Understanding Data - Problem Solving

I am thinking of $4$ numbers.
The average of the $4$ numbers is $44.$
The average of the first $3$ numbers is $33.$

What is the value of the $4^\text{th}$ number?

a, b, c, d and e are five consecutive integers in increasing order. When we delete one of the 5 from the set, then the sum of the numbers would have decreased by 20%

Which one of the numbers was deleted from the set?

What is the average (arithmetic mean) of $3^{15}, 3^{20},$ and $3^{25}?$

(A) $\ \ 20$
(B) $\ \ 60$
(C) $\ \ 3^{20}$
(D) $\ \ 3^{14} + 3^{19} + 3^{24}$
(E) $\ \ 3^{16} + 3^{21} + 3^{26}$

We have a five digit positive integer $N$. We select every pair of digits of $N$ (still retaining their relative order) and arrange them in numerical order to obtain 10 numbers: $33,37,37,37,38,73,77,78,83,87$. Find $N$.

I have a list of twelve numbers where the first number is 1, the last number is 12 and each of the other numbers is one more than the average of its two neighbors. What is the largest number in the list?

The sum of $N$ real numbers (not necessarily unique) is 20. The sum of the 3 smallest of these numbers is 5. The sum of the 3 largest is 7. Which of the following are possible values for $N$?

I. 9
II. 10
III. 11

Calvin is thinking of a sequence of distinct positive integers, which includes the number 35. The average of the numbers is 53. If he removes the number 35 from the list, the average increases to 54.

What is the largest possible number in Calvin's list?