<p>^
Pigeonhole Principle</p>
<p>Bill works at an aquarium. One of the exhibits is being redone. The old structure is a rectangular solid measuring 9ft long x 4ft wide x 1ft high. After Bill cleans out the exhibit, the tank is half full with only water. If Bill is to pour this water into an empty tank with the dimensions 6ft long x 2ft wide x 3ft high, how high will the water reach in the new tank?</p>
<p>^the answer is 1.5</p>
<p>Just creating a compilation:</p>
<p>Section 2
18. What is the greatest four-digit integer that meets the following three restrictions?
(1) All of the digits are different.
(2) The greatest digit is the sum of the other three digits.
(3) The product of the four digits is divisible by 10 and not equal to zero.</p>
<p>Section 6
17. The first term of a sequence is a. Each term after the first is p more than the preceding term. Which of the following expressions is the sum of the first 6 terms of the sequence?
a. 6a + 5p
b. 6a + 15p
c. 6a + 18p
d. 12a + 5p
e. 12a + 30p</p>
<ol>
<li>The sum of r and 5 is less than the square of the difference between r and 5 but greater than the square of one-half r.
Which of the following statement is equivalent to the statement above?
a. 1/4(r^2) < r + 5 < (r-5)^2
b. 1/4(r^2) < r + 5 < r^2 - 5
c. 1/2(r^2) < r + 5 < (r-5)^2
d. 1/2(r^2) < r + 5 < r^2 - 5
e. 1/2(r^2) < r^2 - 5 < r^2 + 5</li>
</ol>
<p>There are 27 students in Mr White’s homeroom. What is the probability that at least 3 of them have their birthdays in the same month?
A) 0
B) 3/27
C) 3/12
D) 1/2
E) 1</p>
<p>Bill works at an aquarium. One of the exhibits is being redone. The old structure is a rectangular solid measuring 9ft long x 4ft wide x 1ft high. After Bill cleans out the exhibit, the tank is half full with only water. If Bill is to pour this water into an empty tank with the dimensions 6ft long x 2ft wide x 3ft high, how high will the water reach in the new tank?</p>
<p>The integers 1-6 appear on the six faces of a cube, one on each face. If three such cubes are rolled, what is the probability that the sum of the numbers on the top faces is 17 or 18?</p>
<p>A) 1/108
B) 1/54
C) 1/27
D) 1/18
E) 1/16</p>