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 March 4th, 2010, 12:42 PM #1 Senior Member   Joined: Jan 2009 Posts: 345 Thanks: 3 Curious problems 1. Paul has twice as many brothers as sisters. His sister Mary has five times as many brothers as sisters. How many sons do their parents have? 2. Find the largest real value of b such that the solutions to the following equations are integers where $x \neq 1$.$(\log _{1024} x^{2b})^{2}$ = $\log _{1024} x^{4}$. Please express your answer in simplest radical form. 3. Triangle A has sides of length 3, 5 and 7. Triangle B has sides of length 7, 8 and 13. Triangle A and triangle B have one angle in common. Find the measure of that angle in degrees. 4. Let x be an integer such that $-10\leq{x}\leq10 \vspace{20 mm}$ If x is chosen at random, determine the probability that it will be a solution to the system of inequalities $|x-3|\geq4 \vspace{20 mm}$ and $x^{2}\leq64 \vspace{20 mm}$ Thank you
 March 4th, 2010, 02:45 PM #2 Senior Member   Joined: Mar 2007 Posts: 428 Thanks: 0 Re: Curious problems What do you think it is that makes them curious? Without doing the math, but just "curious", I tried #3 using a CAD program, suspecting it might be incorrect. I did not find any angle in the one triangle to be the exact same as that in the other. Close, perhaps, but close doesn't count.
 March 4th, 2010, 06:03 PM #3 Global Moderator   Joined: Dec 2006 Posts: 20,942 Thanks: 2210 1.  If their parents have m sons and n daughters, m - 1 = 2n and m = 5(n - 1), so m = 5 (and n = 2). 2.  Does the use of the word "integers" mean that the equation must have more than one integer solution? 3.  By the cosine rule, the cosine of each triangle's obtuse angle is -1/2, so that angle is exactly 120°. 4.  The only integer x such that 10 ? x ? 10 is 10. Is the question typed correctly?

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