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

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BTGmoderatorLU: Moderator; Posts: 2585; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

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: Beat The GMAT — Data Sufficiency | Sat Jul 13, 2019 2:55 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Jul 14, 2019 5:13 am

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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