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TSA 2017 · Question 30 · Logic

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There are two ways of scoring points in a ball game: a 'major' scores 5 points and a 'minor' scores 3 points. In a match played yesterday, the Reds beat the Blues 77–52 despite the fact that the Blues scored exactly twice as many majors as minors, whilst the Reds scored exactly half as many majors as minors.

How many majors were scored altogether in yesterday's match?