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.
Correct Answer: E
- Revenue = Coststore-front*Quantitystore-front + Costbulk*Quantitybulk
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Evaluate Statement (1) alone.
- Store-Front: 75% of 100 packages is 75 packages at the store-front rate.
- Bulk: The remainder (or 25%) of the 100 packages (i.e., 100-75 = 25) is 25 packages at the bulk-rate.
- 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.
- Statement (1) alone is NOT SUFFICIENT.
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Evaluate Statement (2) alone.
- Translate Statement (2) into algebra:
Store-Front > 2(Bulk)
$4 > 2(Bulk)
Bulk < $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.
- Statement (2) alone is NOT SUFFICIENT.
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Evaluate Statements (1) and (2) together.
- Store-Front: 75 packages {from Statement (1)} shipped at $4 each {from Statement (2)} -> $300 in revenue from the store-front rate.
- Bulk: 25 packages shipped at less than $2 each; no more than $50 in revenue from the bulk-rate.
- However, you still cannot calculate the total revenue definitively.
Revenue = Coststore-front*Quantitystore-front + Costbulk*Quantitybulk
Filling in what we found thus far:
Revenue = $4*75 + Costbulk*25
- 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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