Last visit was: 14 Sep 2024, 20:27 It is currently 14 Sep 2024, 20:27
Toolkit
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

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

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 95507
Own Kudos [?]: 658645 [128]
Given Kudos: 87257
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21832
Own Kudos [?]: 11868 [60]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Manager
Joined: 25 Jun 2016
Posts: 58
Own Kudos [?]: 564 [36]
Given Kudos: 4
GMAT 1: 780 Q51 V46
General Discussion
Manager
Joined: 04 Apr 2015
Posts: 83
Own Kudos [?]: 270 [0]
Given Kudos: 3989
Re: The only articles of clothing in a certain closet are shirts, dresses, [#permalink]
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)
Manager
Joined: 18 Sep 2014
Posts: 198
Own Kudos [?]: 238 [3]
Given Kudos: 5
Re: The only articles of clothing in a certain closet are shirts, dresses, [#permalink]
3
Kudos
varundixitmro2512
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
Current Student
Joined: 18 Oct 2014
Posts: 679
Own Kudos [?]: 1807 [11]
Given Kudos: 69
Location: United States
GMAT 1: 660 Q49 V31
GPA: 3.98
Re: The only articles of clothing in a certain closet are shirts, dresses, [#permalink]
8
Kudos
3
Bookmarks
Bunuel
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.

Manager
Joined: 11 Jul 2009
Posts: 63
Own Kudos [?]: 151 [5]
Given Kudos: 83
WE:Design (Computer Software)
Re: The only articles of clothing in a certain closet are shirts, dresses, [#permalink]
4
Kudos
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
Target Test Prep Representative
Joined: 04 Mar 2011
Affiliations: Target Test Prep
Posts: 3036
Own Kudos [?]: 6838 [14]
Given Kudos: 1646
Re: The only articles of clothing in a certain closet are shirts, dresses, [#permalink]
7
Kudos
7
Bookmarks
Bunuel
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.

Intern
Joined: 21 Feb 2018
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 0
The only articles of clothing in a certain closet are shirts, dresses, [#permalink]
i think The answer is (1) if i am correct please tell me
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21832
Own Kudos [?]: 11868 [0]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: The only articles of clothing in a certain closet are shirts, dresses, [#permalink]
ethelcurtis
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
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6803
Own Kudos [?]: 31322 [4]
Given Kudos: 799
The only articles of clothing in a certain closet are shirts, dresses, [#permalink]
3
Kudos
1
Bookmarks
Top Contributor
Bunuel
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

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

Cheers,
Brent

RELATED VIDEO

Originally posted by BrentGMATPrepNow on 07 Mar 2019, 12:39.
Last edited by BrentGMATPrepNow on 17 May 2021, 08:34, edited 1 time in total.
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6065
Own Kudos [?]: 14136 [0]
Given Kudos: 125
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
The only articles of clothing in a certain closet are shirts, dresses, [#permalink]
Bunuel
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

­
Tutor
Joined: 17 Jul 2019
Posts: 1299
Own Kudos [?]: 1791 [1]
Given Kudos: 66
GMAT 1: 780 Q51 V45
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
Re: The only articles of clothing in a certain closet are shirts, dresses, [#permalink]
1
Kudos
Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
Tutor
Joined: 21 Mar 2017
Status:Professional GMAT Trainer
Affiliations: GMAT Coach
Posts: 424
Own Kudos [?]: 1378 [1]
Given Kudos: 204
Location: United States (WA)
GMAT 1: 760 Q50 V44
GMAT 2: 770 Q51 V44
GMAT 3: 770 Q50 V44
GMAT 4: 770 Q50 V45 (Online)
GMAT 5: 780 Q51 V48
The only articles of clothing in a certain closet are shirts, dresses, [#permalink]
1
Kudos
Short solution here (1:49):

Full Playlist (DS "Hards" — OG 2024): https://www.youtube.com/playlist?list=P ... xuFStg_I4s
Intern
Joined: 23 Aug 2022
Posts: 4
Own Kudos [?]: 0 [0]
Given Kudos: 6
Re: The only articles of clothing in a certain closet are shirts, dresses, [#permalink]
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.
Math Expert
Joined: 02 Sep 2009
Posts: 95507
Own Kudos [?]: 658645 [0]
Given Kudos: 87257
Re: The only articles of clothing in a certain closet are shirts, dresses, [#permalink]
ketan770
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.

"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'.
Re: The only articles of clothing in a certain closet are shirts, dresses, [#permalink]
Moderator:
Math Expert
95507 posts