<p>1- At a party, there was one pizza for every 3 people, one salad for every 6 people, and one cake for every 8 people. If the total number of pizzas, salads, and cakes was (n),then ,in terms of (n), how many people were at the party ??
(A) 8/5 N
(B) 3/2 N
(C) 7/4 N
(D) 2N
(E) 9/4 N</p>
<p>2- The surface of a 3-dimensional solid consists of faces, each of which has the shape of a polygon. what is the least number of such faces that the solid can have ?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6</p>
<p>3-Paul has 24 large pieces of candy ,and kate has 40 small pieces of candy. they have agreed to make trades of 1 of paul's large candies for 3 of kate's small candies. After how many such trades will paul and kate each have an equal number of candies?</p>
<p>4-In xy-plane, the line y=ax+5 is parallel to the line3x+8y=10. what is the value of a ?
(A) -6
(B) -8/3
(C) -3/8
(D) 3/8
(E) 8/3</p>
<p>5-The table above shows some values for the function f. which is defined for all positive integers n. if f(n+3)=3f(n) for all values of n, what is the value of f(10) ??</p>
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<li><p>Here is a suggestion: let z be the number of pizzas, s be the number of salads and c be the number of cakes; also let p be the number of people. Since there is one pizza for every three people, what is the relation between z and p? Similarly, you can relate s to p and c to p. You know z + s + c = n, so you can relate n to p. Try it and see what you get. Ask again if you need more help.</p></li>
<li><p>Do you know how to tell if lines are parallel, if the equations for the lines are written in the form y = mx + b?</p></li>
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<li> A good way to analyze this is to think about the effect of a single trade. When Paul trades 1 large piece of candy for 3 of Kate’s small pieces, what is the change in Paul’s number of candies? It is +2. The change in Kate’s number of candies is -2 for each trade. Therefore, after t trades, Paul will have 24 + 2t candies, and Kate will have 40 - 2t candies. Solve for t.</li>
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<li> Do you consider a triangle to be a polygon? I would. There’s no way to make a solid with just 2 faces. The only solid shape with 3 boundary surfaces that I can think of offhand is a cylinder, which would not have polygonal faces. On the other hand, if you think of a tetrahedron . . .</li>
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<li> You know that f(n + 3) = 3 f(n), and you want f(10). This gives you a way to reduce the argument of the function until you get down to the tabulated values. From the general rule, you know that f(10) = f(7 + 3) = 3 f(7). At first, this doesn’t look too useful, because f(7) is not tabulated. But think some more. You can use the rule again to relate f(7) to f(4), since f(7) = f(4 + 3) = 3 f(4). Look up f(4) in the table, plug it in, and then work out f(10).</li>
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<p>You could just start listing how many candies each has after each trade, and look for the point of equality:</p>
<p>Start: Paul 24 and Kate 40
After trade 1: Paul 26 and Kate 38
After trade 2: Paul 28 and Kate 36
After trade 3: Paul 30 and Kate 34
After trade 4: Paul 32 and Kate 32–equal numbers (though not equal quantities of candy!)</p>
<p>The thing to notice is that when the candies are traded, one large from Paul for three small from Kate, Paul has a net gain of two candies on each trade and Kate has a net loss of two. Of course, this is assuming that they are trading with each other!</p>
<p>I think it’s somewhat faster to just use 24 + 2t = 40 - 2t, which gives 16 = 4t, so t = 4.</p>
<p>For number 4, it’s c because you change the equation to y=mx+b form. Recall from algebra 1 or geometry that parallel lines have same slopes. Since the slope on the equation is -3/8 then that means the other equations slope or ‘a’ is -3/8</p>