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C
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Difficulty:
45%
(medium)
Question Stats:
71% (02:04) correct
29%
(02:11)
wrong
based on 233
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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 represent the range of the 3 largest numbers?
I. 0
II. 20
III. 40
A. I only
B. II only
C. I and II only
D.I and III only
E. I, II and III
I. 0
II. 20
III. 40
A. I only
B. II only
C. I and II only
D.I and III only
E. I, II and III
Updated on: 10 Jan 2024, 09:09
Originally posted by GmatMaestro on 10 Jan 2024, 03:27.
Last edited by GmatMaestro on 10 Jan 2024, 09:09, edited 2 times in total.
Last edited by GmatMaestro on 10 Jan 2024, 09:09, edited 2 times in total.
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CORRECTION THANKS TO LUCIENH (This is what happens when you go to fast and don't pay attention to details...)
We have 5 numbers, arranged in increasing order: A, B, C, D, E
The key here is to remember that numbers can be repeated...
The median (middle number) of 5 numbers is 50, so:
A, B, 50, D, E
the median of the 3 smallest numbers is 40, so:
A, 40, 50, D, E
which of the following could represent the range of the 3 largest numbers?
50, D, E (Range is E-50)
D must be EQUAL TO or GREATER THAN 50, and
E must be EQUAL TO or GREATER THAN D.
So, possible values for C, D, and E include:
50, 50, 50 (range: 0)
50, 60, 70 (range: 20)
50, 70, 90 (range: 40) 90 is not a possible value for E because E-A=40
Answer: C
We have 5 numbers, arranged in increasing order: A, B, C, D, E
The key here is to remember that numbers can be repeated...
The median (middle number) of 5 numbers is 50, so:
A, B, 50, D, E
the median of the 3 smallest numbers is 40, so:
A, 40, 50, D, E
which of the following could represent the range of the 3 largest numbers?
50, D, E (Range is E-50)
D must be EQUAL TO or GREATER THAN 50, and
E must be EQUAL TO or GREATER THAN D.
So, possible values for C, D, and E include:
50, 50, 50 (range: 0)
50, 60, 70 (range: 20)
Answer: C
10 Jan 2024, 08:00
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Bunuel
IMO it should be answer C (only I and II)
from the information in the text, we know that the numbers are in the following order
A ; 40 ; 50 ; D ; E
and we know that the range is 40 so E - A = 40
from the given options, 0 could work because that would mean that E = 50, so range of the 5 numbers would be 40 if A = 10 (which is less than 40 so it's okay)
20 could work for the same reason, as E = 70 and the range would be 40 if A = 30 (less than 40)
for 40, it doesn't work, as E = 90 and to satisfy the fact that the range is 40, A should equal 90 - 40 = 50, which is not possible since we know that the median of the 3 smallest numbers is 40
