MATH GRE 5

If A, B, C and D are positive integers such that 4A = 9B, 17C = 11D, and 5C = 12A, then the arrangement of the four numbers from greatest to least is

Keep in mind we need to arrange from greatest to the least.

The total number of people in honor society at Melpomene High School, regardless of other activities, is approximately what percent higher than the total number of people in honor society at Thalia High School, regardless of other activities?

Thalia is the original

In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of gray socks and 2 pairs of orange socks. If socks are removed at random without replacement, what is the minimum number of socks that must be removed in order to ensure that two socks of the same color have been removed?

The question asks "what is the minimum number of socks that must be removed in order to ensure that two socks of the same color have been removed?" The key words here are MINIMUM and ENSURE. Another way to phrase the question is what is the least number of socks that must be removed to guarantee that we have two socks of the same color. For example, if we only remove two socks, we may get 1 black sock and 1 gray sock. In that case, we cannot ENSURE that we have matching socks. However, if we remove 4 socks, we can GUARANTEE that we will have a pair of matching socks. Once we select our 4th sock, we are guaranteed to have a matching pair. So our answer is A

An office has 6 employees; there are 5 female employees and 1 male employee. In how many ways can a 3-person committee be created if the committee must include the male employee?

There are 3 seats in the committee. 1 way to chose male, and 5C2 =10 way to chose Female.

In a list of four positive integers, the range is 60 and the median is 50. What is the highest possible value of the largest number in the list?

There are two middle number 50-D and 50+D Lower number L ( Min 50-D=0, D=0) Highest number L+60 Thus, the highest number is 110