The customs department has 3.2% of its inspected items opened and resealed before being released. It also has 20% of its opened items released but not resealed. What percentage of the items inspected are opened?
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This one got me. I initially thought 20% of the opened items were resealed, not NOT resealed. Reading carefully is half the battle here.
Same! I set up the equation with 0.8x = 3.2 and got 4.0. But I had to read it twice to catch the 'not'.
Classic GMAT trap. They know exactly what they're doing with that wording.
Answer is D, 4.0%. Let x = total items opened. 3.2% of all inspected are opened AND resealed. 20% of opened items are released but NOT resealed, so 80% of opened items are resealed. So 0.8x = 3.2%, x = 4%.
Thanks, that's the cleanest way to set it up.
Wait, how do you know the 3.2% refers to resealed and opened? Couldn't it mean all inspected items that were opened?
The first sentence says 3.2% are opened AND resealed. So that's the overlap of both. The second sentence gives you the split within the opened group.
Ohh okay, so 3.2 is the resealed portion of opened items. Got it, thanks.
This is a solid 650-700 level question. Not hard math, but the phrasing will trip you up if you rush. Took me about 1:45 to get it right.
Agreed, the percentages within percentages is what makes it tricky.
What it tests
Your ability to compute percentage change, percentage of a whole, and to work backwards from a final value.
Common trap
Treating successive percentage changes as additive — a 10% rise then a 10% fall is not back to the start.