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A football club’s memorabilia shop sells only shirts and caps. On a weekend, the shop sold 260 memorabilia items, with each fan buying either one shirt, one cap, or one of each. If 90 fans bought both a shirt and a cap, how many shirts did the shop sell?
(1) 50 fans did not buy a shirt.
(2) 140 fans bought a cap.
(1) 50 fans did not buy a shirt.
(2) 140 fans bought a cap.
30 Apr 2025, 14:50
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Official Solution:
A football club’s memorabilia shop sells only shirts and caps. On a weekend, the shop sold 260 memorabilia items, with each fan buying either one shirt, one cap, or one of each. If 90 fans bought both a shirt and a cap, how many shirts did the shop sell?
90 fans buying both a shirt and a cap accounts for 90 * 2 = 180 items sold. The remaining 80 items were bought by fans who purchased exactly one item. This makes the total number of fans equal to 90 + 80 = 170.
(1) 50 fans did not buy a shirt.
Since there are 170 fans, 50 not buying a shirt means the remaining 120 did, and since each could have bought only one shirt, the total number of shirts sold is also 120. Sufficient.
(2) 140 fans bought a cap.
Since each fan could have bought only one cap, these 140 fans must have bought exactly 140 caps. Given that 260 items were sold in total, the number of shirts sold must have been 260 - 140 = 120. Sufficient.
P.S. To give a complete breakdown: 90 fans bought both shirts and caps, 30 bought only shirts, and 50 bought only caps, making a total of 170 fans. Therefore, 90 + 30 = 120 shirts were sold, and 90 + 50 = 140 caps were sold.
Answer: D
A football club’s memorabilia shop sells only shirts and caps. On a weekend, the shop sold 260 memorabilia items, with each fan buying either one shirt, one cap, or one of each. If 90 fans bought both a shirt and a cap, how many shirts did the shop sell?
90 fans buying both a shirt and a cap accounts for 90 * 2 = 180 items sold. The remaining 80 items were bought by fans who purchased exactly one item. This makes the total number of fans equal to 90 + 80 = 170.
(1) 50 fans did not buy a shirt.
Since there are 170 fans, 50 not buying a shirt means the remaining 120 did, and since each could have bought only one shirt, the total number of shirts sold is also 120. Sufficient.
(2) 140 fans bought a cap.
Since each fan could have bought only one cap, these 140 fans must have bought exactly 140 caps. Given that 260 items were sold in total, the number of shirts sold must have been 260 - 140 = 120. Sufficient.
P.S. To give a complete breakdown: 90 fans bought both shirts and caps, 30 bought only shirts, and 50 bought only caps, making a total of 170 fans. Therefore, 90 + 30 = 120 shirts were sold, and 90 + 50 = 140 caps were sold.
Answer: D
