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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
Five pieces of wood have an average (arithmetic mean) length of 124
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06 Dec 2022, 00:43
06 Dec 2022, 00:43
Expert Reply
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Question Stats:
57% (02:05) correct
42% (01:58) wrong based on 7 sessions
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Five pieces of wood have an average (arithmetic mean) length of 124 centimeters and a median length of 140 centimeters. What is the maximum possible length, in centimeters, of the shortest piece of wood?
A. 90
B. 100
C. 110
D. 130
E. 140
A. 90
B. 100
C. 110
D. 130
E. 140
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
Re: Five pieces of wood have an average (arithmetic mean) length of 124
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07 Dec 2022, 07:51
07 Dec 2022, 07:51
Expert Reply
Sum of lengths is 124*5=620
Median is 140
Sum of the lengths of the other four pieces= 620-140=480
The lengths of pieces-
L1, L2, 140, L4, L5
The sum of the four pieces is constant.
L4 and L5 have to be minimum for L1 to be maximum but the median length must be 140.
The minimum possible values of L4 and L5 could be 140, hence the L1+L2 = 620 - 420 = 200.
The maximum possible value of L1 = 100= L2
Answer: B
Median is 140
Sum of the lengths of the other four pieces= 620-140=480
The lengths of pieces-
L1, L2, 140, L4, L5
The sum of the four pieces is constant.
L4 and L5 have to be minimum for L1 to be maximum but the median length must be 140.
The minimum possible values of L4 and L5 could be 140, hence the L1+L2 = 620 - 420 = 200.
The maximum possible value of L1 = 100= L2
Answer: B
gmatclubot
Re: Five pieces of wood have an average (arithmetic mean) length of 124 [#permalink]
07 Dec 2022, 07:51
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