Test 4 Section 3 - #18 (page 585)

Big time plug-in here. Say x = 10, and z = 2. So the first shirt will cost $10, and each shirt after that will cost $10 - $2 = $8. Now say the customer buys n = 5 shirts. Those shirts would cost

$10 for the first one

+ $8 for the second

+ $8 for the third

+ $8 for the fourth

+ $8 for the fifth

= $42 

So we're looking for the answer that gives us 42 when we plug in the number we chose above.

(A) x + (n - 1)(x - z)


We can translate that to
10 + (5 - 1)(10 - 2) = 10 + (4)(8) = 42.

That's our answer! Make sure, when you plug in, that you try the other answers too to make sure they don't work. In this case they don't, so we're done.

Test 4 Section 3 - #9 (page 583)

This one is pretty tricky, but the 98th 1 will be followed by 98 0's, the 99th will be followed by 99 0's, and the 100th 1 will be followed by 100 0's. Then we'll be at the 101st 1, and we'll be done. The total number of 0's is 98+99+100 = 297. That's choice (D).

Test 4 Section 3 - #20 (page 586)

Variables in the answer choices mean PLUG-IN!! Let's call n anything we want. How about 10, because that's an easy number to work with. So if there are 10 men enrolled, there must be 85 women enrolled (because the question says there are 75 more women than men). So that's 95 people at the college. Of those 95, 10 are men, so the percent of students who are men is 10/95, or about 10.53%. Now just go through each answer to see which one matches that when you use n = 10. That'll be Choice (E).

Test 4 Section 3 - #19 (page 586)

Because we're looking at only 30 degrees, we can figure out what fraction of the circle this slice is. The whole circle would have 360 degrees, so this is only 30/360, or 1/12 of the whole circle. Now use the rest of the info we're given: we know the length of the arc is 6π, and since this is 1/12 of the whole circle, 6π must be 1/12 of the whole circumference. Multiplying 6π times 12 gives us 72π, which would be the circumference of the whole circle. Since circumference = (π)(diameter), the diameter must be 72, and the radius would then be 36.

Still with me? Next step is to find the area of the whole circle. Since the radius is 36, the area would be (36²)(π), which is 1296π. But that's the area of the WHOLE circle; we're only looking at a slice that's 1/12 of the whole circle. So the slice would have an area of 1/12 of 1296π, which is 108π.

Test 4 Section 3 - #14 (page 584)

Since you have a figure and it IS drawn to scale (because it doesn't say "Not drawn to scale"), you can use GUESSTIMATE here. Take a scrap piece of paper to measure the two sides of the shape that aren't labeled and compare them to the sides labeled 6. You'll see they're exactly the same, so all of the sides are 6, so the perimeter must be 30. When you're stuck on a Geometry question, think GUESSTIMATE!