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

Question

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

(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

EMPOWERgmatRichC · Accepted Answer

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:  D

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

GMATAcademy · Answer

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

https://www.youtube.com/watch?v=5iFLsVP2MO0

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

varundixitmro2512 · 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)

FightToSurvive · Answer

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

Divyadisha · Answer

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

mehtakaustubh · Answer

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

JeffTargetTestPrep · Answer

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

ethelcurtis · Answer

i think The answer is (1) if i am correct please tell me

EMPOWERgmatRichC · Answer

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  D . 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

BrentGMATPrepNow · Answer

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
 https://www.youtube.com/watch?v=Yegch7sv6MY

GMATinsight · Answer

Answer: Option D 
  https://www.youtube.com/watch?v=SRLKVVyA5tg

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=Ecqw9pLRxIc

GMATCoachBen · Answer

Short solution here (1:49): https://www.youtube.com/watch?v=SuqCUo5QDcM Full Playlist (DS "Hards" — OG 2024): https://www.youtube.com/playlist?list=P ... xuFStg_I4s

ketan770 · Answer

Possibly a very basic question, but not sure why I am fundamentally getting stuck on it. I obviously agree that any piece of clothing would need to be an integer. But by that logic, 4x, 5x and 9x individually need to be integer, why X.

I Mean it so happens that x is a fraction. 
For eg. I may say that dresses : Jackets are in the ratio 2X:10X ( I know it is 1:5 in simplified form ) but just for illustration. So here if X is 1.5 ( a fraction), still 2X:10X turns out to be integer as 3:15. What am I mising with this logic. I was not able to undertand why X has to be an integer.

Bunuel · Answer

"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", can be expressed as s : d : j = 9x : 4x : 5x, for some positive integer x.

When x = 1, then s, d, and j, become 9, 4, and 5, respectively. 
When x = 2, then s, d, and j, become 18, 8, and 10, respectively. 
When x = 3, then s, d, and j, become 27, 12, and 15, respectively. 
and so on.

So, as x increases, we get all possible value of s, d, and j, respectively. You see this is a common way of representing a ratio, where x serves a scaling factor or a 'ratio multiplier'.

satish_sahoo · Answer

I really liked this question, B was so on the face.
Here is how I solved

Pushing the question:
\(s:d:j = 9:4:5\)
let \(x\) be the ratio multiplier
Now as per ques, \(d>7\) meaning \(4x>7\)

To find: \(Total =\)? or \(18x=\)?

1) \(s+j<30\)
\(14x<30\)
\(x\) can have 2 values \(1\) and \(2\)
But \(4x\) is also \(>7\)
So, putting \(x\) as \(1\)and \(2\) here , only \(2\) satisfies so we can get the total...suff

2) \(s+d=26\)
\(13x=26\)
\(x=2\) .....suff

Answer D

Hope it helps

abcxyzabc134 · Answer

I think the correct Anwser is C, okay after we found the answer for Statement 1 was 2, we have to check with the answer for Statement 2, to see are they the same, if they are the same, I think the both statement have to go together, I mean the only situation that satisfying is s+J < 30 and S + D = 26, which mean both statement have to be sufficient at the same time. You can not go for 3 because it makes the S + J > 30 and S+ D not equal to 26.

Bunuel · Answer

It's not clear what you're trying to argue. In Data Sufficiency, the two statements never contradict each other or the prompt.

Both Statement 1 and Statement 2 independently lead to the same valid case: 18 shirts, 8 dresses, 10 jackets, which gives a total of 36 items.

Since each statement alone is sufficient to determine the answer, the correct choice is D, not C.

Please review the full discussion above, it's already explained clearly.

goaltop30mba · Answer

From the stem, we have below information -

S:D:J is 9:4:5

So, we have Total number of articles = 18k, where k is the ratio multiplier.

Also, 4k>7, which means k>1.75 as per the question stem.

Notice that k cannot be a decimal value as it doesn't make sense considering the items we have - shirts, dresses, and jackets.

So, basically, we have the inequality k>=2, for all k belongs to positive integers.

Statement 1:

We have 14k<30, which is k<2.142..., which means k can either be 1 or 2. (k cannot be zero, of course, because we are already given that there are more than 7 dresses in the closet, which means that k cannot be zero. If it were, then every actual quantity will be zero, which would contradict the question stem itself.)

So, from question stem and statement 1, we have we get k=2. Now that we have a unique value or only one value for k, which is the ratio multiplier, we get 18*2 = 36 total number of clothing articles. Hence, statement 1 is sufficient.

Statement 2:

13k = 26, which gives us k=2, which, again, gives us 18*2 = 36 total number of clothing articles. Hence, statement 2 is sufficient as well.

Each of the two statements is sufficient.

Hence, final answer is D.

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

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GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards