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A jacket lists for $200. At Store P the clerk first takes x percent off the list price and then takes a flat $30 off the reduced price, and the final price is exactly $120. Store Q sells the same jacket by taking the same flat $30 off the list price first and then taking the same x percent off the reduced amount. What is the final price, in dollars, of the jacket at Store Q?
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Correct answer
C
First find x from Store P. The percent comes off first, then the flat $30: 200 × (1 − x/100) − 30 = 120, so 200 × (1 − x/100) = 150. Dividing, 1 − x/100 = 0.75, so x/100 = 0.25 and x = 25. The percent discount therefore keeps a multiplier of 0.75, that is 75 percent of whatever base it acts on.
Now apply Store Q's order, where the flat $30 comes off first. Take $30 off the $200 list price: 200 − 30 = 170. Then take 25 percent off the reduced $170: 170 × 0.75 = 127.50. So (C) $127.50 is the final price at Store Q.
The false summit is (A) $120: a flat-dollar cut and a percent cut do not commute, because the percent acts on a different base in each order. At Store P the 25 percent never touches the $30, but at Store Q the $30 is removed first, so the 25 percent is taken on a base that is already $30 smaller. The whole difference is exactly 25 percent of $30 = $7.50, which is why Store Q costs $7.50 more: 120 + 7.50 = 127.50.
The remaining traps each come from one specific slip. (B) $125 is taking the $30 off first to $170 but then mis-taking 25 percent of $170 as about $45 (170 − 45). (D) $130 is taking the 25 percent off $160 instead of the full $170 (170 − 40). (E) $135 is subtracting only $20 instead of $30 first, reaching $180, then 180 × 0.75.
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