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At a farmers’ market, Mia, Leo, and Owen each bought some oranges. If the total number of oranges they bought is 36, what is the median number of oranges bought by the three people?
(1) The ratio of the number of oranges Mia bought to the number of oranges Owen bought was 7:12.
(2) Owen bought 12 oranges.
(1) The ratio of the number of oranges Mia bought to the number of oranges Owen bought was 7:12.
(2) Owen bought 12 oranges.
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23 Apr 2026, 01:45
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GMAT Club Official Solution:
At a farmers’ market, Mia, Leo, and Owen each bought some oranges. If the total number of oranges they bought is 36, what is the median number of oranges bought by the three people?
(1) The ratio of the number of oranges Mia bought to the number of oranges Owen bought was 7:12.
Since the total number of oranges bought was 36, to satisfy this ratio, Mia and Owen could only have bought 7 and 12 oranges. Thus Mia = 7, Owen = 12, and Leo = 17. The median is 12. Sufficient.
(2) Owen bought 12 oranges.
If Owen bought 12 oranges, then Mia and Leo together bought 24.
Both cannot be greater than 12, because then their sum would exceed 24.
Both cannot be less than 12, because then their sum would be less than 24.
So one must be at most 12 and the other at least 12. Thus, we must have:
<= 12, Owen = 12, >=12
Therefore, 12 must be the median.
Sufficient.
Answer: D.
At a farmers’ market, Mia, Leo, and Owen each bought some oranges. If the total number of oranges they bought is 36, what is the median number of oranges bought by the three people?
(1) The ratio of the number of oranges Mia bought to the number of oranges Owen bought was 7:12.
Since the total number of oranges bought was 36, to satisfy this ratio, Mia and Owen could only have bought 7 and 12 oranges. Thus Mia = 7, Owen = 12, and Leo = 17. The median is 12. Sufficient.
(2) Owen bought 12 oranges.
If Owen bought 12 oranges, then Mia and Leo together bought 24.
Both cannot be greater than 12, because then their sum would exceed 24.
Both cannot be less than 12, because then their sum would be less than 24.
So one must be at most 12 and the other at least 12. Thus, we must have:
<= 12, Owen = 12, >=12
Therefore, 12 must be the median.
Sufficient.
Answer: D.
General Discussion
16 Apr 2026, 23:12
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IMO D.
Statement 1:
7:12, Here we need to see that increasing the ratio to 14:24 would bring total items to 38 and would be greater than actual total.
Not possible.
Thus we have 12 by Owen and 7 by Mia, where 12 becomes the median and last person getting 17 oranges.
SUFFICIENT.
Statement 2:
This is pretty clear.
We have the average value = 36/3 = 12 here.
And any value above must be compensated by a value below the value 12, only then the averages will balance it out.
12 is the median.
SUFFICIENT.
Answer: Option D
Statement 1:
7:12, Here we need to see that increasing the ratio to 14:24 would bring total items to 38 and would be greater than actual total.
Not possible.
Thus we have 12 by Owen and 7 by Mia, where 12 becomes the median and last person getting 17 oranges.
SUFFICIENT.
Statement 2:
This is pretty clear.
We have the average value = 36/3 = 12 here.
And any value above must be compensated by a value below the value 12, only then the averages will balance it out.
12 is the median.
SUFFICIENT.
Answer: Option D
Bunuel
