Bunuel
The tax Jim paid on a shipment of Cognac brandy bottles was $1 for the first bottle and $5 for each additional bottle in the shipment. Were there more than 20 bottles of brandy in the shipment?
(1) The total amount of tax Jim paid for the bottles in the shipment was more than $120.
(2) The average (arithmetic mean) tax Jim paid per bottle in the shipment was $4.84.
Given: The tax Jim paid on a shipment of Cognac brandy bottles was $1 for the first bottle and $5 for each additional bottle in the shipment. Target question: Were there more than 20 bottles of brandy in the shipment?Let x = the total number of bottles in the shipment
So, Jim paid $1 in tax for the first bottle, and then $5 for each of the remaining x - 1 bottles.
We can write: TOTAL taxes paid for x bottles = 1 + 5(x - 1)
Expand: TOTAL taxes paid for x bottles = 1 + 5x - 5
Simplify:
TOTAL taxes paid for x bottles = 5x - 4 Statement 1: The TOTAL amount of tax Jim paid for the bottles in the shipment was more than $120. We can write:
5x - 4 > 120Add 4 to both sides of the inequality: 5x > 124
Divide both sides by 5:
x > 24.8If there were more than 24.8 bottles, the answer to the target question is
YES, there were more than 20 bottles in the shipmentSince we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: The average (arithmetic mean) tax Jim paid per bottle in the shipment was $4.84The average tax per bottle = (TOTAL amount paid in taxes)/(total number of bottles)
In other words: average tax per bottle = (
5x - 4)/(
x)
So we can write the following equation: (
5x - 4)/(
x) = 4.84
Multiply both sides of the equation by x to get: 5x - 4 = 4.84x
Subtract 4.84x from both sides: 0.16x - 4 = 0
Add 4 to both sides: 0.16x = 4
Solve: x = 4/0.16 = 25
The answer to the target question is
YES, there were more than 20 bottles in the shipmentSince we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent