Numbers - Fraction

SOURCE:COMPETITION
Number of Problems: 9. : (Book)

1.

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Let $n$ be a positive integer such that $frac 12 + frac 13 + frac 17 + frac 1n$ is an integer. Which of the following statements is not true:

$mathrm{(A)} 2 ext{divides }nqquadmathrm{(B)} 3 ext{divides }nqquadmathrm{(C)}$ $6 ext{divides }n qquadmathrm{(D)} 7 ext{divides }nqquadmathrm{(E)} n > 84$

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2.

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Which of the following is the same as $dfrac{2-4+6-8+10-12+14}{3-6+9-12+15-18+21}$ ?

$extbf{(A)} -1 qquad extbf{(B)} -frac23 qquad extbf{(C)} frac23 qquad extbf{(D)} 1 qquad extbf{(E)} frac{14}...$

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3.

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Given that $-4leq xleq-2$ and $2leq yleq4$ , what is the largest possible value of $frac{x+y}{x}$ ?

$mathrm{(A) } -1 qquad mathrm{(B) } -frac12 qquad mathrm{(C) } 0 qquad mathrm{(D) } frac12 qquad mathrm{(E)...$

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4.

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Which of the following is equal to $dfrac{frac{1}{3}-frac{1}{4}}{frac{1}{2}-frac{1}{3}}$ ?

$ext{(A) } frac 14qquad ext{(B) } frac 13qquad ext{(C) } frac 12qquad ext{(D) } frac 23qquad ext{(E) } frac 34$

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5.

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Which of the following is equal to the product $frac{8}{4}cdotfrac{12}{8}cdotfrac{16}{12}cdotcdotscdotfrac{4n+4}{4n}cdotcdotscdotfrac{2008}{2004}?$

$extbf{(A)} 251qquad extbf{(B)} 502qquad extbf{(C)} 1004qquad extbf{(D)} 2008qquad extbf{(E)} 4016$

Contents

1 Problem
2 Solution
- 2.1 Solution 1
- 2.2 Solution 2
3 See Also

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6.

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Which of the following is equal to $1 + frac {1}{1 + frac {1}{1 + 1}}$ ?

$extbf{(A)} frac {5}{4} qquad extbf{(B)} frac {3}{2} qquad extbf{(C)} frac {5}{3} qquad extbf{(D)} 2 qquad ...$

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7.

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What is $dfrac{2+4+6}{1+3+5} - dfrac{1+3+5}{2+4+6} ?$

$extbf{(A)} -1qquad extbf{(B)} frac{5}{36}qquad extbf{(C)} frac{7}{12}qquad extbf{(D)} frac{147}{60}qquad ext...$

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8.

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On Halloween Casper ate $frac{1}{3}$ of his candies and then gave $2$ candies to his brother. The next day he ate $frac{1}{3}$ of his remaining candies and then gave $4$ candies to his sister. On the third day he ate his final $8$ candies. How many candies did Casper have at the beginning?

$extbf{(A)} 30 qquad extbf{(B)} 39 qquad extbf{(C)} 48 qquad extbf{(D)} 57 qquad extbf{(E)} 66$

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9.

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The number halfway between $dfrac{1}{6}$ and $dfrac{1}{4}$ is

$ext{(A)} dfrac{1}{10} qquad ext{(B)} dfrac{1}{5} qquad ext{(C)} dfrac{5}{24} qquad ext{(D)} dfrac{7}{24} ...$

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