Son ranked fourth in club with 17.833 points and fifth in ribbon with 17.050 points, closely trailed by Deng Senyue of China who came in fifth in club with 17.700 points and sixth in ribbon with 16.950 points.
On Tuesday, Son won the bronze in hoop, becoming the first Asian to win a medal at the World Championships.
Both Son and Deng are set to compete again in the 2014 Asian Games which are underway in Incheon, South Korea.
Yana Kudryavtseva of Russia grabbed the gold medal in the club contest, and Margarita Mamun also of Russia won the gold in the ribbon competition.
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