Claim worth checking, stated narrowly: "The item is 20% off, and I have a 10%-off coupon, so I get 30% off."

Work it with $100.

• After the 20% sale: $80.
• 10% off the sale price: $8.
• You pay $72 — that's 28% off, not 30%.

The algebra: successive discounts multiply, (1−x)(1−y) = 1 − x − y + xy, so the real discount is x + y − xy. Dropping the xy term is the entire error. For 20%+10% it costs 2 points; for 50%+50% the shortcut says "free" while the true figure is 75%. Since xy is never negative, the additive version always overstates — in the customer's favor, but still wrong, and stores quietly make it correct by excluding coupons on sale items or by computing the coupon off the full price. In the first case you should not expect 30%; in the second, the "additive" claim is actually right. Check the coupon's exclusions before arguing either way.

What it refutes: only the "add the percentages" shortcut for price discounts. It does not transfer to averaging rates (see 2o) or to any claim where the second discount is defined off the original price.