The only articles of clothing in a certain closet are shirts, dresses,

Hi All,

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:

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

The Chart Method for Ratios works well here. Here's a video explanation for this question:



For more on the chart method for ratios, see the videos below:

Intro to the Ratio Chart: https://www.youtube.com/watch?v=WfHm5SF95vU

Using the Ratio Chart to solve DS questions quickly: https://www.youtube.com/watch?v=MA686n6S4z8

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.

IMO answer is B
The ratio given is 9:4:5 , so we can say that number of shirts , dresses and jackets are 9x, 4x, and 5x respectively.

From 1 the total number of shirts and jackets(14x) can be 14 or 28 ,both of which are <30.

From 2 we can have value of x as 2 since sum od shirts and dresses is 26(13x=26)

You are missing the information presented in the question stem"there are more than 7 dresses " so it cannot be 14.

Posted from my mobile device

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

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

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
_________________

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 . If you'd like help in dealing with this question, then you should talk through how you worked through it and post your 'steps.'

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

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

RELATED VIDEO

Given: 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.

Asked: If there are more than 7 dresses in the closet, what is the total number of articles of clothing in the closet?

Let the number of shirts, dresses and jackets in the closet be 9x, 4x & 5x respectively
4x > 7
x > 7/4 > 1
Since x is an integer, x>=2

(1) The total number of shirts and jackets in the closet is less than 30
9x + 5x = 14x < 30
x < 30/14 <3
2<=x<3
x = 2
The total number of articles of clothing in the closet = 9x + 4x + 5x = 18x = 36
SUFFICIENT

(2) The total number of shirts and dresses in the closet is 26
9x + 4x = 13x = 26
x = 2
The total number of articles of clothing in the closet = 9x + 4x + 5x = 18x = 36
SUFFICIENT

IMO D

Total articles must be multiple of 18 (9:4:5), Dresses are more than 7

(1) Shirts and Jacket will be multiple of 14, individually each can't be less than 9 and 5 respectively. On the other hand, dresses have to be more than 7 and multiple of 4, i.e, 8, 16, 32..
Now, if the Jackets are 9 and the shirts are 5 then 14+8 = 28, 14+16 = 30 or 14+32 = 46 are not multiple of 18
So, if Jackets are 18 and Shirts are 10 the total 28 is multiple of 14 and dresses become 8 the final number 28+8=36 is multiple of 18.

Option 1 is Sufficient.

(2) We need a number which added with 26, will be multiple of 5 and the total will be divisible 18. 10 is such a number. It can't 20 because 46 is not divisible by 18.
Option 2 is sufficient.

Answer D.
_________________

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


S D J
9x 4x 5x

if D > 7
so
if 4x > 7
x > 7/4
so x is greater than 1
we can only take integer values for x since we are talking about concrete things like dresses

total number of articles of clothing in the closet = 9x + 4x + 5x

dissected question
x = ?


1) The total number of shirts and jackets in the closet is less than 30
9x + 5x < 30
14 x < 30
x < 30/14
x is less than 3

from the given info we know that x is also more than 1
so combined
1< x < 3

only integer that satisfies is x = 2

sufficient


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

9x + 4x = 26
you can solve for x which gives only one integer since you have 1 equation with 1 unkown

sufficient


solution: D

Stem analysis:
Shirts:Dresses:Jackets can be represented as 9x:4x:5x, and we are told that 4x>7, so x MUST be >=2.

Statement 1:
9x + 5x < 30, which means that 14x<30 so x MUST be less than or equal to 2. Before concluding look at the condition we determine in our stem analysis -- aha, so x MUST be 2 since x >= 2 and x <= 2.

Statement 2:
9x + 4x = 26, so 13x=26 then x is 2. Sufficient.

D is the answer.

Answer: Option D

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