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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
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16 Jun 2016, 06:33
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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
Both statement are individually sufficient. Both give the required values. D is the answer.
_________________
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16 Jun 2016, 12:38
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Bunuel 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
Statement 1:-
Since ratio of S:D= 9:4
For S+D<30, there are two possible cases
S+D= 9+4 or S+D= 18+8
9+4 is not possible as J>7
So, S+D= 18+8+10= 36 Sufficient
Statement 2:-
S+D= 26 9x+4x= 26
We will get the value of x , and hence can find out the total number of clothes. Sufficient.
D is the answer
_________________
I welcome critical analysis of my post!! That will help me reach 700+
Re: The only articles of clothing in a certain closet are shirts, dresses, [#permalink]
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16 Jun 2016, 20:50
Divyadisha wrote:
Bunuel 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
Statement 1:-
Since ratio of S:D= 9:4
For S+D<30, there are two possible cases
S+D= 9+4 or S+D= 18+8
9+4 is not possible as J>7
So, S+D= 18+8+10= 36 Sufficient
Statement 2:-
S+D= 26 9x+4x= 26
We will get the value of x , and hence can find out the total number of clothes. Sufficient.
D is the answer
Hi,
Please review highlighted part as statement 1 is about Shirts and Jackets so it should be Shirts + Jackets <30 and hence you should take the ratio between shirts and jacket to be 9:5
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18 Jun 2016, 04:17
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IMO D 1. 9x+5x<30 therefore 14x<30 therefore x = 1 or 2 but dresses >7 so x!= 1 so x=2 sufficient 2). 9x+4x=26 13x=26 x=2 dresses =8 sufficient so both A and B are sufficient
_________________
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
We are given that the ratio of shirts to dresses to jackets is 9 to 4 to 5. Thus:
shirts : dresses : jackets = 9x : 4x : 5x
We also are given that there are more than 7 dresses in the closet and must determine the total number of articles of clothing in the closet, i.e., the value of 9x + 4x + 5x = 18x.
Statement One Alone:
The total number of shirts and jackets in the closet is less than 30.
Using the information in statement one, we can create the following inequality:
9x + 5x < 30
14x < 30
x < 30/14
x < 2 1/7
Thus, x could either be 1 or 2.
If x = 1, then there are 4 dresses. If x = 2, then there are 8 dresses. Since the number of dresses is greater than 7, x must be 2. So there are 9(2) + 4(2) + 5(2) = 18 + 8 + 10 = 36 articles of clothing in the closet. Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.
Statement Two Alone:
The total number of shirts and dresses in the closet is 26.
Using the information in statement two, we can create the following equation:
9x + 4x = 26
13x = 26
x = 2
Once again, since we have determined the value of x, we have enough information to answer the question. Statement two is also sufficient to answer the question.
Answer: D
_________________
Jeffery Miller Head of GMAT Instruction
GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions
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.
i think The answer is (1) if i am correct please tell me
Hi ethel curtis,
If you click the correct answer (it's underneath the question) or you read any of the explanations in this thread, you see that the correct answer is actually