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Number theory Difficulty 2.0 Junior Find the answer United Kingdom

Eight cards are numbered from 1 to 8. The cards are placed in two boxes $P$ and $Q$ so that the sum of the numbers on the three cards in box $P$ is equal to the sum of the numbers on the five cards in box $Q$ . Which of the following statements must be true?

(A) The card numbered 1 is not in box $Q$ (B) Four cards in box $Q$ have even numbers on (C) The card numbered 5 is in box $Q$ (D) The card numbered 2 is in box $Q$ (E) Exactly three cards in box $Q$ have odd numbers on.

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Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.