S1=1/4 S2=1/5 S3=1/6 S4=3/20 S5=2/15 S6=1/10

Six shipments of machine parts were shipped from a factory on two trucks, with each shipment entirely on one of the trucks. Each shipment was labeled either S1, S2, S3, S4, S5, or S6. The table shows the value of each shipment as a fraction of the total value of the six shipments. If the shipments on the first truck had a value greater than 1/2 of the total value of the six shipments, was S3 shipped on the first truck?

(1) S2 and S4 were shipped on the first truck.
(2) S1 and S6 were shipped on the second truck
OA B

We might be able to solve this one faster by first converting the fractions to decimals.
S1=0.25
S2=0.2
S3=0.17 (approx)
S4=0.15
S5=0.13 (approx)
S6=0.1

Statement 1: S2 and S4 were shipped on the first truck.
First truck has 0.2 + 0.15 = 0.35
Since the first truck holds more than 0.5, S3 may or may not be on that truck. For example, consider these two possible cases:
case a: first truck holds S2, S3 and S4, and second truck holds S1, S5 and S6,
case b: first truck holds S1, S2, and S4, and second truck holds S3, S5 and S6,

Statement 2: S1 and S6 were shipped on the second truck
Second truck has 0.25 + 0.1 = 0.35
Since the first truck holds more than 0.5, the second truck must have less than 0.5
Since S3 = 0.17, S3 cannot be on the second truck, otherwise the second truck would have more than 0.5
Since S3 cannot be on the second truck, we can be certain that it's on the first truck, in which case statement 2 is sufficient and the answer is B

Cheers,
Brent

Hi babynavreet,

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