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You are correct about K and Q being calculated in the same way. From what I've been seeing, in questions involving Q, K is usually given and you are asked to find Q in order to determine whether or not the reaction is at equilibrium and in what way the reaction will occur to approach equilibrium. I can't think of a case in which Q would be involved in a question without the value of K already being given.
K is a constant that never changes which allows you to compare it to Q to determine the state of a reaction. So when Q<K the reaction tends to move towards the products, when Q=K the reaction is in equilibrium, and when Q>K the reverse reaction is spontaneous.
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