NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 16:06 It is currently 26 Apr 2024, 16:06
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

How much tea worth $0.93 per pound must be mixed with tea worth $0.75

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619238 [3]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
How much tea worth $0.93 per pound must be mixed with tea worth $0.75 [#permalink] New post   24 Jan 2016, 06:29
2
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

25% (medium)

Question Stats:

76% (02:02) correct 24% (02:26) wrong based on 112 sessions
Hide Show timer Statistics
How much tea worth $0.93 per pound must be mixed with tea worth $0.75 per pound to produce 10 pounds worth $0.85 per pound?

A. 2 2⁄9
B. 3 1⁄2
C. 4 4⁄9
D. 5 5⁄9
E. 9 1⁄2
ShowHide Answer
Official Answer
D
User avatar
L
Skywalker18
Verbal Forum Moderator
Joined: 08 Dec 2013
Status:Greatness begins beyond your comfort zone
Posts: 2100
Own Kudos [?]: 8811 [3]
Given Kudos: 171
Location: India
Concentration: General Management, Strategy
GPA: 3.2
WE:Information Technology (Consulting)
Send PM
GMAT ToolKit User Reviews Badge
Re: How much tea worth $0.93 per pound must be mixed with tea worth $0.75 [#permalink] New post   24 Jan 2016, 09:18
1
Kudos
2
Bookmarks
Let weight of tea worth .75 $ = w1
and weight of tea worth .93 $ = w2
w1 + w2 = 10 --- equation 1

.85 = ( w1*.75 + w2* .93 )/(w1+ w2 )
=> .85 w1 + .85 w2 = .75 w1 + .93 w2
=> .10 w1 -.08 w2 = 0
=> 10 w1 - 8 w2 = 0 --- equation 2
From 1 ,
8 w1 + 8 w2 = 80 --- equation 3
From equations 2 and 3 , we get
18 w1 = 80
=> w1 = 40/9
and w2 = 50/9
Answer D , which is in mixed fraction.

Alternatively , we can use scale method
.75 -----.85 ---- .93
.85 is at a distance of .1 from .75 and .08 from .93
The distances of .85 from .75 and 93 are in ratio of 10 : 8 , that is 5:4
Therefore , the weights will be in inverse proporation 4:5
Therefore , w2 = 5/(4+5) * 10 = 50/9
Alternatively, We can also use estimation here and eliminate options A, B and C as the weight of .93 $ variant
has to be more than 50% of 10 pound , i.e 5 pounds . If w1=w2 , then resultant mix would have been of .84 $.
We can also eliminate option E because then the resultant mix will be very close to .93 , only marginally less .
User avatar
L
Mo2men
RSM Erasmus Moderator
Joined: 26 Mar 2013
Posts: 2461
Own Kudos [?]: 1360 [1]
Given Kudos: 641
Concentration: Operations, Strategy
Schools: Erasmus (II)
Send PM
Reviews Badge
How much tea worth $0.93 per pound must be mixed with tea worth $0.75 [#permalink] New post   25 Jan 2016, 12:01
1
Kudos
if we use equal amount (i.e 5 pounds from each tea type), then the resulted mix will equal to the mean of two types which is $0.84

scanning the choices quickly, we need the resulted to have tea of $0.93 a bit higher than 5 pounds.

Answer: D
User avatar
L
generis
Senior SC Moderator
Joined: 22 May 2016
Posts: 5330
Own Kudos [?]: 35497 [1]
Given Kudos: 9464
Send PM
CAT Tests
How much tea worth $0.93 per pound must be mixed with tea worth $0.75 [#permalink] New post   30 Dec 2017, 23:05
1
Kudos
Expert Reply
Bunuel wrote:
How much tea worth $0.93 per pound must be mixed with tea worth $0.75 per pound to produce 10 pounds worth $0.85 per pound?

A. 2 2⁄9
B. 3 1⁄2
C. 4 4⁄9
D. 5 5⁄9
E. 9 1⁄2


A weighted average approach, where one kind of tea is worth an average of $0.93 per pound and another kind of tea is worth an average of .$75 per pound.

One variable in the weighted average formula

Let \(A\) = # of pounds of tea worth $0.93/lb
Let \(B\) = # of pounds of tea worth $0.75/lb
\(A + B = 10\) pounds
\(B = (10 - A)\) pounds

\(.93(A) + .75(B) = .85(A+B=10)\)

\(.93A +.75(10 - A) = .85(10)\)

\(.93 A + 7.5 - .75A = 8.5\)

\(.18A = 1\)

\(A=\frac{1}{.18}=\frac{100}{18}=\frac{50}{9}= 5\frac{5}{9}\)

ANSWER D

Two variables in the weighted average formula

You could also find the ratio of A to B and then use total weight to find number of pounds of A:

\(.93(A) + .75(B) = .85(A + B)\)

\(.93A + .75B = .85A + .85B\)

\(.08A = .10B\)

\(8A = 10B\)

\(B = \frac{8}{10} = \frac{4}{5}A\)

We know that together the two teas weigh 10 pounds.
\(A + B = 10\)

\(A +\frac{4}{5}A = 10\)
\(5A + 4A = 50\)

\(9A = 50\)

\(A = \frac{50}{9} = 5\frac{5}{9}\)

ANSWER D


*where\(A = w_1, 0.93 = A_1, B = w_2, 0.75 = A_2\)

From this weighted average formula

\(\frac{w_1}{w_2} = \frac{(A_2 – A_{avg})}{(A_{avg} – A_1)}\),

we can derive this weighted average formula

\(A_{avg}= \frac{(A_1*w_1) + (A_2*w_2)}{(w_1 + w_2)}\)

And we can multiply both sides of that formula by the RHS denominator to derive yet another weighted average formula:

\((A_1)(w_1) + (A_2)(w_2) = A_{avg}(w_1 + w_2)\).

In these formulas, an average can be a straightforward average, a percentage, a concentration (e.g. of vinegar in a solution), a rate (e.g. an interest rate), and more. Preferences vary. But they are all weighted average formulas.
User avatar
B
tryambaks
Manager
Manager
Joined: 24 Jul 2014
Posts: 71
Own Kudos [?]: 121 [1]
Given Kudos: 39
Location: India
WE:Information Technology (Computer Software)
Send PM
Re: How much tea worth $0.93 per pound must be mixed with tea worth $0.75 [#permalink] New post   25 Jan 2016, 09:59
1
Bookmarks
Let X and Y pounds to mixed
so X+ Y =10
Again from price we have
0.93X+0.75Y=0.85X+0.85Y
=>0.08X=0.1Y
=>4X=5Y
=>Y=4X/5

Since X+Y=10 =>X+4X/5 =10
=>X=5 5/9
Answer = D
User avatar
B
y4nkee
Intern
Intern
Joined: 16 Feb 2016
Posts: 41
Own Kudos [?]: 42 [0]
Given Kudos: 26
Concentration: Other, Other
Send PM
GMAT ToolKit User Reviews Badge
Re: How much tea worth $0.93 per pound must be mixed with tea worth $0.75 [#permalink] New post   08 Mar 2016, 00:22
0.93x+(10-x)*0.75=10*0.85
Multiply everything by 100

93x+750-75x=850

x= (850-750)/(93-75)
x=100/18 ~ 100/20
answer is slightly over 5.
avatar
ks11
Intern
Intern
Joined: 25 Sep 2016
Posts: 4
Own Kudos [?]: 8 [1]
Given Kudos: 8
Schools: LBS MiM"18 MBS '18
WE:Analyst (Consulting)
Send PM
Re: How much tea worth $0.93 per pound must be mixed with tea worth $0.75 [#permalink] New post   06 Oct 2016, 04:33
1
Bookmarks
How much tea worth $0.93 per pound must be mixed with tea worth $0.75 per pound to produce 10 pounds worth $0.85 per pound?

A. 2 2⁄9
B. 3 1⁄2
C. 4 4⁄9
D. 5 5⁄9
E. 9 1⁄2
--------------------------------------------------------------------------------------------
Cost of Tea A = $0.93 per pound
Cost of Tea B = $0.75 per pound
Cost of Tea A and Tea B Mixture = $0.85 per pound

Using Alligation Method

Tea A------------------Tea B

$0.93------------------$0.75
-----------$0.85------------
$0.10------------------$0.08

Ratio of Tea A to Tea B is 10:8 or 5:4

In order to find the weight of Tea A in the mixture
= Ratio of Tea A / Ratio of Tea A + Ratio of Tea B * Total weight of Tea A and Tea B mixture
= 5 / 5+4 * 10 pounds
= 5 / 9 * 10
= 50 / 9
= 5 5⁄9
--------------------------------------------------------------------------------------------
+1 Kudos if you find this post helpful. Thanks!
User avatar
L
AkshdeepS
VP
VP
Joined: 13 Apr 2013
Status:It's near - I can see.
Posts: 1479
Own Kudos [?]: 1603 [0]
Given Kudos: 1002
Location: India
Concentration: International Business, Operations
GPA: 3.01
WE:Engineering (Real Estate)
Send PM
Reviews Badge
How much tea worth $0.93 per pound must be mixed with tea worth $0.75 [#permalink] New post   Updated on: 31 Dec 2017, 23:28
Bunuel wrote:
How much tea worth $0.93 per pound must be mixed with tea worth $0.75 per pound to produce 10 pounds worth $0.85 per pound?

A. 2 2⁄9
B. 3 1⁄2
C. 4 4⁄9
D. 5 5⁄9
E. 9 1⁄2



Method - 1 (Making equations)

Say, Tea A = $ 0.93/pound

Tea B = $ 0.75/pound

We know A + B = 10 -------> (I); as we want the quantity of A to be mixed with B, better to solve for A

Therefore B = 10 - A

Equation becomes, 0.93A + 0.75B = 0.85 (A + B)

93A + 75B = 85 (A+B) ------>(II)

From (I) & (II ) we get 93A + 75(10 - A) = 85 * 10

93A + 750 - 75A = 850
18A = 100

A = 100/18 = \(5\) \(\frac{5}{9}\)

(D)

Method -2 (Weighted average)

\(\frac{Wt A}{Wt B}\) = \(\frac{0.93 - 0.85}{0.85 - 0.75}\)

\(\frac{Wt A}{Wt B}\)= \(\frac{8}{10}\) = \(\frac{4}{5}\)

\(\frac{Wt A}{Wt B}\) (weights will be in inverse proportion) =\(\frac{5}{4}\)

(We have total 5 + 4 = 9 units. average 0.85 is more closer to 0.93 than to 0.75. This means we have more A than B)

Wt A = \(\frac{5}{9}\)*10 = \(\frac{50}{9}\)= \(5\) \(\frac{5}{9}\)

Originally posted by AkshdeepS on 31 Dec 2017, 00:58.
Last edited by AkshdeepS on 31 Dec 2017, 23:28, edited 2 times in total.
User avatar
L
EgmatQuantExpert
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3726
Own Kudos [?]: 16844 [0]
Given Kudos: 165
Send PM
Re: How much tea worth $0.93 per pound must be mixed with tea worth $0.75 [#permalink] New post   31 Dec 2017, 09:23
Expert Reply
Bunuel wrote:
How much tea worth $0.93 per pound must be mixed with tea worth $0.75 per pound to produce 10 pounds worth $0.85 per pound?

A. 2 2⁄9
B. 3 1⁄2
C. 4 4⁄9
D. 5 5⁄9
E. 9 1⁄2


Method ( Using Alligation)



Let X be the first variety of Tea : \($0.93\) per pound and

Let Y be the second variety of Tea : \($ 0.75\) per pound.

The final mixture Z costs \($ 0. 85\) per pound

The ratio in which X and Y are mixed \(= (0.85 - 0.75) : (0.93 - 0.85) = 10 : 8 = 5 : 4\)

Thus, the amount of X in the 10 pound of variety Y is \(\frac{5}{{(5+4)}} * 10 = 5 \frac{5}{9}\) (Option D)


Regards,
Saquib
e-GMAT
Quant Expert
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32689
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: How much tea worth $0.93 per pound must be mixed with tea worth $0.75 [#permalink] New post   02 Feb 2020, 13:52
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: How much tea worth $0.93 per pound must be mixed with tea worth $0.75 [#permalink]
02 Feb 2020, 13:52
Moderators:
Bunuel
Math Expert
92948 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions