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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Can anyone explain when to use this weighted average method. And can anyone explain this concept as well.

Thanks in advance.
_________________

I've failed over and over and over again in my life and that is why I succeed--Michael Jordan Kudos drives a person to better himself every single time. So Pls give it generously Wont give up till i hit a 700+

First of all i would like to rate this problem as 700+. This question can be a very good DS candidate. Now coming back to the solution part

Price (in cents) of 4 types of peanuts 54, 72, 120, 144 Ratio of Price of 4 types of peanuts 9 : 12 : 20 : 24 parts Ratio is taken in order to reduce complexity Average Price of mixture = 96 cents Average Price of mixture = 16 parts (because we have reduced the individual prices by 6 times)

The only way to solve this problem is to PLUG the options available As we know Sum of (Respective Quantity x Respective Price) = Total Price = Average price x Total Quantity Option 1 Ratio of quantity mixed - 8a:4a:4a:7a Total quantity = 23a parts (8+4+4+7) (8a.9 + 4a.12 + 4a.20 + 7a.24) = 16.23a 368a = 368a LHS = RHS Thus option 1 satisfy the condition

Option 2 Ratio of quantity mixed - 24a:12a:12a:50a or 12a:6a:6a:25a Total quantity = 49a parts (12a.9 + 6a.12 + 6a.20 + 25a.24) = 16.49a 900a = 784a LHS is not equal to RHS Thus option 2 does not satisfy the condition

Option 3 Ratio of quantity mixed - 4a:8a:7a:4a Total quantity = 23a parts (4a.9 + 8a.12 + 7a.20 + 4a.24) = 16.23a 368a = 368a LHS = RHS Thus option 3 satisfy the condition

As we are asked a unique case, a problem can't have two solutions. Thus answer is it Cannot be uniquely determined Answer E
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS. Kudos always maximizes GMATCLUB worth-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

First of all i would like to rate this problem as 700+. This question can be a very good DS candidate. Now coming back to the solution part

Price (in cents) of 4 types of peanuts 54, 72, 120, 144 Ratio of Price of 4 types of peanuts 9 : 12 : 20 : 24 parts Ratio is taken in order to reduce complexity Average Price of mixture = 96 cents Average Price of mixture = 16 parts (because we have reduced the individual prices by 6 times) The only way to solve this problem is to PLUG the options available As we know Sum of (Respective Quantity x Respective Price) = Total Price = Average price x Total Quantity Option 1 Ratio of quantity mixed - 8a:4a:4a:7a Total quantity = 23a parts (8+4+4+7) (8a.9 + 4a.12 + 4a.20 + 7a.24) = 16.23a 368a = 368a LHS = RHS Thus option 1 satisfy the condition

Option 2 Ratio of quantity mixed - 24a:12a:12a:50a or 12a:6a:6a:25a Total quantity = 49a parts (12a.9 + 6a.12 + 6a.20 + 25a.24) = 16.49a 900a = 784a LHS is not equal to RHS Thus option 2 does not satisfy the condition

Option 3 Ratio of quantity mixed - 4a:8a:7a:4a Total quantity = 23a parts (4a.9 + 8a.12 + 7a.20 + 4a.24) = 16.23a 368a = 368a LHS = RHS Thus option 3 satisfy the condition

As we are asked a unique case, a problem can't have two solutions. Thus answer is it Cannot be uniquely determined Answer E

Hi, Can you pls explain from where did the above highlighted part come ?

As we are asked a unique case, a problem can't have two solutions. Thus answer is it Cannot be uniquely determined Answer E[/quote]

Hi, Can you pls explain from where did the above highlighted part come ?[/quote]

Price (in cents) of 4 types of peanuts 54:72:120:144 -----(1) Ratio of Price of 4 types of peanuts 9 : 12 : 20 : 24 parts----(2) Multiply equation (2) by 6 , you will get equation (1). I have only reduced the ratios , & nothing more than that.

Hope it helps
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS. Kudos always maximizes GMATCLUB worth-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

is there any other way to solve this in less than 2 min. If i plugin the answer choice it will be little lengthy.

This is a 10 second problem and involves no calculations. Think of weighted averages.

Four types of peanuts: 54 c, 72 c, 120 c and 144 c We need the average to be 96 c.

There are various ways to obtain 96c: Take a combination of 54 c and 120 c (and the rest in negligible quantities if you must use all) Take a combination of 72 c and 120 c (and the rest in negligible quantities if you must use all) Take a combination of 54 c and 144 c (and the rest in negligible quantities if you must use all) ... etc

Hence there is no unique combination. Answer (E)

Whenever 3 or more quantities are involved, you can usually get a weighted average in many ways.
_________________

is there any other way to solve this in less than 2 min. If i plugin the answer choice it will be little lengthy.

This is a 10 second problem and involves no calculations. Think of weighted averages.

Four types of peanuts: 54 c, 72 c, 120 c and 144 c We need the average to be 96 c.

There are various ways to obtain 96c: Take a combination of 54 c and 120 c (and the rest in negligible quantities if you must use all) Take a combination of 72 c and 120 c (and the rest in negligible quantities if you must use all) Take a combination of 54 c and 144 c (and the rest in negligible quantities if you must use all) ... etc

Hence there is no unique combination. Answer (E)

Whenever 3 or more quantities are involved, you can usually get a weighted average in many ways.

is there any other way to solve this in less than 2 min. If i plugin the answer choice it will be little lengthy.

This is a 10 second problem and involves no calculations. Think of weighted averages.

Four types of peanuts: 54 c, 72 c, 120 c and 144 c We need the average to be 96 c.

There are various ways to obtain 96c: Take a combination of 54 c and 120 c (and the rest in negligible quantities if you must use all) Take a combination of 72 c and 120 c (and the rest in negligible quantities if you must use all) Take a combination of 54 c and 144 c (and the rest in negligible quantities if you must use all) ... etc

Hence there is no unique combination. Answer (E)

Whenever 3 or more quantities are involved, you can usually get a weighted average in many ways.

Hi Karishma,

Can you explain a little further about this? I don't understand the part of negligible quantities.... 120 and 54 don't reach 96.... Can you explain a bit more?

is there any other way to solve this in less than 2 min. If i plugin the answer choice it will be little lengthy.

This is a 10 second problem and involves no calculations. Think of weighted averages.

Four types of peanuts: 54 c, 72 c, 120 c and 144 c We need the average to be 96 c.

There are various ways to obtain 96c: Take a combination of 54 c and 120 c (and the rest in negligible quantities if you must use all) Take a combination of 72 c and 120 c (and the rest in negligible quantities if you must use all) Take a combination of 54 c and 144 c (and the rest in negligible quantities if you must use all) ... etc

Hence there is no unique combination. Answer (E)

Whenever 3 or more quantities are involved, you can usually get a weighted average in many ways.

Hi Karishma,

Can you explain a little further about this? I don't understand the part of negligible quantities.... 120 and 54 don't reach 96.... Can you explain a bit more?

Two quantities can be mixed in some ratio to give any value in between i.e. say we have two types of peanuts costing 30 c and 60 c per pound. Can they be mixed in a way such that the cost is 45 c per pound? Sure! Mix them in equal quantities. Can they be mixed to get a mix costing 40 c per pound? Sure! Mix them in the ratio 2:1. Can they be mixed to get a mix costing 50 c per pound? Sure! Mix them in the ratio 1:2. All these are very simple calculations using the scale method discussed here: http://www.veritasprep.com/blog/2011/03 ... -averages/

You can get mix of any cost price lying between 30 and 60.

Here you have 4 cost prices: 54 c, 72 c, 120 c and 144 c The average needs to be 96c

For simplicity, assume we are working with only two cost prices and other two we mix in very little quantity i.e. we put .000001 gms of each of the other two just because we need to use all 4. But their overall effect on the mix will be as good as 0.

You can mix 54 c and 120 c in some ratio to get 96 c since 96 c lies between the two. (In this we will put the other types of peanuts costing 72 c and 144 c in very little quantity such that they have no effect on the mix at all. If we are allowed to use only two types of peanuts and not all 4, we will not put the two types costing 72 c and 144 c)

You can mix 72 c and 144 c in some ratio to get 96 c since 96 c lies between the two too. (In this we will put the other types of peanuts costing 54 c and 120 c in very little quantity such that they have no effect on the mix at all. If we are allowed to use only two types of peanuts and not all 4, we will not put the two types costing 54 c and 120 c)

We see that we already have 2 ways of mixing the 4 types of peanuts such that we will get a mix which costs 96 c. Hence there is no unique way.

This question is around 600-650 level in my opinion but note that it is not a GMAT type question. In GMAT questions, 'Cannot be determined' is not an option. Though this question is good for conceptual understanding.
_________________

Re: How must a grocer mix 4 types of peanuts worth 54 c, 72 c, $ [#permalink]

Show Tags

20 Aug 2017, 07:18

Interesting one. Forces you to think than just get an answer. Here is my process - the question asks what is the unique case of ratios that would give us 96c as average price of a pound --> If we add 54c + 72c + 120c + 144c = 96 --> c = 16/65 approx 1/4 (and little more => I took 16/64 which is 1/4) So basically we need just SLIGHTLY more than 1/4th of every kind --> if we look at the options, none of them are that way: (A) 8:4:4:7 --> not possible at all (B) 24:12:12:50 --> same (C) 4:8:7:4 --> no (D) 16:42:28:10 --> not at all

This leaves us with E. Admittedly, after getting 1/4 I was stuck - I didn't how to interpret it- but looking at the options helped If there are any more questions like this, please do post, need practice on these!