At a cookware shop, customers who buy three items receive an

Question

At a cookware shop, customers who buy three items receive an instant rebate of half the price of the least expensive item. Two customers each buy three items, including items priced at $80.00 and $150.00. If each customer’s rebate is equal to 10% of the total purchase price, what could be the difference between the amounts the two customers paid after the rebate?

A. $90.00
B. $101.25
C. $112.50
D. $121.50
E. $135.00

Show Answer

Official Answer

B

A. $90.00
B. $101.25
C. $112.50
D. $121.50
E. $135.00

Edskore · Answer

This is a percent word problem that's really a case-split problem wearing a percent costume, and the case split is the whole game here.

1. Each customer buys 3 items, and two of those items are fixed at $80 and $150 for both customers. Let x be the price of the third, unknown item. Total price before rebate is 230 + x.

2. The rebate is defined two ways: half the price of the cheapest item, and also 10% of the total price. Since we don't know where x sits relative to 80 and 150, you need to check both cases for which item is actually the cheapest.

3. Case 1: x is the cheapest item (x ≤ 80). Rebate = x/2 = 0.10(230+x). Solve: 0.4x = 23, x = 57.5. That's under 80, so this case holds. Total = 287.5, rebate = 28.75, paid = 258.75.

4. Case 2: x is not the cheapest (x ≥ 80, so $80 is the cheapest item). Rebate = 80/2 = 40 = 0.10(230+x). Solve: 230+x = 400, x = 170, consistent with x ≥ 80. Total = 400, rebate = 40, paid = 360.

5. These are the two valid customer scenarios, so the difference between what the two customers paid is 360 - 258.75 = 101.25.

Answer is B.

The trap I fell into the first time I saw this style of problem was picking one case, solving it, and calling it done without checking whether the x I found actually satisfied the assumption I started with. If you solve case 1 and get an x bigger than 80, that scenario is impossible and you have to throw it out.

Quick takeaway: whenever a word problem says "the least expensive item" without telling you which one that is, that's your cue to split into cases before you write a single equation.

paragw · Answer

Here's my solution for this question

GMATcracker101 · Answer

Each customer buys 3 items of them two are prices 80 and 150.

So, C1 = a, 80, 150 where a is the least priced -- Total = a + 230; rebate = a/2 
C2 = 80, b, 150 where b is the least priced -- Total = b + 230; rebate = 80/2 = 40

Therefore for C1 a/2 = a/10 + 23 therefore a = 57.5 
and for C2 40 = b/10 + 23 therefore b = 170

We need the difference in amount paid after rebate which is 90% of Total = 0.9(b+230) - 0.9(a+230)
this is 0.9(170-57.5) = 101.25 hence option B

At a cookware shop, customers who buy three items receive an

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