BTGmoderatorDC wrote:The only articles of clothing in a certain closet are shirts, dresses, and jackets. The ratio of the number of shirts to the number of dresses to the number of jackets in the closet is 9:4:5, respectively. If there are more than 7 dresses in the closet, what is the total number of articles of clothing in the closet?
(1) The total number of shirts and jackets in the closet is less than 30
(2) The total number of shirts and dresses in the closet is 26
OA D
Source: Official Guide
Target question: What is the total number of articles of clothing in the closet?
Given: The ratio of the number of shirts to the number of dresses to the number of jackets in the closet is 9:4:5, respectively.
If shirts : dresses : jackets = 9 : 4 : 5, then there are infinitely many scenarios:
- There are 9 shirts, 4 dresses and 5 jackets
- There are 18 shirts, 8 dresses and 10 jackets
- There are 27 shirts, 12 dresses and 15 jackets
- There are 36 shirts, 16 dresses and 20 jackets
- There are 45 shirts, 20 dresses and 25 jackets
etc...
Also given: There are more than 7 dresses in the closet
This means the first scenario (9 shirts, 4 dresses and 5 jackets) is not possible. This leaves us with the following cases:
case i: 18 shirts, 8 dresses and 10 jackets
case ii 27 shirts, 12 dresses and 15 jackets
case iii 36 shirts, 16 dresses and 20 jackets
case iv 45 shirts, 20 dresses and 25 jackets
.
.
.
etc
Statement 1: The total number of shirts and jackets in the closet is less than 30
When we check the
possible cases, we see that only
case i meets this condition.
This means there MUST be 18 shirts, 8 dresses and 10 jackets
So, the answer to the target question is
the total number of articles of clothing = 18 + 8 + 10 = 36
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: The total number of shirts and dresses in the closet is 26
Only
case i meets this condition.
So, the answer to the target question is
the total number of articles of clothing = 18 + 8 + 10 = 36
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent
