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The inventory of grape jelly on a store's shelves consists only of 2-o

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The inventory of grape jelly on a store's shelves consists only of 2-o  [#permalink]

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New post 03 Dec 2019, 21:48
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  75% (hard)

Question Stats:

38% (01:56) correct 63% (01:55) wrong based on 16 sessions

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The inventory of grape jelly on a store's shelves consists only of 2-ounce, 6-ounce, and 16-ounce jars. If the average jar size of the current inventory is 6.4 ounces, how many additional 2-ounce jars must be put on the shelves to reduce the average size to 6.0 ounces?

(1) The current ratio of 2-ounce to 6-ounce to 16-ounce jars is 15:27:8.

(2) There are initially 7 more 2-ounce jars than 16-ounce jars.
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Re: The inventory of grape jelly on a store's shelves consists only of 2-o  [#permalink]

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New post 03 Dec 2019, 22:26
1
No of :
2-ounce Jar= A
6-ounce Jar =B
16-ounce jar = C
average jar size of the current inventory is 6.4 ounces
i.e. (2A+6B+16C)/(A+B+C)=6.4.............(i)
Let additional 2-ounce jars put on the shelves be X, New total of 2 ounce Jars= A+X
New Average:
(2(A+X)+6B+16C)/ (A+X+B+C) = 6..........(ii)
Solving (i) and (ii)
X=(A+B+C)/10
In order to calculate X we must know A, B & C

Statement 1:
A:B:C::15:27:8
Therefore A+B+C=50K but we do not know the value of constant K, so insufficient

Statement 2:
A=C+7, but we cannot calculate A B C from that, additionally we know nothing about B., Insufficient.

Combining:
(C+7):C=15:8 => C= 8 A=15 Therefore B=27
Therefore A+B+C=50 => X=5

Answer :C
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Re: The inventory of grape jelly on a store's shelves consists only of 2-o  [#permalink]

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New post 04 Dec 2019, 00:24
JiddiHuMain wrote:
The inventory of grape jelly on a store's shelves consists only of 2-ounce, 6-ounce, and 16-ounce jars. If the average jar size of the current inventory is 6.4 ounces, how many additional 2-ounce jars must be put on the shelves to reduce the average size to 6.0 ounces?

(1) The current ratio of 2-ounce to 6-ounce to 16-ounce jars is 15:27:8.

(2) There are initially 7 more 2-ounce jars than 16-ounce jars.



The average of all jars in the store right now is 6.4 ounces. How many of each we have is irrelevant.
We need to add 2 oz jars to bring down the average to 6.

We are mixing two groups, one with avg 6.4 and another with avg 2 to get the avg of 6.

w1/w2 = (A2 - Aavg)/(Aavg - A1) = (2 - 6)/(6 - 6.4) = 10/1

So for every 10 jars that we have, we need to put one 2 oz jar to bring down the average to 6. Now the only thing left to do is to find out how many total jars the inventory has right now.

(1) The current ratio of 2-ounce to 6-ounce to 16-ounce jars is 15:27:8.

This doesn't tell us the total number of jars, just their ratio. Not sufficient.

(2) There are initially 7 more 2-ounce jars than 16-ounce jars.

This doesn't tell us the total number of jars either. Not sufficient.

Using both, we know that the diff between 16 ounce jars and 2 ounce jars is 7. So the actual number of jars is 15, 27 and 8 (2 oz, 6 oz and 16 oz respectively). So now we know the actual number of jars and hence we can find the answer.
Sufficient

Answer (C)

Check these links for discussions on weighted avg and ratios:
https://www.veritasprep.com/blog/2011/0 ... -averages/
https://www.veritasprep.com/blog/2011/0 ... of-ratios/
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Re: The inventory of grape jelly on a store's shelves consists only of 2-o   [#permalink] 04 Dec 2019, 00:24
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