All of the numbers in this series are 2^n-1. The number that we are looking for is the eighth number. So 2^8–1 = 2⁷ = 128.

She can only buy 2 tulips at $80, because if she bought 3 she wouldn’t have enough to afford the other 2 kinds of flowers.  She has to spend at least 30 dollars (20 + 10) on 1 rose and 1 lily.

A rational number is a number that can be written in the form of a/b, where a and b are integers, aka a real number that can be written as a simple fraction or ratio. 4 of the 5 answer choices can be written as fractions and are thus rational. 

5 = 5/1, 1.75 = 7/4, .001 = 1/1000, 0.111... = 1/9

√2 cannot be written as a fraction because it is irrational. The two most famous irrational numbers are √2 and pi. 

The prime digits are 2, 3, 5, and 7.

The perfect square digits are 0, 1, 4, and 9.

The only digits not represent in these two groups are 6 and 8, which are, coincidentally, found in the number 68.

By observing each of these sets, we can easily determine the largest number in each; however, the problem is asking for us to find the greatest possible sum if we select four different integers, one from each set. The largest number is 11. We will either select this number from set Y or set Z.

We will select set

Y for the 11

because the next larger number in set

Z is 10, which is greater than the next largest number is set Y, 7.

We can use set Z for 10.

Because the 10 has already been selected, choosing the integer from W and X should be easy because 9 is the next largest integer from set W

and 

8 is the next largest integer from set X.

11 + 10 + 9 + 8 = 38

If a team's ratio of wins to losses increases from  to  by winning six games, they must have 12 wins initially and 3 losses. 

The rule is as follows: add 2 to the previous number then multiply times 2.

The answer is (16 + 2) * 2 = 36.

In order to find the missing number (X), you must first identify the pattern in the set of numbers. Upon a glance, you can determine that the pattern starts with 4 and then the next number is 2n+1, with n being the preceding number in the set.

For example, let's start with 4. Multiplying 2*4+1 gives us 9, the next number in the set. 

Therefore, the missing number in the set is .

The lower right number of each box is the sum of the other three numbers, which are found as follows:

The upper left numbers are simply the natural numbers in order;

The upper right numbers are the powers of 2, beginning with ;

The lower left numbers are the terms of the Fibonacci sequence, which is formed by setting the first two terms equal to 1 and each subsequent term equal to its predecessors.

Therefore, the ninth box in the sequence includes the number 9 as its upper left entry, and  as its upper right entry. The lower left entry is the ninth Fibonacci number, which can be found as follows:

The lower right entry is the sum of the other entries: