garbage sale!

[KICKGMATASS123]

At a garage sale, all of the prices of the items sold were different. If the price of a radio sold at the garage sale was both the 15th highest price and the 20th lowest price among the prices of the items sold, how many items were sold at the garage sale?

A. 33
B. 34
C. 35
D. 36
E. 37

OA is B

Can someone show me an approach as to how to handle such problems in a methodical fashion?

[jjk]

If it's the 15th most expensive item at the sale, you know that 14 other items are more expensive than it.

If it's the 20th cheapest item at the sale, you know that 19 other items are cheaper than it.

The key here is to not double-count the item.

14 items that are more expensive
19 items that are cheaper
1 (the item itself
-----
34

[KICKGMATASS123]

If it's the 15th most expensive item at the sale, you know that 14 other items are more expensive than it.

If it's the 20th cheapest item at the sale, you know that 19 other items are cheaper than it.

The key here is to not double-count the item.

14 items that are more expensive
19 items that are cheaper
1 (the item itself
-----
34

Of the books standing in a row on a shelf, an atlas is the 30th book from the left and the 33rd book from the right. If 2 books to the left of the atlas and 4 books to the right of the atlas are removed from the shelf, how many books will be left on the shelf?

A. 56
B. 57
C. 58
D. 61
E. 63

OA is A

[truplayer256]

If the atlas is the 30th book from the left, then there are 29 books to the left of it.

If the atlas is the 33rd book from the right, then there are 32 books to the right of it.

Total No. of books= 32+29+1=62

A total of 6 books are removed:

62-6=56 books will remain on the shelf after 6 books are removed.

[goelmohit2002]

If it's the 15th most expensive item at the sale, you know that 14 other items are more expensive than it.

If it's the 20th cheapest item at the sale, you know that 19 other items are cheaper than it.

The key here is to not double-count the item.

14 items that are more expensive
19 items that are cheaper
1 (the item itself
-----
34

Awesome jjk !