Explanations
Explanations

1.      D     

In order for the mean of her scores to be 5.8, the sum of the three judges’ scores, S, divided by three, must equal 5.8. The sum of the scores she needs to win is:

If one of the judges gives her a 5.5, then the sum of the other two judges’ scores must be 17.4 – 5.5 = 11.9. The lowest score she could receive would have to be averaged out by the highest scores she could receive, which would be a 6. Therefore, the lowest score would be 11.9 – 6.0 = 5.9.

2.      D     

Immediately you can eliminate the last answer choice as a possibility, because the probability of an event is always between 0 and 1. Because the events are independent, the probability of any series of events happening is the product of their respective probabilities: . From this equation you can see that

3.      D     

Because the two tests are independent of each other, the probability of any series of events happening is the product of their respective probabilities. Also, if P is the probability of an event happening, the probability of that event not happening is 1 – P.Therefore, the probability of not getting a perfect score on the SAT II Math IIC is 1 – .01 = .99 and for the SAT II Writing is 1 – .05 = .95. The answer is the product of these two probabilities:

4.      E     

Since the order of the scoops doesn’t matter, this is a combination question. To find the number of subgroups of size r that can be formed from a larger set n, use the following formula:

This problem asks you to take groups of 3 from a larger group of 15:

5.      D     

Since it matters which role an actress gets, this is a permutation question. In order to find the number of permutations of size r that can be taken from a set with n elements, use the following formula:

This problem asks you to take groups of 3 from a larger group of 40:

6.      C     

To minimize CD, minimize C and maximize D. The fewest possible elements in the union of a and b is 9, if b is a subset of a (i.e. all of the elements in b are also in a). This arrangement also maximizes the intersection of the sets: they must share 4 elements (all the elements in b). Therefore, CD = 9 – 4 = 5. Any other situation results in a greater value for CD.

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