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05 Jul 2012, 12:25
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
54% (01:53) correct
46%
(02:31)
wrong
based on 316
sessions
History
Date
Time
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Not Attempted Yet
How must a grocer mix 4 types of peanuts worth 54 c, 72 c, $1.2 and $1.44 per pound so as to obtain a mixture at 96 cents per pound?
(A) 8:4:4:7
(B) 24:12:12:50
(C) 4:8:7:4
(D) 16:42:28:10
(E) Cannot be uniquely determined
(A) 8:4:4:7
(B) 24:12:12:50
(C) 4:8:7:4
(D) 16:42:28:10
(E) Cannot be uniquely determined
05 Jun 2014, 21:09
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ronr34
VeritasPrepKarishma
ankur1901
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: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/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.
20 Jan 2014, 23:57
Kudos
Bookmarks
ankur1901
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.
