Numbers - Absolute Value

SOURCE:COMPETITION
Number of Problems: 4. : (Book)

1.

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If $|x - 2| = p$ , where $x < 2$ , then $x - p =$

$mathrm{(A) -2 } qquad mathrm{(B) 2 } qquad mathrm{(C) 2-2p } qquad mathrm{(D) 2p-2 } qquad mathrm{(E) |2p-...$

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2.

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Define $x heartsuit y$ to be $|x-y|$ for all real numbers $x$ and $y$ . Which of the following statements is not true?

$mathrm{(A) } x heartsuit y = y heartsuit x$ for all $x$ and $y$

$mathrm{(B) } 2(x heartsuit y) = (2x) heartsuit (2y)$ for all $x$ and $y$

$mathrm{(C) } x heartsuit 0 = x$ for all $x$

$mathrm{(D) } x heartsuit x = 0$ for all $x$

$mathrm{(E) } x heartsuit y > 0$ if $x eq y$

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3.

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What is the value of $x$ if $|x-1|=|x-2|$ ?

$mathrm{(A) } -frac12 qquad mathrm{(B) } frac12 qquad mathrm{(C) } 1 qquad mathrm{(D) } frac32 qquad mathr...$

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4.

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Let $a$ , $b$ , $c$ , and $d$ be real numbers with $|a-b|=2$ , $|b-c|=3$ , and $|c-d|=4$ . What is the sum of all possible values of $|a-d|$ ?

$mathrm{(A)} 9qquadmathrm{(B)} 12qquadmathrm{(C)} 15qquadmathrm{(D)} 18qquadmathrm{(E)} 24$

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