Discussion
A number is increased by 25% and then decreased by 15%. The resulting number is 17 more than the original number. Find the original number.
Answer: D
The original number is 272. After a 25% increase and then a 15% decrease the number is 1.25 × 0.85 = 1.0625 times the original, so the net change is 6.25%.
\[ 0.0625x = 17 \]\[ x = \frac{17}{0.0625} = 272 \]340, 289 and 110 do not give a 17 difference: 6.25% of 340 is 21.25 and 6.25% of 289 is 18.06.
Check: 1.25 × 272 = 340, and 340 × 0.85 = 289, and 289 - 272 = 17, which agrees with the statement. The net change is not 10% (25 minus 15) but 6.25%, because the 15% decrease is on the larger, increased number.
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