GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 20 Mar 2019, 06:28

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

The ratio of blue to black denims at a certain shop is 15:16. If there

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Manager
Manager
avatar
B
Joined: 03 Feb 2017
Posts: 74
Location: Australia
GMAT 1: 720 Q48 V40
The ratio of blue to black denims at a certain shop is 15:16. If there  [#permalink]

Show Tags

New post 20 Jun 2017, 02:52
2
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

89% (02:11) correct 11% (02:29) wrong based on 75 sessions

HideShow timer Statistics

The ratio of blue to black jeans at a certain shop is 15:16. If there were 35 additional black jeans in the shop, the ratio of blue to black jeans would be 15:21. How many blue jeans does the shop have?

A) 100
B) 103
C) 105
D) 107
E) 110
Director
Director
User avatar
V
Joined: 04 Dec 2015
Posts: 750
Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
WE: Information Technology (Consulting)
GMAT ToolKit User
The ratio of blue to black denims at a certain shop is 15:16. If there  [#permalink]

Show Tags

New post 20 Jun 2017, 03:04
1
danlew wrote:
The ratio of blue to black jeans at a certain shop is 15:16. If there were 35 additional black jeans in the shop, the ratio of blue to black jeans would be 15:21. How many blue jeans does the shop have?

A) 100
B) 103
C) 105
D) 107
E) 110


Let number of Blue jeans be \(= X\)

Let number of Black jeans be \(= Y\)

Blue jeans / Black jeans \(= \frac{X}{Y} = \frac{15}{16}\)

\(Y = \frac{16}{15} * X\) --------- (i)

Blue jeans / Black jeans + 35 additional black jeans \(= \frac{X}{Y + 35} = \frac{15}{21}\)

\(\frac{X}{Y + 35} = \frac{15}{21}\)

\(21 X = 15 (Y + 35)\)

\(21 X = 15 Y + 525\) ---------- (ii)

Substituting value of Y from (i) in (ii), we get;

\(21 X = 15 (\frac{16}{15} * X) + 525\)

\(21 X = 16 X + 525\)

\(21 X - 16 X = 525\)

\(5 X = 525\)

\(X = \frac{525}{5} = 105 .\) Answer (C) ...
Manager
Manager
User avatar
B
Joined: 17 Feb 2016
Posts: 90
Location: India
Concentration: General Management, Entrepreneurship
GMAT 1: 660 Q47 V36
GPA: 3.12
WE: Education (Internet and New Media)
Reviews Badge
Re: The ratio of blue to black denims at a certain shop is 15:16. If there  [#permalink]

Show Tags

New post 20 Jun 2017, 03:45
The ratio of blue to black jeans at a certain shop is 15:16. If there were 35 additional black jeans in the shop, the ratio of blue to black jeans would be 15:21. How many blue jeans does the shop have?

Let Blue/Black original value, \(\frac{15}{16}\)= \(\frac{15x}{16x}\)
By data,
16x=16x+35
\(\frac{15x}{16x+35}\)=\(\frac{15}{21}\)
Solving above, x=7
Blue= 15x=15*7=105
_________________

Never stop fighting until you arrive at your destined place - that is, the unique you. Have an aim in life, continuously acquire knowledge, work hard, and have the perseverance to realise the great life. A. P. J. Abdul Kalam

Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3361
Location: India
GPA: 3.12
Premium Member
The ratio of blue to black denims at a certain shop is 15:16. If there  [#permalink]

Show Tags

New post 20 Jun 2017, 04:05
1
Given :
Initial ratio of Jeans (Blue:Black = 15x:16x)
Final ratio of Jeans (Blue:Black = 15x:21x)

Hence difference of 21x - 16x is caused by the addition of the 35 black jeans, x = 7.
Hence the blue jeans is 15x = 105(Option C)
_________________

You've got what it takes, but it will take everything you've got

Board of Directors
User avatar
P
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4402
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member CAT Tests
Re: The ratio of blue to black denims at a certain shop is 15:16. If there  [#permalink]

Show Tags

New post 20 Jun 2017, 08:05
danlew wrote:
The ratio of blue to black jeans at a certain shop is 15:16. If there were 35 additional black jeans in the shop, the ratio of blue to black jeans would be 15:21. How many blue jeans does the shop have?

A) 100
B) 103
C) 105
D) 107
E) 110


15 + 16 = 31
15 + 21 = 36

SO, 5 represents 35 Black jeans or 1 represents 7 Black jeans , as no blue jeans were added...

So, the total number of blue jeans is 15*7 = 105 Blue Jeans...

Answer will be (C)
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

CEO
CEO
User avatar
V
Joined: 12 Sep 2015
Posts: 3511
Location: Canada
The ratio of blue to black denims at a certain shop is 15:16. If there  [#permalink]

Show Tags

New post 20 Jun 2017, 08:42
2
Top Contributor
danlew wrote:
The ratio of blue to black jeans at a certain shop is 15:16. If there were 35 additional black jeans in the shop, the ratio of blue to black jeans would be 15:21. How many blue jeans does the shop have?

A) 100
B) 103
C) 105
D) 107
E) 110


We can actually solve this question WITHOUT using the information in the second sentence.

The ratio of blue to black jeans at a certain shop is 15:16
There are many possibilities. Here are a few:
- There are 15 blue jeans and 16 black jeans
- There are 30 blue jeans and 32 black jeans
- There are 45 blue jeans and 48 black jeans
- There are 60 blue jeans and 64 black jeans
- There are 75 blue jeans and 80 black jeans
etc

Notice that, since the number of each type of jeans must be an INTEGER, the number of blue jeans must be a multiple of 15

Check the answer choices....only one answer choice is a multiple of 15

Answer:

RELATED VIDEO

_________________

Test confidently with gmatprepnow.com
Image

VP
VP
User avatar
D
Status: Learning
Joined: 20 Dec 2015
Posts: 1025
Location: India
Concentration: Operations, Marketing
GMAT 1: 670 Q48 V36
GRE 1: Q157 V157
GPA: 3.4
WE: Engineering (Manufacturing)
Reviews Badge CAT Tests
Re: The ratio of blue to black denims at a certain shop is 15:16. If there  [#permalink]

Show Tags

New post 20 Jun 2017, 10:54
Blue/Black (x/y)=15\16
If additional 35 black jeans are added the ration becomes
(x/y+35)=15/21

Solving for X and Y We get number of blue jeans 105
_________________

Please give kudos if you found my answers useful

Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2825
Re: The ratio of blue to black denims at a certain shop is 15:16. If there  [#permalink]

Show Tags

New post 20 Jun 2017, 19:08
danlew wrote:
The ratio of blue to black jeans at a certain shop is 15:16. If there were 35 additional black jeans in the shop, the ratio of blue to black jeans would be 15:21. How many blue jeans does the shop have?

A) 100
B) 103
C) 105
D) 107
E) 110


We are given that the ratio of blue to black jeans at a certain shop is 15x : 16x. We are also given that if there were 35 additional black jeans in the shop, the ratio of blue to black jeans would be 15 : 21. Thus:

15x/(16x + 35) = 15/21

15x/(16x + 35) = 15/21

15x(21) = 15(16x + 35)

21x = 16x + 35

5x = 35

x = 7

Thus, the shop has 15(7) = 105 blue jeans.

Answer: C

(Note: We also could have recognized that the number of blue jeans must be a multiple of 15 and the only answer choice that is a multiple of 15 is answer choice C, 105.)
_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

CEO
CEO
User avatar
V
Joined: 12 Sep 2015
Posts: 3511
Location: Canada
Re: The ratio of blue to black denims at a certain shop is 15:16. If there  [#permalink]

Show Tags

New post 21 Jun 2017, 06:21
Top Contributor
danlew wrote:
The ratio of blue to black jeans at a certain shop is 15:16. If there were 35 additional black jeans in the shop, the ratio of blue to black jeans would be 15:21. How many blue jeans does the shop have?

A) 100
B) 103
C) 105
D) 107
E) 110


Here's a solution that uses two variables:

The ratio of blue to black jeans at a certain shop is 15:16
Let B = number of blue jeans PRESENTLY in the shop
Let K = number of black jeans PRESENTLY in the shop
So, we can write: B/K = 15/16
Cross multiply to get: 16B = 15K

If there were 35 additional black jeans in the shop, the ratio of blue to black jeans would be 15:21.
So, B = number of blue jeans in the shop AFTER 35 black jeans are added
And K + 35 = number of black jeans in the shop AFTER 35 black jeans are added
So, we can write: B/(K + 35) = 15/21
Cross multiply to get: 21B = 15(K + 35)
Expand: 21B = 15K + 525
Subtract 525 from both sides to get: 21B - 525 = 15K

How many blue jeans does the shop have?
We now have the following system of equations:
16B = 15K
21B - 525 = 15K

Since both equations are set equal to 15K, we can write: 16B = 21B - 525
Subtract 21B from both sides: -5B = -525
Divide both sides by -5 to get: B = 105

Answer:

Cheers,
Brent
_________________

Test confidently with gmatprepnow.com
Image

Intern
Intern
avatar
B
Joined: 09 Dec 2018
Posts: 2
Re: The ratio of blue to black denims at a certain shop is 15:16. If there  [#permalink]

Show Tags

New post 19 Feb 2019, 14:06
RaguramanS wrote:
The ratio of blue to black jeans at a certain shop is 15:16. If there were 35 additional black jeans in the shop, the ratio of blue to black jeans would be 15:21. How many blue jeans does the shop have?

Let Blue/Black original value, \(\frac{15}{16}\)= \(\frac{15x}{16x}\)
By data,
16x=16x+35
\(\frac{15x}{16x+35}\)=\(\frac{15}{21}\)
Solving above, x=7
Blue= 15x=15*7=105


Why did we add X to the numerator and denominator in the fraction?
GMAT Club Bot
Re: The ratio of blue to black denims at a certain shop is 15:16. If there   [#permalink] 19 Feb 2019, 14:06
Display posts from previous: Sort by

The ratio of blue to black denims at a certain shop is 15:16. If there

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.