Challenge: 700 Level Questions
shameekv1989
GMAT 3: 720 Q50 V38
Posts: 820
10 Feb 2020, 08:20
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A, B, C, D, and E are five friends. The sums of the weights of each group of four of them are 132, 138, 113, 131, and 126. What is the positive difference of the weights of the heaviest and lightest among them?
A. 25
B. 26
C. 27
D. 28
E. 29
Let a<b<c<d<e
a+b+c+d = 113 -> i) (Lowest total will be with the sum of weights of friends with lowest weights)
b+c+d+e = 138 -> ii) (Highest total will be with the sum of weights of friends with highest weights)
we need to find e-a -> Subtracting ii) from i) -> 138-113 = 25 -> Answer - A
A. 25
B. 26
C. 27
D. 28
E. 29
Let a<b<c<d<e
a+b+c+d = 113 -> i) (Lowest total will be with the sum of weights of friends with lowest weights)
b+c+d+e = 138 -> ii) (Highest total will be with the sum of weights of friends with highest weights)
we need to find e-a -> Subtracting ii) from i) -> 138-113 = 25 -> Answer - A
General Discussion
10 Feb 2020, 06:40
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Total combinations : 5C4= 5!/4!(5-1)!= 5!/4!= 5
--> A+B+C+D=132
--> A+B+C+E=138
--> A+B+D+E=113
--> A+C+D+E=131
--> B+C+D+E=126
----------------------
4*(A+B+C+D+E)= 132+138+113+131+126= 640
A+B+C+D+E= 160
Heaviest weight:
A+B+C+D+E= 160
A+B+D+E=113
--> C= 160-113= 47
Lightest weight:
A+B+C+D+E= 160
A+B+C+E=138
--> D= 160 -138= 22
The difference of the weights of the heaviest and lightest= 47-22 = 25
The answer is A.
--> A+B+C+D=132
--> A+B+C+E=138
--> A+B+D+E=113
--> A+C+D+E=131
--> B+C+D+E=126
----------------------
4*(A+B+C+D+E)= 132+138+113+131+126= 640
A+B+C+D+E= 160
Heaviest weight:
A+B+C+D+E= 160
A+B+D+E=113
--> C= 160-113= 47
Lightest weight:
A+B+C+D+E= 160
A+B+C+E=138
--> D= 160 -138= 22
The difference of the weights of the heaviest and lightest= 47-22 = 25
The answer is A.
