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

It is currently 19 Feb 2019, 20:13

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
Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
  • Free GMAT Prep Hour

     February 20, 2019

     February 20, 2019

     08:00 PM EST

     09:00 PM EST

    Strategies and techniques for approaching featured GMAT topics. Wednesday, February 20th at 8 PM EST
  • Online GMAT boot camp for FREE

     February 21, 2019

     February 21, 2019

     10:00 PM PST

     11:00 PM PST

    Kick off your 2019 GMAT prep with a free 7-day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.

A bucket contains a mixture of two liquids A & B

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

Hide Tags

 
Intern
Intern
avatar
B
Joined: 13 Aug 2018
Posts: 10
A bucket contains a mixture of two liquids A & B  [#permalink]

Show Tags

New post 17 Oct 2018, 02:59
11
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

48% (02:36) correct 52% (02:43) wrong based on 142 sessions

HideShow timer Statistics

A bucket contains a mixture of two liquids A & B in the proportion 5 : 3. If 16 litres of the mixture is replaced by 16 litres of liquid B , then the ratio of the two liquids becomes 3 : 5. How much of the liquid B was there in the bucket ?


(A) 12 litres
(B) 15 litres
(C) 18 litres
(D) 6 litres
(E) 24 litres

Posted from my mobile device
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7334
Premium Member Reviews Badge
A bucket contains a mixture of two liquids A & B  [#permalink]

Show Tags

New post 21 Oct 2018, 10:47
1
2
jackfr2 wrote:
A bucket contains a mixture of two liquids A & B in the proportion 5 : 3. If 16 litres of the mixture is replaced by 16 litres of liquid B , then the ratio of the two liquids becomes 3 : 5. How much of the liquid B was there in the bucket ?


(A) 12 litres
(B) 15 litres
(C) 18 litres
(D) 6 litres
(E) 24 litres

Posted from my mobile device



Responding to a PM

I would think of the problem in two ways..

(I) logical..
Now 16 litres of MIXTURE is removed, so A removed is \(16*\frac{5}{8}=10\)...
This removal of 10 litres leads to 2 units of A going down, so 2 units =10
1 unit =10/2=5...
B is 3 units ( from 5:3) , so 3*5=15

(II) Algebraic
Let the initial ratio be 5x:3x....
Removal of 16 in same ratio MEANS 10:6..
So A becomes = 5x-10 and B becomes =3x-6
When we add 16 litres to B ...
\(\frac{5x-10}{3x-6+16}=\frac{3}{5}\)..
\(25x-50=9x+30.......16x=80......x=5\)
So 3x=3*5=15

B
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html


GMAT Expert

Most Helpful Community Reply
Intern
Intern
avatar
B
Joined: 19 Sep 2017
Posts: 2
Re: A bucket contains a mixture of two liquids A & B  [#permalink]

Show Tags

New post 20 Oct 2018, 01:58
8
3
I didn't find any clearer explanation, thats why I am just sharing my approach. Hope this helps.

Initially the ratio is \(\frac{5x}{3x}\). We know that 16 litres is removed from TOTAL MIXTURE, so the removal is in the same ratio. After removal of the total 16 litres, the removal will be in the ratio of 5:3, which will result is 10 ltrs from A and 6 ltrs from B.

So, \(\frac{(5x-10)}{(3x-6)}\). Further, 16 litres is added to B.

\(\frac{(5x-10)}{(3x-6+16)} = \frac{(5x-10)}{(3x+10)}\) this ratio now becomes \(\frac{3}{5}\). hence solving for \(\frac{(5x-10)}{(3x+10)}\)= \(\frac{3}{5}\), we get x= 5.

now using \(x=5\), we know the initial Value of \(\frac{A}{B}\)= \(\frac{5x}{3x}\) is \(\frac{25}{15}\).
Hence B is 15.


Please Give kudos if this helped.
General Discussion
Manager
Manager
avatar
G
Joined: 01 Mar 2015
Posts: 76
Re: A bucket contains a mixture of two liquids A & B  [#permalink]

Show Tags

New post 17 Oct 2018, 03:28
jackfr2 wrote:
A bucket contains a mixture of two liquids A & B in the proportion 5 : 3. If 16 litres of the mixture is replaced by 16 litres of liquid B , then the ratio of the two liquids becomes 3 : 5. How much of the liquid B was there in the bucket ?


(A) 12 litres
(B) 15 litres
(C) 18 litres
(D) 6 litres
(E) 24 litres

Posted from my mobile device


Here the fraction A:B changes from 5:3 to 3:5 when the 16 litres of A is replaced by 16 litres of B

If we take solution to be 5x + 3x = 8x
Initially
A = 5x
B = 3x

As total solution remains same, 16 litres is removed and 16 litres is added. Therefore final in solution

A' = 3x
B' = 5x

A' = A - 16
=> 5x - 16 = 3x
=> 2x = 16
=> x = 8 litres

B = 3x = 3*8 = 24 litres

So, initially 24 litres of liquid B was there in the bucket.

Answer Choice (E)
Intern
Intern
avatar
B
Joined: 13 Aug 2018
Posts: 10
Re: A bucket contains a mixture of two liquids A & B  [#permalink]

Show Tags

New post 17 Oct 2018, 10:30
v12345 wrote:
jackfr2 wrote:
A bucket contains a mixture of two liquids A & B in the proportion 5 : 3. If 16 litres of the mixture is replaced by 16 litres of liquid B , then the ratio of the two liquids becomes 3 : 5. How much of the liquid B was there in the bucket ?


(A) 12 litres
(B) 15 litres
(C) 18 litres
(D) 6 litres
(E) 24 litres

Posted from my mobile device


Here the fraction A:B changes from 5:3 to 3:5 when the 16 litres of A is replaced by 16 litres of B

If we take solution to be 5x + 3x = 8x
Initially
A = 5x
B = 3x

As total solution remains same, 16 litres is removed and 16 litres is added. Therefore final in solution

A' = 3x
B' = 5x

A' = A - 16
=> 5x - 16 = 3x
=> 2x = 16
=> x = 8 litres

B = 3x = 3*8 = 24 litres

So, initially 24 litres of liquid B was there in the bucket.

Answer Choice (E)



this is wrong when you back check your answer .

if initially B is 24 A must be 40.
after removal B should be 18 and A 30 .
after adding 16 litre of B , B should be 32 and A 32 which isn't a 3:5 ratio .
VP
VP
avatar
P
Joined: 07 Dec 2014
Posts: 1156
A bucket contains a mixture of two liquids A & B  [#permalink]

Show Tags

New post 17 Oct 2018, 11:35
1
jackfr2 wrote:
A bucket contains a mixture of two liquids A & B in the proportion 5 : 3. If 16 litres of the mixture is replaced by 16 litres of liquid B , then the ratio of the two liquids becomes 3 : 5. How much of the liquid B was there in the bucket ?


(A) 12 litres
(B) 15 litres
(C) 18 litres
(D) 6 litres
(E) 24 litres

Posted from my mobile device


let x=total original mixture
3/8*(x-16)+16=5x/8
x=40
3/8*40=15
B
Senior Manager
Senior Manager
User avatar
P
Joined: 18 Jun 2018
Posts: 262
Premium Member CAT Tests
Re: A bucket contains a mixture of two liquids A & B  [#permalink]

Show Tags

New post 20 Oct 2018, 07:50
1
jackfr2 wrote:
A bucket contains a mixture of two liquids A & B in the proportion 5 : 3. If 16 litres of the mixture is replaced by 16 litres of liquid B , then the ratio of the two liquids becomes 3 : 5. How much of the liquid B was there in the bucket ?


(A) 12 litres
(B) 15 litres
(C) 18 litres
(D) 6 litres
(E) 24 litres

Posted from my mobile device


OA:B

Initial Amount of A: \(5x\)
Initial Amount of B: \(3x\)
Total mixture amount: A+B \(= 5x+3x = 8x\)

\(16\) Litre of this mixture is taken out

Amount of A left :\(\frac{5}{8}*(8x-16)=5x-10\)

Amount of B left :\(\frac{3}{8}*(8x-16)=3x-6\)

16 Litre of B added

Final Amount of A :\(\frac{5}{8}*(8x-16)=5x-10\)

Final Amount of B :\(\frac{3}{8}*(8x-16)+16=3x+10\)

According to the question,

\(\frac{5x-10}{3x+10} =\frac{3}{5}\)

\(25x-50=9x+30\)

\(16x=80\)

\(x=\frac{80}{16}=5\)

Initial Amount of B \(= 3x = 3*5 = 15\) Litres
Founder
Founder
User avatar
V
Joined: 04 Dec 2002
Posts: 17239
Location: United States (WA)
GMAT 1: 750 Q49 V42
GPA: 3.5
GMAT ToolKit User Premium Member CAT Tests
A bucket contains a mixture of two liquids A & B  [#permalink]

Show Tags

New post 20 Oct 2018, 08:03
chetan2u - what do you think of this question?

(testing notifications - pardon for the interruption)
_________________

Founder of GMAT Club

Just starting out with GMAT? Start here...
OG2019 Directory is here!
Want to know application stats & Profiles from last year? Check the Decision Tracker

Co-author of the GMAT Club tests

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7334
Premium Member Reviews Badge
Re: A bucket contains a mixture of two liquids A & B  [#permalink]

Show Tags

New post 20 Oct 2018, 08:15
bb wrote:
chetan2u - what do you think of this question?

(testing notifications - pardon for the interruption)



BB,

no notifications in the mails. I just checked the notifications on site and saw this...
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html


GMAT Expert

SVP
SVP
User avatar
D
Joined: 26 Mar 2013
Posts: 2067
Reviews Badge CAT Tests
Re: A bucket contains a mixture of two liquids A & B  [#permalink]

Show Tags

New post 20 Oct 2018, 10:34
1
jackfr2 wrote:
A bucket contains a mixture of two liquids A & B in the proportion 5 : 3. If 16 litres of the mixture is replaced by 16 litres of liquid B , then the ratio of the two liquids becomes 3 : 5. How much of the liquid B was there in the bucket ?


(A) 12 litres
(B) 15 litres
(C) 18 litres
(D) 6 litres
(E) 24 litres

Posted from my mobile device


Dear GMATGuruNY

Can you share your thoughts in this problem?
Senior Manager
Senior Manager
avatar
S
Joined: 04 Aug 2010
Posts: 350
Schools: Dartmouth College
A bucket contains a mixture of two liquids A & B  [#permalink]

Show Tags

New post 20 Oct 2018, 12:27
1
jackfr2 wrote:
A bucket contains a mixture of two liquids A & B in the proportion 5 : 3. If 16 litres of the mixture is replaced by 16 litres of liquid B , then the ratio of the two liquids becomes 3 : 5. How much of the liquid B was there in the bucket ?


(A) 12 litres
(B) 15 litres
(C) 18 litres
(D) 6 litres
(E) 24 litres


We can use ALLIGATION.
Let:
S = the original solution
B = the 16 liters of pure B
M = the final mixture
Alligation can be performed only with percentages or fractions.

Step 1: Convert the ratios to FRACTIONS with the same denominator.
S --> Since A:B = 5:3, \(\frac{B}{total} = \frac{3}{8}\)
B --> \(\frac{B}{total} = \frac{{16}}{{16}} = \frac{8}{8}\)
M --> Since A:B = 3:5, \(\frac{B}{total} = \frac{5}{8}\)

Step 2: Plot the 3 numerators on a number line, with the numerators for S and B on the ends and the numerator for the mixture in the middle.
S 3------------5-----------8 B

Step 3: Calculate the distances between the numerators.
S 3-----2-----5-----3-----8 B

Step 4: Determine the ratio in the mixture.
The ratio of S to B is equal to the RECIPROCAL of the distances in red.
S:B = 3:2 = 24:16.

The ratio in blue indicates that the mixture is composed of 24 liters of original solution and 16 liters of pure B, implying that the total volume in the bucket = 40 liters.
Since B constitutes \(\frac{3}{8}\) of the original 40 liters in the bucket, we get:
\(\frac{3}{8} * 40 = 15\) liters


_________________

GMAT and GRE Tutor
Over 1800 followers
Click here to learn more
GMATGuruNY@gmail.com
New York, NY
If you find one of my posts helpful, please take a moment to click on the "Kudos" icon.
Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.

Intern
Intern
User avatar
S
Joined: 05 Jan 2017
Posts: 39
GMAT ToolKit User
Re: A bucket contains a mixture of two liquids A & B  [#permalink]

Show Tags

New post 22 Oct 2018, 03:29
1
by weighted avg approach:
B initial- 3/8
B after - 5/8

applying in the formula- (5-8)/(8-3)
=> 3/5

hence ratio a:b = 3:2
16% of sol was replaced. hence a:b can be 24:16
total sol = 40
after replace B= 3/8 * 40 = 15 (B)
_________________

----------------------------
Kudos if my post helps!

GMAT Club Bot
Re: A bucket contains a mixture of two liquids A & B   [#permalink] 22 Oct 2018, 03:29
Display posts from previous: Sort by

A bucket contains a mixture of two liquids A & B

  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®.