1) A tank holds water with a base 2 ft by 6 ft. If a rectangular solid whose dimensions are 1 foot by 1 foot by 2 feet is totally immersed in water, how many inches with the water rise?
A)1/6
B)1
C)2
D)3
E)12
^I got B
2)
AB+BA= CDC
IF each of the four letters in the sum above represent a different digit, which of the following can't be a value of A?
A)6
B)5
C)4
D)3
E)2
^ I got E
3) IF ab =40, a/b=5/2, and which a and b are positive numbers, find the value of a.
^I got a=20
a 1-foot slice of the tank holds 12 ft^3
Your brick only fills 1 ft^3
so, (A)
#2 I agree
#3 a=20 means b=2 but 20/2 ≠ 5/2
b=40/a, so
a/(40/a) = a^2/40 = 5/2
See what you can do with that
A=10?
1) To find the answer, we need to calculate the volume of water displaced by the rectangular solid and convert it to inches to determine the rise in water level.
The volume of the rectangular solid is given by its length, width, and height, which are 1 ft, 1 ft, and 2 ft, respectively. Therefore, the volume is 1 ft x 1 ft x 2 ft = 2 cubic ft.
Since the tank has a base area of 2 ft x 6 ft = 12 square ft, and the height of water rise is the volume of water displaced divided by the base area, the water level rise is 2 cubic ft / 12 square ft = 1/6 ft = 2 inches.
Therefore, the correct answer is A) 1/6.
2) In this question, we need to find the digit value of A in the equation AB + BA = CDC, where A, B, C, and D represent different digits.
Let's analyze the equation: AB + BA = CDC
Since A and B are distinct digits, the sum of two 2-digit numbers can be at most 198 (99 + 99). Therefore, CD cannot be greater than 198.
To check for the values of A, we need to examine the carry-over when adding AB and BA. Notice that for AB + BA, the tens digit is A+B, so if there is a carry-over, the value of A must be lower than 5.
By testing the options, we find that with A = 2, the equation becomes 2B + 2B = CD2. The maximum sum of 2B + 2B is 36 (18 + 18), so CD cannot be greater than 362.
Therefore, the correct answer is E) 2, as A cannot be equal to 2.
3) In this question, we are given the equations ab = 40 and a/b = 5/2, where a and b are positive numbers, and we need to find the value of a.
From the equation a/b = 5/2, we can cross-multiply to get 2a = 5b. Then, we can substitute this into the equation ab = 40 to get 2a^2 = 40.
Simplifying, we divide both sides by 2 to get a^2 = 40/2, which is a^2 = 20. Taking the square root of both sides, we find a = √20, which simplifies to a = 2√5.
Therefore, the value of a is 2√5.