Basic Mathematics

Reasoning Skills

Checking Cases

         

Which of the following could be an internal angle in a regular polygon?

I. 108II. 120III.167\begin{array}{r r l} &\text{I.}\ & 108 ^ \circ\\ & \text{II.}\ & 120 ^ \circ\\ &\text{III.} &167 ^ \circ\\ \end{array}

(A)  \ \ I only
(B)  \ \ III only
(C)  \ \ I and II only
(D)  \ \ II and III only
(E)  \ \ I, II, and III

If nn is a perfect square, which of the following could be true?

I. n is a perfect cube.II. n2+6 is a perfect square.III. n2+1 is a multiple of 3.\begin{array}{r r l} &\text{I.}\ & n\ \text{is a perfect cube.}\\ & \text{II.}\ & n^2 + 6\ \text{is a perfect square.}\\ & \text{III.}\ & n^2 + 1\ \text{is a multiple of 3.}\\ \end{array}

(A)  \ \ I only
(B)  \ \ II only
(C)  \ \ I and II only
(D)  \ \ I and III only
(E)  \ \ I, II, and III

If x3<8x+9 x^3 < 8 x + 9 , which of the following could be a value of xx?

I.8II.0III.8\begin{array}{r r l} & \text{I.} & 8\\ & \text{II.} & 0\\ & \text{III.} & -8\\ \end{array}

(A)  \ \ I only
(B)  \ \ III only
(C)  \ \ I and II only
(D)  \ \ I and III only
(E)  \ \ II and III only

For all numbers aa and bb, let ab a \heartsuit b be defined by ab=ab+ab a \heartsuit b = ab + a -b . For all numbers xx and yy, which of the following must be true?

I. xy=yxII. xy=(y)(x)III. xy=(y+3)(x3)\begin{array}{r r l} &\text{I.}\ & x \heartsuit y = y \heartsuit x\\ &\text{II.}\ & x \heartsuit y = (-y) \heartsuit (-x)\\ &\text{III.}\ & x \heartsuit y = (y+3) \heartsuit (x-3)\\ \end{array}

(A)  \ \ II only
(B)  \ \ III only
(C)  \ \ II and III only
(D)  \ \ I, II, and III
(E)  \ \ None of the statements

If PP is a prime number greater than 10, which of the following could represent another prime number for some value of PP?

I. P+26II. 5PIII. P2+1\begin{array}{r r l} &\text{I.}\ &P+26\\ &\text{II.}\ & 5P\\ &\text{III.}\ & P^2 + 1\\ \end{array}

(A)  \ \ I only
(B)  \ \ III only
(C)  \ \ I and II only
(D)  \ \ I and III only
(E)  \ \ II and III only

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