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Whenever you're given an average, determine the sum.rickyishere wrote:Five pieces of wood have an average length of 124 centimeters and a median length of 140 centimeters. What is the maximum possiblel length (in centimeters) of the shortest piece of wood?
a) 90
b) 100
c)110
d) 130
e) 140
Thanks in advance !!
rickyishere wrote:Five pieces of wood have an average length of 124 centimeters and a median length of 140 centimeters. What is the maximum possiblel length (in centimeters) of the shortest piece of wood?
a) 90
b) 100
c)110
d) 130
e) 140
Thanks in advance !!
GMATGuruNY wrote:Whenever you're given an average, determine the sum.rickyishere wrote:Five pieces of wood have an average length of 124 centimeters and a median length of 140 centimeters. What is the maximum possiblel length (in centimeters) of the shortest piece of wood?
a) 90
b) 100
c)110
d) 130
e) 140
Thanks in advance !!
Sum = (number of things) * (average) = 5 * 124 = 620.
Median = 140 centimeters.
Let's call the 5 pieces, from shortest to longest: w, x, 140, y, z.
Since we want to maximize w, we need to minimize y and z. Let y=140 and z=140.
Thus, the 5 pieces are: w, x, 140, 140, 140.
Thus, w+x = 620 - 3*140 = 200.
Now we can plug in the answer choices for w (the shortest piece of wood). Since the median is 140, and the average is 124, w and x must each be less than 124. Eliminate D and E.
Answer choice C: w=110
If w =110, then x = 200-110 = 90. Doesn't work because x cannot be less than w.
Eliminate C.
Answer choice B: w=100
If w=100, then x = 200-100 = 100. This works. The 5 pieces will be 100, 100, 140, 140, 140.
The correct answer is B.
Unless the question states emphatically that all the values must be distinct, we must not make that assumption. Thus, the maximum possible length of the shortest piece is 100.Night reader wrote:@Mitch, nope - we need the shortest and 100 is both two values below the median, but not the shortest.GMATGuruNY wrote:Whenever you're given an average, determine the sum.rickyishere wrote:Five pieces of wood have an average length of 124 centimeters and a median length of 140 centimeters. What is the maximum possiblel length (in centimeters) of the shortest piece of wood?
a) 90
b) 100
c)110
d) 130
e) 140
Thanks in advance !!
Sum = (number of things) * (average) = 5 * 124 = 620.
Median = 140 centimeters.
Let's call the 5 pieces, from shortest to longest: w, x, 140, y, z.
Since we want to maximize w, we need to minimize y and z. Let y=140 and z=140.
Thus, the 5 pieces are: w, x, 140, 140, 140.
Thus, w+x = 620 - 3*140 = 200.
Now we can plug in the answer choices for w (the shortest piece of wood). Since the median is 140, and the average is 124, w and x must each be less than 124. Eliminate D and E.
Answer choice C: w=110
If w =110, then x = 200-110 = 90. Doesn't work because x cannot be less than w.
Eliminate C.
Answer choice B: w=100
If w=100, then x = 200-100 = 100. This works. The 5 pieces will be 100, 100, 140, 140, 140.
The correct answer is B.
/indicates on one not two possible pieces.Mitch - thanks. What level of diffculty would you consider this question to be ?GMATGuruNY wrote:Unless the question states emphatically that all the values must be distinct, we must not make that assumption. Thus, the maximum possible length of the shortest piece is 100.Night reader wrote:@Mitch, nope - we need the shortest and 100 is both two values below the median, but not the shortest.GMATGuruNY wrote:Whenever you're given an average, determine the sum.rickyishere wrote:Five pieces of wood have an average length of 124 centimeters and a median length of 140 centimeters. What is the maximum possiblel length (in centimeters) of the shortest piece of wood?
a) 90
b) 100
c)110
d) 130
e) 140
Thanks in advance !!
Sum = (number of things) * (average) = 5 * 124 = 620.
Median = 140 centimeters.
Let's call the 5 pieces, from shortest to longest: w, x, 140, y, z.
Since we want to maximize w, we need to minimize y and z. Let y=140 and z=140.
Thus, the 5 pieces are: w, x, 140, 140, 140.
Thus, w+x = 620 - 3*140 = 200.
Now we can plug in the answer choices for w (the shortest piece of wood). Since the median is 140, and the average is 124, w and x must each be less than 124. Eliminate D and E.
Answer choice C: w=110
If w =110, then x = 200-110 = 90. Doesn't work because x cannot be less than w.
Eliminate C.
Answer choice B: w=100
If w=100, then x = 200-100 = 100. This works. The 5 pieces will be 100, 100, 140, 140, 140.
The correct answer is B.
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