GMAT Prep - Average/Median

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 !!

Whenever you're given an average, determine the sum.

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.

IOM A
pieces of wood: a,b,c,d,e; c is median, c=d=e=140; (a+b+c+d+e)=124*5=620; a+b=620-140*3=200;
a<b, and a is the shortest piece, a+b=200; 200-b<b ----> 200<2b, 100<b
if b>100, then a<100 or answer a) 90

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 !!

@Mitch, nope - we need the shortest and 100 is both two values below the median, but not the shortest.

GMATGuruNY wrote:

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 !!

Whenever you're given an average, determine the sum.

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.

Night reader wrote:@Mitch, nope - we need the shortest and 100 is both two values below the median, but not the shortest.

GMATGuruNY wrote:

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 !!

Whenever you're given an average, determine the sum.

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.

agree, without article the+superlative; emphate... /sorry can't spell this one /indicates on one not two possible pieces.

GMATGuruNY wrote:

Night reader wrote:@Mitch, nope - we need the shortest and 100 is both two values below the median, but not the shortest.

GMATGuruNY wrote:

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 !!

Whenever you're given an average, determine the sum.

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.

Mitch - thanks. What level of diffculty would you consider this question to be ?

@Night reader - the OA is B