Data Sufficiency

Gmat_mission wrote: ↑

Sun May 03, 2020 1:51 pm

table.png

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 SI, 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) SI and S6 were shipped on the second truck.

[spoiler]OA=B[/spoiler]

Source: Official Guide

Target question: Was S3 shipped on the first truck?

Given: The shipments on the first truck had a value greater than 1/2 of the total value of the six shipments

It might help to first convert 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,
As we can see, it's possible for S3 to be on EITHER truck 1 OR truck 2
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

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 S3 is on the first truck.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent