A drawer holds 4 red hats and 4 blue hats. What is the probability of getting exactly three red hats or exactly three blue hats when taking out 4 hats randomly out of the drawer and immediately returning every hat to the drawer before taking out the next?
Answer(s): C
Getting three red out of 4 that are taken out has 4 options (4! / (3!*1!)) each option has a probability of (1/2)4 since drawing a red or blue has a 50% chance. 4*1/16= 1/4 to get three red hats. The same goes for three blue hats so 1/4+1/4 =1/2. The correct answer is C.
If 4XZ + YW = 3 and XW + YZ = 6, what is the value of the expression (2X + Y)(2Z + W)?
(2X + Y) (2Z + W) = 4XZ + 2XW + 2ZY + WY.Now, plug in this data to get: 3 + 2 x 6 = 15. The correct answer is C.
X is an even number and Y is a positive odd number. Which of the following expressions cannot be even?
Answer(s): E
The fastest way to solve this problem is by plugging in some numbers. Let’s say: X = 2, Y = 1.According to answer e: 1 x 1 = 1 and that must be an odd number. The correct answer is E.
How much interest will $2,400 earn at an annual rate of 8% in one year if the interest is compounded every 4 months?
Here, it is enough to calculate the simple interest of 8% per year.$2,400 x 8/100 x 1 = $192. Since we are calculating as a compounded rate, the interest should be a bit higher or C as the correct answer.
X is a prime number bigger than 10. Also, Y = X+X3+X5+X7. What is definitely true about Y?
Because X is a prime number bigger than 10, it must be odd. Ignoring the powers of X in the expression of Y, you’ll see that Y is a sum of 4 odd numbers therefore it must be even. The correct answer is C.
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