BTGmoderatorDC wrote:At a bakery, cakes are sold every day for a certain number of days. If 6 or more cakes were sold for 20% of the total number of days, is the median number of cakes sold less than 4?
(1) On 75% of the days that less than 6 cakes were sold, the number of cakes sold each day was less than 4.
(2) On 50% of the days that 4 or more cakes were sold, the number of cakes sold each day was 6 or more.
Say the number of days for which cakes were sold be 10.
The median number of cakes sold would be on 5.5th day, i.e. the average of 5th days and the 6th day.
From the information, "6 or more cakes were sold for 20% of the total number of days," the number of days, 6+ cakes were sold each day = 20% of 10 = 2 days
Thus, the number of day, less than 6 number of cakes were sold = 10 - 2 = 8 days
Let's take each statement one by one.
(1) On 75% of the days that less than 6 cakes were sold, the number of cakes sold each day was less than 4.
=> The number of cakes sold each day, less than 4 = 75% of 8 = 3/4 x 8 = 6 days
=> The number of cakes sold each day, more than or equal to 4 but less than 6 = 8 - 6 = 2 days
The distribution of the number of cakes in an ascending order for 10 days is given by: ≥6, ≥6, ≥4, ≥ 4,
<4, <4, <4, <4, <4, <4
The number of cakes sold on the 5th days as well as on the 6th days = less than 4 each; thus, the median = less than 4. The answer is Yes. A unique answer. Sufficient.
(2) On 50% of the days that 4 or more cakes were sold, the number of cakes sold each day was 6 or more.
=> The number of cakes sold each day was 6 or more = 50% of the number of cakes sold each day was 4 or more
We know that the number of cakes sold each day was 6 or more = 2 days
=> 2 = 50% of the number of cakes sold each day was 4 or more
=> The number of cakes sold each day was 4 or more = 2/50% = 4 days
=> The number of cakes sold each day was less than 4 = 10 - 4 = 6 days
Now the situation is the same as that in Statement 1. Sufficient.
The correct answer:
D
Hope this helps!
-Jay
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