Got confused on this average problem from the GMAT, can anyone break it down?

Question

In a numerical table with 10 rows and 10 columns, each entry is either a 9 or a 10. If the number of 9s in the nth row is n – 1 for each n from 1 to 10, what is the average (arithmetic mean) of all the numbers in the table?
 
A. 9.45 
B. 9.50 
C. 9.55
 D. 9.65 
E. 9.70

Aarushi S · Accepted Answer

Start by figuring out how many total entries are in the table. It&rsquo;s a 10 &times; 10 grid, so that&rsquo;s 100 numbers.
Now look at how many 9s are in each row. Row 1 has 0 nines, row 2 has 1 nine, row 3 has 2, and so on up to row 10, which has 9 nines. That forms an arithmetic sequence: 0 + 1 + 2 + &hellip; + 9. The sum of that is (9 &times; 10) &divide; 2 = 45, so there are 45 entries with the value 9.
Since there are 100 total entries, the rest &mdash; 100 &ndash; 45 = 55 &mdash; must be 10s. Now calculate the total sum: (45 &times; 9) + (55 &times; 10) = 405 + 550 = 955.
Average = 955 &divide; 100 = 9.55, so the answer is C.

B.K Sharma · Answer

This one&rsquo;s easier if you step back and organize what you know.

There are 100 total entries in the table (10 rows &times; 10 columns)
The number of 9s in each row follows the pattern: row n has (n &ndash; 1) nines
Add up all the 9s: 0 + 1 + 2 + &hellip; + 9 = 45
So, 45 entries are 9s, the other 55 must be 10s
Total sum = (45 &times; 9) + (55 &times; 10) = 955 &rarr; average = 955 &divide; 100 = 9.55

Final answer is C. Always helps to spot when a pattern is forming a simple arithmetic series.