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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

by BTGmoderatorLU » Sat Jul 13, 2019 2:55 pm

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Source: GMAT Paper Tests

There are three varieties of sugar in a store. Sugar (\(S_1\)) costs $6 per kilogram and sugar (\(S_2\)) costs $9.00 per kilogram. Sugar (\(S_1\)) is mixed with sugar (\(S_2\)) and a new variety of sugar (\(S_3\)) is formed. If 20 kilograms of sugar (\(S_3\)) consists of \(A\) kilograms of sugar (\(S_1\)) and \(B\) kilograms of sugar (\(S_2\)), is \(A > B\)?

1. \(A > 9\)
2. The cost of 20 kilograms of sugar (\(S_3\)) is more than $150.

The OA is B
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Source: — Data Sufficiency |
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by GMATGuruNY » Sun Jul 14, 2019 5:13 am

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BTGmoderatorLU wrote:Source: GMAT Paper Tests

There are three varieties of sugar in a store. Sugar (\(S_1\)) costs $6 per kilogram and sugar (\(S_2\)) costs $9.00 per kilogram. Sugar (\(S_1\)) is mixed with sugar (\(S_2\)) and a new variety of sugar (\(S_3\)) is formed. If 20 kilograms of sugar (\(S_3\)) consists of \(A\) kilograms of sugar (\(S_1\)) and \(B\) kilograms of sugar (\(S_2\)), is \(A > B\)?

1. \(A > 9\)
2. The cost of 20 kilograms of sugar (\(S_3\)) is more than $150.
Statement 1:
Case 1: A=10 kg and B=10 kg, for a total of 20 kg
In this case, A=B, so the answer to the question stem is NO.
Case 2: A=11 kg and B=9 kg, for a total of 20 kg
In this case, A>B, so the answer to the question stem is YES.
Since the answer is NO in Case 1 but YES in Case 2, INSUFFICIENT.

Statement 2:
Average cost per kg = (more than $150)/20 = more than $7.50.
Since the average cost (more than $7.50) is closer to B's cost per kg ($9) than to A's cost per kg ($6), B>A in the mixture.
Thus, the answer to the question stem is NO.
SUFFICIENT.

The correct answer is B.
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