List A consists of four numbers. The smallest possible average (arithm

Question

List A consists of four numbers. The smallest possible average (arithmetic mean) of three of these four numbers is 30 and the largest possible average (arithmetic mean) of three of these four numbers is 40. What is the range of possible averages of list A?

A. 2
B. 3
C. 5
D. 6
E. 10

Are You Up For the Challenge: 700 Level Questions

A. 2
B. 3
C. 5
D. 6
E. 10

Are You Up For the Challenge: 700 Level Questions

GMATinsight · Answer

Please find below the step by step explanation of the problem asked

https://www.youtube.com/watch?v=pVIKWwcZFLI

Answer: Option C

Regor60 · Answer

Let a,b,c and d be the numbers in ascending order. 
So:

a+b+c=90 and 
b+c+d=120

are constraints

The maximum value of a is 30, since if a>30 at least one of b and c will be less than a, which would violate the ascending order, so this means the minimum value of

b+c=60

Similarly, the minimum value of d is 40, since if it were lower, at least one of b and c would be >d, also violating the ascending order. This means the maximum of

b+c=80

Now, we want to both maximize and minimize the potential averages and subtract the two.

Now if we minimize d at 40 this maximizes b+c,80, and also has the effect of minimizing a, which must be 10 in that case, as follows:

10 40 40 40

If we maximize a at 30, this minimizes b+c to 60, which has the effect of maximizing d, which must be 60, as follows:

30 30 30 60

So, the lower average is

3*40+10= 130/4 and the higher

3*30+60= 150/4

The difference is (150-130/4=

20/4 = 5

Posted from my mobile device

sayan640 · Answer

MartyMurray   KarishmaB  Would you like to explain this question ?

chetan2u · Answer

sayan640 , refer your PM

We have numbers, a, b, c and d.
Now, sum of the lower three or upper three is fixed. We can manipulate the values to increase or decrease the overall mean.

Let us work on the upper three => b+c+d = 3*40 = 120
a would depend on what we take b and c as.

Maximize the mean/sum:  a should be the maximum, and that will be possible only when a=b=c=30 as 30 is the average of these three numbers.
so,   Sum = a+b+c+d = 30+120 = 150.  .............a,b,c,d = 30,30,30,60

Minimize the mean/sum:  a should be the minimum, and that will be possible only when b and c are maximized, that is b=c=d=40 as 40 is the average of these three numbers. Thus, a+40+40 = 3*30 = 90 or a=10
so,   Sum = a+b+c+d = 10+120 = 130.  .............a,b,c,d = 10,30,30,60

Range of mean  =  \frac{150}{4}-\frac{130}{4}=\frac{20}{4}=5

sayan640 · Answer

I think there is a typo.It would be 10 , 40 , 40 40.Kindly check the highlighted part.

Posted from my mobile device

KarishmaB · Answer

Let's put 4 numbers in ascending order to get: Least, B, C, Greatest

We get the smallest possible average of 3 numbers when we pick the 3 smallest numbers. So
 (Least + B + C) = 3*30 = 90

We get the greatest possible average of 3 numbers when we pick the 3 greatest numbers. So
 (B + C + Greatest) = 3*40 = 120

Average of all 4 numbers =  \frac{90 + 120 - (B+C)}{4}

The smallest value of this average is when B+C is greatest. The greatest values  they can take is 40 each in which case the Greatest number is 40 too. If B and C are more than 40, then the average of greatest 3 numbers will be more than 40 too. 
Least Average of all 4 numbers =  \frac{90 + 120 - 80}{4} = \frac{130}{4}

The greatest value of this average is when B+C is smallest. The smallest values  they can take is 30 each in which case the Least number is 30 too. If B and C are less than 30, then the average of smallest 3 numbers will be less than 30 too. 
Greatest Average of all 4 numbers =  \frac{90 + 120 - 60}{4} = \frac{150}{4}

Range = \frac{150}{4} - \frac{130}{4} = 5

Answer (C)

Mean has been discussed here:  https://youtu.be/W-qhIZ29UIs

bumpbot · Answer

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List A consists of four numbers. The smallest possible average (arithm

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List A consists of four numbers. The smallest possible average (arithm

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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My Rewards