Difference between revisions of "1973 Canadian MO Problems"
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==Problem 1== | ==Problem 1== | ||
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| + | <math>\text{(i)}</math> Solve the simultaneous inequalities, <math>x<\frac{1}{4x}</math> and <math>x<0</math>; i.e. find a single inequality equivalent to the two simultaneous inequalities. | ||
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| + | <math>\text{(ii)}</math> What is the greatest integer that satisfies both inequalities <math>4x+13 < 0</math> and <math>x^{2}+3x > 16</math>. | ||
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| + | <math>\text{(iii)}</math> Give a rational number between <math>11/24</math> and <math>6/13</math>. | ||
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| + | <math>\text{(iv)}</math> Express <math>100000</math> as a product of two integers neither of which is an integral multiple of <math>10</math>. | ||
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| + | <math>\text{(v)}</math> Without the use of logarithm tables evaluate <math>\frac{1}{\log_{2}36}+\frac{1}{\log_{3}36}</math>. | ||
Revision as of 21:27, 16 December 2011
Problem 1
Solve the simultaneous inequalities, 
and 
; i.e. find a single inequality equivalent to the two simultaneous inequalities.
What is the greatest integer that satisfies both inequalities 
and 
.
Give a rational number between 
and 
.
Express 
as a product of two integers neither of which is an integral multiple of 
.
Without the use of logarithm tables evaluate 
.
