MegB07
A box of chocolates has 15 rows with 10 spaces for chocolates in each row, how many chocolates are in the box?
(1) There is an average (arithmetic mean) of 6 empty spaces in the first 8 rows.
(2) There is an average (arithmetic mean) of 9 empty spaces in the last 9 rows.
Why is C wrong? If we take first 8 rows and 9 rows from the bottom we will get the total number of empty spaces for all 15? where am i going wrong
This is basically an overlapping sets problem in disguise.
From statement (1), the first 8 rows have 6 empty spaces on average which means 48 empty spaces and 32 chocolates.
From statement (2), the last 9 rows have 9 empty spaces on average which means 81 empty spaces and 9 chocolates.
Rows 7 and 8 are included in both groups. Because we do not know how many chocolates are in these two overlap rows, we cannot resolve the double count.
If all 9 chocolates from the last 9 rows are in rows 7 and 8, the total could be 32. If rows 7 and 8 are completely empty and the 9 chocolates are in rows 9 through 15, the total could be 41. So the total number of chocolates can be as low as 32 or as high as 41 or something in between.
Answer: E.