$28,571 is Emma's adjusted basis in the necklace.
Emma's basis will be summation of her grandmother's basis in the property and the share of the gift tax attributable to the appreciation corresponding to the gifted date.
$20,000 + [$10,000 × ($50,000-20,000) / $35,000]
$20,000 + [($10,000 × $30,000) / $35,000]
$20,000 + [($10,000 × $30,000) / $35,000]
$20,000 + [$3000,000,000 / $35,000]
$20,000+$8571
$28,571.