Last Updated on May 9, 2023
GMAT OFFICIAL GUIDE DS
Solution:
We are given a table that has 6 shipments that were shipped on two trucks, and we are given the value of each shipment as a fraction of the total value of the six shipments.
S1 = 1/4
S2 = 1/5
S3 = 1/6
S4 = 3/20
S5 = 2/15
S6 = 1/10
If we put each fraction in terms of the common denominator of 60 we have:
S1 = 15/60
S2 = 12/60
S3 = 10/60
S4 = 9/60
S5 = 8/60
S6 = 6/60
We are also given that the shipments on the first truck had a value greater than 1/2 of the total value of the six shipments. We need to determine whether S3, which was 10/60 of the entire shipment, was on the first truck.
Statement One Alone:
S2 and S4 were shipped on the first truck.
From our given information we know that S2 and S4 made up 12/60 + 9/60 = 21/60 of the total shipment. Since we are given that the shipments on the first truck had a value greater than ½, we know that additional shipments must have been on the first truck. There are many ways that fit the criterion that over ½ of the value could be on the first truck. Here are a few examples:
S2 + S4 + S3 = 31/60 OR S2 + S4 + S1 = 36/60 OR S2 + S4 + S5 + S6 = 35/60
In the first example, S3 is on the first truck, but in the other two examples it is not. Therefore, there is not enough information to determine whether S3 was on the first truck. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.
Statement Two Alone:
S1 and S6 were shipped on the second truck.
From our given information we know that S1 and S6 made up 15/60 + 6/60 = 21/60 of the total shipment. Since we are given that the shipments on the first truck had a value greater than ½, we know that the shipments on the second truck had a value less than ½. If the second truck only had these two shipments, then the first truck must have all the remaining four shipments (which includes S3). Of course, the second truck could have had another shipment besides S1 and S6. Let’s see which shipment it could be.
The remaining shipments are:
S2 = 12/60
S3 = 10/60
S4 = 9/60
S5 = 8/60
Of these four shipments, only S5 could have gone on the second truck also, since the sum of the shipments on the 2nd truck must be less than ½ and S1 + S6 + S5 = 29/60. This means that all the remaining 3 shipments (which includes S3) must have gone on the first truck. Statement two is sufficient to answer the question.
Answer: B
