Re: A retailer purchases an item at $700 per piece and sells it at a profi
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06 Feb 2022, 09:54
The retailer is selling a product purchased for $700 at a 30% markup, so for $910. After the discounts the retailer still wants to make a 10% profit, or $770, so the retailer doesn't want the discount to amount to more than $140. If a customer applied a 10% discount first to the $910 price, saving $91, then received a $50 discount, the discount would amount to $141, so the retailer cannot offer those two coupons. And since the 8% discount will amount to more than $50, the retailer also can't offer the 10% and 8% coupons. The retailer can only offer the $50 and 8% coupons (which clearly works, because the $50 and 10% combination only barely failed).
But I don't think the question setup really makes sense, because it's not clear how we'd answer the question if it turned out that, say, any two of the three coupons would work. There's no corresponding answer choice. So if this question has a unique answer, it must be true that only one combination of coupons meets the retailer's requirements, and that needs to be the combination producing the smallest discount, which is the $50 and 8% combination. That's the only logically possible answer besides "none", so we just need to check that this one combination produces an acceptable discount.