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The median of 5 numbers is 50, and their range is 40. If the

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The median of 5 numbers is 50, and their range is 40. If the

by Max@Math Revolution » Wed May 23, 2018 5:03 pm

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[GMAT math practice question]

The median of 5 numbers is 50, and their range is 40. If the median of the 3 smallest numbers is 40, which of the following could be the range of the 3 largest numbers?

I. 0
II. 20
III. 40

A. I only
B. II only
C. I & II only
D.I & III only
E. I, II & III
Last edited by Max@Math Revolution on Fri May 25, 2018 9:44 pm, edited 1 time in total.
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by GMATGuruNY » Thu May 24, 2018 2:25 am
I suspect that the question stem has a typo and should read as follows:
Max@Math Revolution wrote:[GMAT math practice question]

The median of 5 numbers is 50, and their range is 40. If the median of the 3 smallest numbers is 40, which of the following COULD be the range of the 3 largest numbers?

I. 0
II. 20
III. 40

A. I only
B. II only
C. I & II only
D.I & III only
E. I, II & III
The median of 5 numbers is 50.
The median of the 3 smallest numbers is 40.
The 5 numbers are as follows:
__ 40 __ 50 __ __

Test whether I, II and III could be the range of the 3 largest numbers.

If the range of the 3 largest numbers is 0, we get:
__ 40 __ 50 __ 50
Since the range of the 5 numbers must be 40, the 5 numbers could be as follows:
10, 40, 50, 50, 50.
Since option I is possible, eliminate any answer that does not include I (B).

If the range of the 3 largest numbers is 20, we get:
__ 40 __ 50 __ 70
Since the range of the 5 numbers must be 40, the 5 numbers could be as follows:
30, 40, 50, 50, 70.
Since option II is possible, eliminate any remaining answers that do not include II (A and D).

If the range of the 3 largest numbers is 40, we get:
__ 40 __ 50 __ 90
Since the range of the 5 numbers must be 40, we get:
50, 40, 50 __ 70
Since the red number is greater than the blue number, option III is not possible.
Eliminate any remaining answers that include III (E).

The correct answer is C.
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by Max@Math Revolution » Fri May 25, 2018 1:30 am
=>

Suppose a, b, c, and d satisfy a ≤ b ≤ 50 ≤ c ≤ d. Since the median of the 3 smallest numbers is 40, we must have b = 40.

The range of the 3 largest numbers is d - 50.

Since we are told that d - a = 40, the maximum range of the 3 largest numbers occurs when a = b = 40.
Then d = 80, and the maximum range is d - 50 = 80 - 50 = 30.

The minimum range of the 3 largest numbers occurs when a = 10 and b = 40.
Then we have c = 50 and d = 50, and the range is d - 50 = 50 - 50 = 0.

The range of the 3 largest numbers lies between 0 and 30, inclusive.
Thus, 0 and 20 are the only possible values.

Therefore, the answer is C.
Answer: C
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by deloitte247 » Sat May 26, 2018 9:51 am
The median of 5 numbers is 50.
let the 5 numbers be a, b, c, d, e
median c =50
a, b, 50, d, e
3 smallest number = a, b, 50
median of 3 smallest number = b= 40
a, 40, 50, d, e
3 largest number = 50, d, e
if the range of three largest number is 0
e =50+0
a, 40, 50, d, 50
if e =50
and the range of 5 number = 40
40 =50 - a
a =10
Therefore the 5 numbers = 10, 40, 50, 50, 50
i.e option 1 is possible and range of 3 largest number can be 0
if the range of 3 largest number is 20
a, 40, 50, d , 70
Since the range of the 5 numbers must be 40, we have 30, 40, 50, 50,70.
i.e option ii is possible and the range of the three largest numbers could be 20
if the range of the three largest number is 40, we get a, 40, 50, d, 70
since the range of 5 numbers must be 40 the 5 numbers will be as follows; 50,40, 50, d, 90.
All the 5 numbers are in ascending order the first number is greater than the second number,
so option three is not possible and the range of 3 largest number could not be 40.
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