Question

Shipment	S1	S2	S3	S4	S5	S6
Fraction of the Total Value of the Six Shipments	$\frac{1}{4}$	$\frac{1}{5}$	$\frac{1}{6}$	$\frac{3}{20}$	$\frac{2}{15}$	$\frac{1}{10}$

Six shipments of machine parts were shipped from a factory on two trucks, with each shipment entirely on one ofthe trucks. Each shipment was labeled either Sl, 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 $\frac{1}{2}$ 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.

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

Answer: (B)

Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

Given that the shipments on the first truck had a value greater than of the total value of the 6 shipments, determine if S3 was shipped on the first truck. To avoid dealing with fractions, it will be convenient to create scaled values of the shipments by multiplying each fractional value by 60, which is the least common denominator of the fractions. Thus, the scaled values associated with S1, S2, S3, S4, S5, and S6 are 15, 12, 10, 9, 8, and 6, respectively. The given information is that the scaled value of the shipments on the first truck is greater than .

1. Given that the first truck includes shipments with scaled values 12 and 9, it may or may not be the case that S3 (the shipment with scaled value 10) is on the first truck. For example, the first truck could contain only S2, S3, and S4, for a total scaled value 12 + 10 + 9 = 31 > 30. Or, the first truck could contain only S1, S2, and S4, for a total scaled value 15 + 12 + 9 = 36 > 30; NOT sufficient.
2. Given that the second truck includes shipments with scaled values 15 and 6, the second truck cannot contain S3. Otherwise, the second truck would contain shipments with scaled values 15, 6, and 10, for a total scaled value 15 + 6 + 10 = 31, leaving at most a total scaled value 29 (which is not greater than 30) for the first truck; SUFFICIENT.

• The correct answer is B; statement 2 alone is sufficient.