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15 Apr 2020, 05:40
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C
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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
15 Apr 2020, 06:37
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Bunuel
Please find below the step by step explanation of the problem asked
Answer: Option C
21 Sep 2022, 16:29
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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
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
