ziyuenlau wrote:At a hospital, babies are born every day for a certain number of days. If 6 or more babies were born for 20% of the total number of days, is the median number of babies born less than 4?
1) On 75% of the days that less than 6 babies were born, the number of babies born each day was less than 4.
2) On 50% of the days that 4 or more babies were born, the number of babies born each day was 6 or more.
Source : Math Revolution
Official answer : D
You can basically rephrase this question, as follows:
In a list of elements, 20% of the elements have a value of 6 or greater. Is the median of the list less than 4?
1) Let's take a simple set. Say we have 5 elements. ___, ___, ___, ___, 6. There are four elements less than 6, and we know that 75% of them should be less than 4, meaning 3 of the elements must be less than 4. So we could have the following: 3, 3, 3, 5, 6. Median = 3. So we get a YES, the median is less than 4.
The answer will always be YES, no matter what set we construct: Elements 6 or more = .2T; Elements less than 6 = .8T. Of that .8T, we know that 75% will be less than 4, so .75 * .8T = .6T are less than 4. If 60% of the elements are less than 4, then the median will have to be less than 4. Sufficient.
2) Notice that we could use our same set: 3, 3, 3, 5, 6. Median = 3. So we get a YES, the median is less than 4. The logic ends up the same. If 50% of the elements that are 4 or greater are 6 or more, then of the elements 4 or greater, half are 6 or more and half between 4 and 6, meaning there are an equal number of both. This means that if there are .2T elements that are 6 or greater, there are also .2T elements that are between 4 and 6, meaning that .2T + .2T = .4T are 4 or greater and .6T are less than 4. Again, if 60% of the set is less than 4, then the median must be in this range. Sufficient.
The answer is
D
