SAT Math Question(s)

<h1>17) 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?</h1>

<p>A) 2
B) 3
C) 4
D) 5
E) 6</p>

<p>ANS: C</p>

<h1>18) 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?</h1>

<p>A) (8/5)N
B) (3/2)N
C) (7/4)N
D) 2N
E) (9/4)N</p>

<p>ANS: A</p>

<p>I don't understand how these answers can be achieved. Your help would be greatly appreciated!!</p>

<h1>17) 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?</h1>

<p>A) 2
B) 3
C) 4
D) 5
E) 6</p>

<p>ANS: C</p>

<p>This question is essentially asking about the smallest number of faces a 3D object could have. A good way to approach this problem is to consider the polygon with the smallest number of sides. Naturally, the 3D object formed from this shape would also have the smallest number of faces. We can’t use a circle, b/c we can’t make a 3D object out of just circles. We can’t use a 2 sided polygon, b/c it doesn’t exist. That brings us to the triangle. </p>

<p>If we put an equilateral triangle at the edge of another triangle, we’d get a triangular pyramid/tetrahedron. This would have 4 sides (imagine a pyramid with a triangular base). This fits our criterion, so the answer is 4 (C).</p>

<p>for the first problem, if you think about logically, a triangle is the smallest 2d polygon, and to make a triangular pyramid, which would be its 3d counter part, it would have to have 4 faces, and C is your answer.</p>

<p>First one i spretty simple. There is only a limited number of such solids. One of them is cube (6-faces). I have no idea how is it called in english but it has 4 trinagle-shaped faces (hope that helps…).
Second, letš say x=number of people. N=x/3+x/6+x/8 > N= 15x/24 > N=5x/8 > x=8N/5
Seems pretty simple.</p>

<p>First: Think of a three dimensional shape (can’t be a cylinder/sphere, since each face has to form a polygon) that has the least amount of faces. That would be a triangular pyramid, or tetrahedron. It has 4 faces, so the answer is C.</p>

<p>Second: Think about it this way: what number would you have to multiply the total amount of food items by to get the number of people at the party? Well, let’s say there are 24 people, since the LCM of 3, 6, and 8 is 24. Then there must be 15 food items. This means that the ratio of people to food items is 8:5 (24/15). Simply multiply this ratio by the actual amount of food at the party to get the amount of people present. The answer is A.</p>