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EMPOWERgmat Instructor V
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Data Sufficiency Pack 4, Question 1) Each of the canisters in....  [#permalink]

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Difficulty:   85% (hard)

Question Stats: 47% (02:01) correct 53% (02:03) wrong based on 147 sessions

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QUANT 4-PACK SERIES Data Sufficiency Pack 4 Question 1 Each of the canisters in...

Each of the canisters in a warehouse is classified as a small canister or a large canister. What is the ratio of small canisters to large canisters in the warehouse?

1) An average large canister holds 6 ounces more than the average of all the canisters in the warehouse.
2) An average small canister holds 4 ounces less than the average of all the canisters in the warehouse.

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This question is part of the Quant 4-Pack series

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Originally posted by EMPOWERgmatRichC on 20 Nov 2015, 15:18.
Last edited by EMPOWERgmatRichC on 06 Dec 2015, 12:49, edited 1 time in total.
Manager  Joined: 11 Sep 2013
Posts: 105
Re: Data Sufficiency Pack 4, Question 1) Each of the canisters in....  [#permalink]

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EMPOWERgmatRichC wrote:
QUANT 4-PACK SERIES Data Sufficiency Pack 4 Question 1 Each of the canisters in...

Each of the canisters in a warehouse is classified as a small canister or a large canister. What is the ratio of small canisters to large canisters in the warehouse?

1) An average large container holds 6 ounces more than the average of all the containers in the warehouse.
2) An average small container holds 4 ounces less than the average of all the containers in the warehouse.

48 Hour Window Answer & Explanation Window
Earn KUDOS! Post your answer and explanation.
OA, and explanation will be posted after the 48 hour window closes.

This question is part of the Quant 4-Pack series

Scroll Down For Official Explanation

An average large container = A with the quantity: a
An average small container = B with the quantity: b

a/b =?

1) An average large container holds 6 ounces more than the average of all the containers in the warehouse

=> A - (Aa+Bb)/(a+b)=6
=>b(A-B)/((a+b)=6

Insufficient
2) An average small container holds 4 ounces less than the average of all the containers in the warehouse.

=> a(A-B)/((a+b)=4

Insufficient

Combine 1 and 2 => a/b = 4/6=2/3

Sufficient

Ans: C
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Re: Data Sufficiency Pack 4, Question 1) Each of the canisters in....  [#permalink]

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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Each of the canisters in a warehouse is classified as a small canister or a large canister. What is the ratio of small canisters to large canisters in the warehouse?

1) An average large container holds 6 ounces more than the average of all the containers in the warehouse.
2) An average small container holds 4 ounces less than the average of all the containers in the warehouse.

This is a "2by2" question, one of the most common type of questions in GMAT math
Attachment: GCDS EMPOWERgmatRichC Data Sufficiency Pack 4, Question 1) Each (20151121).jpg [ 26.55 KiB | Viewed 1870 times ]

There are 4 variables (L,S,a,b), but only 2 equations are given by the 2 conditions, so there is high chance (E) will be the answer.
Looking at the conditions together,
a=[aL+bS/L+S]+6, b=[aL+bS/L+S]-4.
If both sides of b=[aL+bS/L+S]-4 are multiplied by 3/2,
3b/2=3/2[aL+bS/L+S]-6, and if this is added to the equation of a,
a+3b/2=(3/2)[aL+bS/L+S]+[aL+bS/L+S]=(5/2)[aL+bS/L+S], and if 2(L+S) is multiplied to both sides,
(2a+3b)(L+S)=5(aL+bS), 2aL+2aS+3bL+3bS=5aL+5bS,
2aS+3bL=3aL+2bS, 2S(a-b)=3L(a-b).
If both sides are divided by a-b, we get 2S=3L, so the ratio of S:L becomes 3:2 and we can obtain the answer.
The answer therefore becomes (C).

For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
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Re: Data Sufficiency Pack 4, Question 1) Each of the canisters in....  [#permalink]

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Cannisters ---> Containers? Also, I was thinking that the question asked for the ratio of containers.
Is there a typo in the question? I did not understand it at all.
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Re: Data Sufficiency Pack 4, Question 1) Each of the canisters in....  [#permalink]

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To solve this problem, a formula for weighted averages is very helpful. Why should we care about weighted averages? This is because all the statements talk is concerned with difference among overall average ounce per can, average ounce per large can and average ounce per small can.

let L be the number of large cans , S be the number of small cans, oa be overall weighted average, al be average ounce per large can and as be overall average per small can
then
L/S = oa-as/al-oa
statement #1 tells that al-oa is 6
L/S = oa-as/6.. This still needs numerator to be determined
statement #2 tells about numerator but not about denominator
combining we know that L/S = 4/6.
So why do we expect large cans to be less in number? This is because the average of the entire set is closer to small can average cheers!
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Re: Data Sufficiency Pack 4, Question 1) Each of the canisters in....  [#permalink]

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Good question - Test of weighted average concept.

S ------------- WA --------------- L

Statement 1) An average large container holds 6 ounces more than the average of all the containers in the warehouse.
S-------------- WA ----------------L = WA+6 => no idea about S => insuff

Statement 2) An average small container holds 4 ounces less than the average of all the containers in the warehouse.
S = WA-4 ----------WA ---------------S => no idea about L => insuff

1 + 2
WA-4 ------------WA ---------------WA + 6

so weights are in ratio (6/4), i.e. weightage of small canister(number of small canister)/weight of Large canister (number of large canister) = 3/2 => (C) Re: Data Sufficiency Pack 4, Question 1) Each of the canisters in....   [#permalink] 08 Jan 2018, 13:02
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