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1. After being dropped a certain ball always bounces back to 2/5 of the height of its previous bounce. After the first bounce it reaches a height of 125 inches. How high (in inches) will it reach after its fourth bounce?
A. 20
B. 15
C. 8
D. 5
E. 3.2
2. n and p are integers greater than 1
5n is the square of a number
75np is the cube of a number.
The smallest value for n + p is
A. 14
B. 18
C. 20
D. 30
E. 50
1.Correct Answer: C
Explanation:
If after each bounce it reaches 2/5 of the previous height, then after the second bounce it will reach 2/5 x 125. After the third it will reach 2/5 x 2/5 x 125. After the fourth it will reach 2/5 x 2/5 x 2/5 x 125. This cancels down to 2 x 2 x 2 = 8
2.Correct Answer: A
Explanation:
The smallest value for n such that 5n is a square is 5. 75np can now be written as 75 x 5 x p. This gives prime factors.... 3 x 5 x 5 x 5 x p To make the expression a perfect cube, p will have to have factors 3 x 3 , and hence p =9 n + p = 5 + 9 = 14
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