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## OG 2017 Ratio Question

This topic has 4 expert replies and 1 member reply
mv2019 Newbie | Next Rank: 10 Posts
Joined
12 Jul 2016
Posted:
2 messages

#### OG 2017 Ratio Question

Wed Jul 13, 2016 10:14 am
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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### GMAT/MBA Expert

Matt@VeritasPrep GMAT Instructor
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Fri Jul 22, 2016 2:04 am
S1:

We know that Shirts + Jackets = 9*(some integer) + 5*(some integer) = 14*(some integer)

Since this number < 30, we must have 14 or 28. But if we only have 14, then we'd have 4 dresses (ratio 9 : 4 : 5) ... and we've got more than 4 dresses! So the only possibility is 28, with 8 dresses and a ratio of 18 : 8 : 10. SUFFICIENT

S2:

Similar to the above, we'd have 9*some integer + 4*some integer = 26, so "some integer" = 2, and we're set: we know that the ratio multiplier is 2. SUFFICIENT

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### GMAT/MBA Expert

Scott@TargetTestPrep GMAT Instructor
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Fri Dec 08, 2017 7:39 am
mv2019 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.
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.

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### GMAT/MBA Expert

Matt@VeritasPrep GMAT Instructor
Joined
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Posted:
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GMAT Score:
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Fri Jul 22, 2016 2:04 am
S1:

We know that Shirts + Jackets = 9*(some integer) + 5*(some integer) = 14*(some integer)

Since this number < 30, we must have 14 or 28. But if we only have 14, then we'd have 4 dresses (ratio 9 : 4 : 5) ... and we've got more than 4 dresses! So the only possibility is 28, with 8 dresses and a ratio of 18 : 8 : 10. SUFFICIENT

S2:

Similar to the above, we'd have 9*some integer + 4*some integer = 26, so "some integer" = 2, and we're set: we know that the ratio multiplier is 2. SUFFICIENT

Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

### GMAT/MBA Expert

Scott@TargetTestPrep GMAT Instructor
Joined
25 Apr 2015
Posted:
548 messages
Followed by:
3 members
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Fri Dec 08, 2017 7:39 am
mv2019 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.
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.

_________________

Scott Woodbury Stewart Founder & CEO
GMAT Quant Self-Study Course - 500+ lessons 3000+ practice problems 800+ HD solutions
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### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
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Wed Jul 13, 2016 11:33 am
Hi mv2019,

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.

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

_________________
Contact Rich at Rich.C@empowergmat.com

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