Numbers - the Property of Integers

SOURCE:COMPETITION
Number of Problems: 16. : (Book)

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The positive integers $A, B, A-B,$ and $A+B$ are all prime numbers. The sum of these four primes is

$mathrm{(A)} mathrm{even}qquadmathrm{(B)} mathrm{divisible by }3qquadmathrm{(C)} mathrm{divisible by }5qquadm...$

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14.

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For how many integers $n$ is $dfrac n{20-n}$ the square of an integer?

$mathrm{(A)} 1qquadmathrm{(B)} 2qquadmathrm{(C)} 3qquadmathrm{(D)} 4qquadmathrm{(E)} 10$

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15.

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The sum of the two 5-digit numbers $AMC10$ and $AMC12$ is $123422$ . What is $A+M+C$ ?

$mathrm{(A) } 10qquad mathrm{(B) } 11qquad mathrm{(C) } 12qquad mathrm{(D) } 13qquad mathrm{(E) } 14$

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16.

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Suppose that $frac{2x}{3}-frac{x}{6}$ is an integer. Which of the following statements must be true about $x$ ?

$mathrm{(A)} ext{It is negative.}\qquadmathrm{(B)} ext{It is even, but not necessarily a multiple of 3.}\qquadmat...$

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