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Five boxes together weigh 100 pounds. What is the median weight of the

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Bunuel
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Five boxes together weigh 100 pounds. What is the median weight of the [#permalink] Five boxes together weigh 100 pounds. What is the median weight of the   24 Mar 2020, 04:06
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Five boxes together weigh 100 pounds. What is the median weight of the five boxes?


(1) One of the boxes weighs 20 pounds.

(2) When arranged in ascending order, the weight of the boxes form an arithmetic progression, i.e. the difference between the weights of any two consecutive boxes is the same.

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Re: Five boxes together weigh 100 pounds. What is the median weight of the [#permalink] Five boxes together weigh 100 pounds. What is the median weight of the   24 Mar 2020, 04:16
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Five boxes together weigh 100 pounds. What is the median weight of the five boxes?

(1) One of the boxes weighs 20 pounds.
(2) When arranged in ascending order, the weight of the boxes form an arithmetic progression, i.e. the difference between the weights of any two consecutive boxes is the same.

(1) One of the boxes weighs 20 pounds.
Case 1: Possible weights of boxes = {18, 19, 20, 21, 22} --> Median = 20
Case 2: Possible weights of boxes = {10, 10, 10, 20, 50} --> Median = 10
--> No Unique Value --> Insufficient

(2) When arranged in ascending order, the weight of the boxes form an arithmetic progression, i.e. the difference between the weights of any two consecutive boxes is the same.
We can assume the weights of AP as {a - 2d, a - d, a, a + d, a + 2d} --> Median = a
Sum of all weights = 100
--> a - 2d + a - d + a + a + d + a + 2d = 100
--> 5a = 100
--> a = 20
--> Median = 20 ALWAYS --> Sufficient

Option B
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Re: Five boxes together weigh 100 pounds. What is the median weight of the [#permalink] Five boxes together weigh 100 pounds. What is the median weight of the   20 May 2023, 23:21
Sum of AP =\( \frac{n}{2} \)\(( 2a + (n-1) d) = 100\)

\( \frac{5}{2} \)\(( 2a + 4 d) = 100\)

\(a+2d=20\)

Median = 3rd term = a+2d =20

Answer = B
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Re: Five boxes together weigh 100 pounds. What is the median weight of the [#permalink]
20 May 2023, 23:21
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