Practice GMAT Data Sufficiency Question

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John’s Pack and Ship uses price discrimination to capture consumer surplus. How much revenue did John's firm earn last week if it shipped 100 packages for customers?

For 75% of the packages John shipped, he charged the store-front rate. John charged the bulk-rate for the remainder of the packages.
John’s store-front rate was $4, more than double his bulk-rate.

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)	Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Correct Answer: E

Revenue = Cost_store-front*Quantity_store-front + Cost_bulk*Quantity_bulk
Evaluate Statement (1) alone.
1. Store-Front: 75% of 100 packages is 75 packages at the store-front rate.
2. Bulk: The remainder (or 25%) of the 100 packages (i.e., 100-75 = 25) is 25 packages at the bulk-rate.
3. Without any dollar amounts (such as the cost of the bulk-rate and the cost of the store-front rate), it is impossible to calculate John’s total revenue.
4. Statement (1) alone is NOT SUFFICIENT.
Evaluate Statement (2) alone.
1. Translate Statement (2) into algebra:
  Store-Front > 2(Bulk)
  $4 > 2(Bulk)
  Bulk < $2
2. Although Statement (2) tells us the dollar amount of each shipping rate, without information about the number of packages shipped at each rate, it is impossible to calculate John’s revenue.
3. Statement (2) alone is NOT SUFFICIENT.
Evaluate Statements (1) and (2) together.
1. Store-Front: 75 packages {from Statement (1)} shipped at $4 each {from Statement (2)} -> $300 in revenue from the store-front rate.
2. Bulk: 25 packages shipped at less than $2 each; no more than $50 in revenue from the bulk-rate.
3. However, you still cannot calculate the total revenue definitively.
  Revenue = Cost_store-front*Quantity_store-front + Cost_bulk*Quantity_bulk
  Filling in what we found thus far:
  Revenue = $4*75 + Cost_bulk*25
4. Statements (1) and (2), even when taken together, are NOT SUFFICIENT.
Since Statement (1) alone is NOT SUFFICIENT, Statement (2) alone is NOT SUFFICIENT, and Statements (1) and (2), even when taken together are NOT SUFFICIENT, answer E is correct.

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