Congruences and probability

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Suppose that $6x \equiv 10y \pmod{14}$. Which of the following are guaranteed to be true?

(a) $3x \equiv 5y \pmod{14}$: True

(b) $6x \equiv 10y \pmod{7}$: True

(c) $3x \equiv 5y \pmod{7}$: True

(d) $6x \equiv 10y \pmod{28}$: False

Am I right?