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A meal-kit service charges $16 to deliver the first meal-kit box in an order and $2 for each additional meal-kit box in the same order. If Jordan placed an order of at least one meal-kit box, did the order include more than 30 meal-kit boxes?
(1) If the order had included 4 additional meal-kit boxes, the delivery charge would have been more than $76.
(2) The average (arithmetic mean) delivery charge per meal-kit box in the order was $2.50.
(1) If the order had included 4 additional meal-kit boxes, the delivery charge would have been more than $76.
(2) The average (arithmetic mean) delivery charge per meal-kit box in the order was $2.50.
06 Aug 2026, 08:08
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Official Solution:
A meal-kit service charges $16 to deliver the first meal-kit box in an order and $2 for each additional meal-kit box in the same order. If Jordan placed an order of at least one meal-kit box, did the order include more than 30 meal-kit boxes?
Let \(n\) be the number of meal-kit boxes in Jordan’s order. The question asks whether \(n > 30\). Since the first meal-kit box costs $16 to deliver and each additional meal-kit box costs $2, the total delivery charge is:
\(16 + 2(n - 1) = 2n + 14\)
(1) If the order had included 4 additional meal-kit boxes, the delivery charge would have been more than $76.
Then the order would have included \(n + 4\) meal-kit boxes, so the delivery charge would have been:
\(16 + 2(n + 4 - 1) = 2n + 22\)
So:
\(2n + 22 > 76\)
\(2n > 54\)
\(n > 27\)
This does not determine whether \(n > 30\).
Not sufficient.
(2) The average delivery charge per meal-kit box in the order was $2.50.
So:
\(\frac{2n + 14}{n} = 2.50\)
\(2n + 14 = 2.5n\)
\(n = 28\)
So the order did not include more than 30 meal-kit boxes.
Sufficient.
Answer: B
A meal-kit service charges $16 to deliver the first meal-kit box in an order and $2 for each additional meal-kit box in the same order. If Jordan placed an order of at least one meal-kit box, did the order include more than 30 meal-kit boxes?
Let \(n\) be the number of meal-kit boxes in Jordan’s order. The question asks whether \(n > 30\). Since the first meal-kit box costs $16 to deliver and each additional meal-kit box costs $2, the total delivery charge is:
\(16 + 2(n - 1) = 2n + 14\)
(1) If the order had included 4 additional meal-kit boxes, the delivery charge would have been more than $76.
Then the order would have included \(n + 4\) meal-kit boxes, so the delivery charge would have been:
\(16 + 2(n + 4 - 1) = 2n + 22\)
So:
\(2n + 22 > 76\)
\(2n > 54\)
\(n > 27\)
This does not determine whether \(n > 30\).
Not sufficient.
(2) The average delivery charge per meal-kit box in the order was $2.50.
So:
\(\frac{2n + 14}{n} = 2.50\)
\(2n + 14 = 2.5n\)
\(n = 28\)
So the order did not include more than 30 meal-kit boxes.
Sufficient.
Answer: B
