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There are three varieties of sugar in a store. Sugar (S1)

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There are three varieties of sugar in a store. Sugar (S1) [#permalink] New post 27 Oct 2012, 00:21
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There are three varieties of sugar in a store. Sugar (S1) costs $6 per kilogram and sugar (S2) costs $9 per kilogram. Sugar (S1) is mixed with Sugar (S2) and a new variety of Sugar (S3) is formed. If 20 kilograms of Sugar (S3) consists of A kilogram of Sugar (S1) and B kilogram of Sugar (S2), is A > B ?

(1) A > 9
(2) The cost of 20 kilogram of Sugar (S3) is more than $150.
[Reveal] Spoiler: OA

Last edited by Bunuel on 29 Oct 2012, 04:51, edited 1 time in total.
Renamed the topic and edited the question.
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Re: There are three varieties of sugar in a store [#permalink] New post 27 Oct 2012, 16:02
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(1) Insufficient. A could be, for example, 10 or 11. If A = 10, then B=10 and A is not bigger than B. However, if A = 11, then B = 9 and A>B.

(2) Sufficient. If you would have to pay $150 for 20kg, then 1kg costs 150/20 = $7.50. Note that this would be exactly the price for 1kg if S3 consisted of equal parts of S1 and S2, since (6+9)/2 = 7.5. Since the statement tells us that the price per kg for S3 is greater than $7.50 we know that there has to be more of the more expensive sugar (= S2) in the mixture. This means A<B and we have our answer.
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Re: There are three varieties of sugar in a store. Sugar (S1) [#permalink] New post 06 Nov 2012, 01:15
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GMATBaumgartner wrote:
There are three varieties of sugar in a store. Sugar (S1) costs $6 per kilogram and sugar (S2) costs $9 per kilogram. Sugar (S1) is mixed with Sugar (S2) and a new variety of Sugar (S3) is formed. If 20 kilograms of Sugar (S3) consists of A kilogram of Sugar (S1) and B kilogram of Sugar (S2), is A > B ?

(1) A > 9
(2) The cost of 20 kilogram of Sugar (S3) is more than $150.


(1) Given: A+B = 20 kg
When A=10kg , B= 10kg
When A = 11 kg, B = 9 kg.
Hence, not sufficient.

(2) Assume cost of 20 kg = $ 150.
Then, cost of 1 kg = \(\frac{150}{20}\)= $7.5
Hence the cost of 1 kg of S3 is $7.5.

The cost of 1 kg can also be expressed as \(\frac{Total Cost}{Total Weight}\)
or, \(\frac{6A+9B}{A+B}= 7.5\)

7.5 is the weighted average between 6 and 9, and is equidistant from both 6 and 9. This means that when the cost is equal to $150, then A = B. But if it is greater than $ 150, then the balance of weighted average will shift towards B, and hence, B>A. Sufficient.
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Re: There are three varieties of sugar in a store. Sugar (S1) [#permalink] New post 19 Feb 2013, 00:17
There are three varieties of sugar in a store. Sugar (S1) costs $6 per kilogram and sugar (S2) costs $9 per kilogram. Sugar (S1) is mixed with Sugar (S2) and a new variety of Sugar (S3) is formed. If 20 kilograms of Sugar (S3) consists of A kilogram of Sugar (S1) and B kilogram of Sugar (S2), is A > B ?

(1) A > 9. A=B if A=10 or A>B
(2) The cost of 20 kilogram of Sugar (S3) is more than $150. IF A=B=10 then , we can get cost = 150 . But cost is more than 150, so B>A.
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Re: There are three varieties of sugar in a store. Sugar (S1) [#permalink] New post 04 Jul 2014, 00:33
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There are three varieties of sugar in a store. Sugar (S1) [#permalink] New post 23 May 2015, 08:20
2nd statement:
6x + 9x > 150
15x >150
x > 10

Therefore, because S3 consists of only 20 kgs you have sufficient information to prove that one of the quantities (S1 or S2, it does not matter which one) is bigger than the other.
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Re: There are three varieties of sugar in a store. Sugar (S1) [#permalink] New post 26 Jun 2015, 10:41
GMATBaumgartner wrote:
There are three varieties of sugar in a store. Sugar (S1) costs $6 per kilogram and sugar (S2) costs $9 per kilogram. Sugar (S1) is mixed with Sugar (S2) and a new variety of Sugar (S3) is formed. If 20 kilograms of Sugar (S3) consists of A kilogram of Sugar (S1) and B kilogram of Sugar (S2), is A > B ?

(1) A > 9
(2) The cost of 20 kilogram of Sugar (S3) is more than $150.


State 1: is clearly insufficient

State 2: Total cost is > 150, implies that:
6a+9b > 150 & we know that a + b = 20
2a + 3b >50 ; substituting for a and simplifying will give us a>10
& since a + b is 20, b has to be less than a.
Re: There are three varieties of sugar in a store. Sugar (S1)   [#permalink] 26 Jun 2015, 10:41
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