A survey of triangle ABC, with D on AB and E on AC, records AB = 15 cm, AD = 9 cm, AC = 20 cm and EC = 7 cm. Is DE parallel to BC?

$\frac{AD}{AB}=\frac{9}{15}=\frac{3}{5}=0.6$. The other side gives $AE=AC-EC=20-7=13$ cm, so $\frac{AE}{AC}=\frac{13}{20}=0.65$. The two ratios differ, so $DE$ is not parallel to $BC$. For parallelism $AE$ would have to be $\frac{3}{5}\times 20=12$ cm, i.e. $EC=8$ cm. The last option is wrong because $DB=15-9=6$ cm is already determined by the data.