Number Play

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All eight expressions formed by placing + and - signs between four consecutive numbers always have the same parity (all even or all odd). This happens because switching any sign changes the value by a

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Parity refers to whether a number is even or odd. Rules: odd ± odd = even, even ± even = even, odd ± even = odd. The expressions a±b always have the same parity regardless of the signs chosen.

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2a + 2b always gives an even number because it equals 2(a + b), which has 2 as a factor. 3g + 5h may be even or odd depending on the values of g and h.

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Two cases: (1) Both numbers are multiples of 4: 4p + 4q = 4(p+q). (2) Both numbers leave remainder 2 when divided by 4: (4p+2) + (4q+2) = 4(p+q+1). When one is multiple of 4 and other leaves remainder

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If a divides M and a divides N, then a also divides M+N and M-N. In other words, if M and N are multiples of a, then M+N and M-N are also multiples of a.

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TRUE. If A is divisible by k, then A is divisible by all factors of k. Since 12 = 2² × 3, factors of 12 are 1, 2, 3, 4, 6, 12. Any multiple of 12 contains all these factors.

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NO, not always. A is divisible by LCM(6,4) = 12, but not necessarily by 24. Example: 12 is divisible by both 6 and 4, but not by 24. A is divisible by 24 only if it's divisible by both 3 and 8.

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Numbers of the form 5k + 3 where k ≥ 0. Examples: 3, 8, 13, 18, 23, 28... These can also be written as 5k - 2 where k ≥ 1.