How to read a quantified statement? Having trouble :(

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Set up: in a box there are 6 ping-pong balls, each either purple or yellow, and marked with numbers as follows: Yellow balls: 2, 8 Purple balls: 1, 5, 6, 7

I do not understand why these statements are true about these balls:

There is a colour C such that there is a ball of colour C which has a number double the number on a certain ball of the other colour.

This is how I'm reading this one: There is a ball of a color that has a number double the number on another ball of another color.

( ∃ yellow ball y) such that ( ∀ purple balls p) the number on y is greater than the number on p.

This is how I am reading this one: There is a yellow ball such that for every purple ball the number on the yellow ball is greater than the number on the purple ball.

Am I reading them right?