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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