Data Sufficiency

Vincen 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

The OA is D.

Here I need a lot of help. I got really confused. Experts, can you help me here.
I would really appreciate it. Thanks.

It is given that 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.

Say, the number of shirts = 9x ; the number of dresses = 4x; the number of jackets = 5x. where x is a common factor.

Thus, the total number of clothing = 9x + 4x + 5x = 18x; where 4x > 7 => x > 7/4 => x ≥ 2 since x is a positive integer.

Statement 1: The total number of shirts and jackets in the closet is less than 30.

=> 9x + 5x < 30 => 14x < 30 => x < 2... => x = 1 or 2. Since we know that x ≥ 2, thus x = 2. This means that there are a total of 18x = 18*2 = 36 clothings. Sufficient.

Statement 2: The total number of shirts and dresses in the closet is 26.

=> 9x + 4x = 26 => x = 2. This means that there are a total of 18x = 18*2 = 36 clothings. Sufficient.

The correct answer: D

Hope this helps!

-Jay

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Hi Vincen,

This DS question can be solved rather easily with a bit of 'brute force' and some simple arithmetic. To start, it's worth noting that you CANNOT have a 'fraction' of a piece of clothing. We're told that the ratio of shirts:dresses:jackets is 9:4:5, so the number of shirts MUST be a multiple of 9, the number of dresses MUST be an equivalent multiple of 4 and the number of jackets MUST be an equivalent multiple of 5. I'm going to put together a quick list of the first few potential possibilities...

There COULD be...
9 shirts/4 dresses/5 jackets
18 shirts/8 dresses/10 jackets
27 shirts/12 dresses/15 jackets
36 shirts/16 dresses/20 jackets
Etc.

We're also told that there are MORE than 7 dresses. We're asked for the total number of articles of clothing.

(1) The total number of shirts and jackets in the closet is less than 30.

With this Fact, we can look at our notes and find whatever options fit this information (AND include MORE than 7 dresses). There's only one...
18 shirts/8 dresses/10 jackets
Fact 1 is SUFFICIENT.

(2) The total number of shirts and dresses in the closet is 26.

With this Fact, we can again look at the available options. There's only one...
18 shirts/8 dresses/10 jackets
Fact 2 is SUFFICIENT.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich