#test 11

[aipdesigns]

Material (In)Formation

RECIPE 11

4ml glycerin

3tsp vinegar

3tsp corn starch

Top Left: Hour 0 Top Right: Hour 4 Bottom Left: Hour 14 Bottom Right: Hour 62

p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px 'Helvetica Neue'} li.li1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px 'Helvetica Neue'} ul.ul1 {list-style-type: hyphen}

[pwnthesat]

Prom Bluebook DVD Section 8 number 12: If the tick marks are equally spaced on the number line above, what is the value of 7? Ticks are as follows from left to right: 3,x,y,unnamed tick, 2x. a. 5 b. 6 c. 7 d. 8 e. 9

The value of 7? You mean the value of y???

Backsolve to find this. Start with (C). If y = 7, then x = 5. Does that work? No, because if you follow that pattern and count up by 2, then 2x equals 11, when you know 2(5) = 10. That tells you you chose a y that was too big. 

Try (B). If y = 6, then x = 4.5, and the tick marks are all 1.5 apart. Does 2x give you what it should now? Yes it does! the marks go: 3, 4.5, 6, 7.5, 9.

[pwnthesat]

The figure above represents a stretch of fencing that is 500 feet long. If fence posts are placed each every 5 feet along the fence for support, how many fence posts in all are there in this stretch of fencing?

This is from Blue Book Test 11 (the test that comes on the DVD if you buy the DVD version). 

The key to this one is to think small at first. How many fenceposts are there  in 10 feet of fence? There are 3! One at the beginning of the fence, and then one every 5 feet. 10/5 = 2, of course, but that gives you 1 less than the answer you want, because it doesn’t count the first fencepost.

The general formula for number of fence posts for n feet of fence (n is a multiple of 5) is:

n/5 + 1

The “+1” accounts for the first fencepost.

Since we’re looking for the number of posts in 500 feet of fence, we put 500 into the formula:

500/5 + 1 = 101

[pwnthesat]

If the average of the measures of two noncongruent angles of an isosceles triangle is 70, which of the following is the measure of one of the angles of the triangle? A)50 B)60 C)80 D)90 E)100

If the average of the measures of two noncongruent angles is 70, then their sum is 140, which means the other angle in the triangle must be 40. 

If you have an isosceles triangle with one angle that’s 40 degrees, it can either be a 40-40-100 triangle, or a 70-70-40 triangle. The latter doesn’t work for this question because in that case the two angles with an average measure of 70 degrees aren’t noncongruent. So it has to be the former, the 40-40-100 triangle. Therefore, the answer is (E).

[pwnthesat]

A fitness center purchased a number of exercise machines: 4 costing $1700 each, 8 costing 1300, and X costing 1200 each, where X is a positive odd integer. If the median price for all the exercise machines purchased by the fitness center was 1300, what is the greatest possible value of X? Pls help solve it! Thx a lot!!!

The easiest way to get this one might be to recognize that the median is when you have the same number of machines at a greater or equal value and at a lesser or equal value.

If you want the median to be $1300, well, you already know all the machines that are of a greater or equal value. There are 8 $1300 machines, and 4 $1700 machines. That’s 12 machines. If your median is going to be one of the $1300 machines, there will be 11 at a greater or equal value. Which means you can purchase 11 $1200 machines (lesser value) and still have a $1300 median.

If that’s not working for you, the other, almost-as-fast way is just to list things out. Start by listing the ones you know:

$1300  $1300  $1700$1300  $1300  $1700$1300  $1300  $1700$1300  $1300  $1700

Now start writing $1200s, crossing off the list as you go:

$1200  $1300  $1300  $1700$1200  $1300  $1300  $1700$1200  $1300  $1300  $1700$1200  $1300  $1300  $1700

$1200  $1200  $1300  $1300  $1700 $1200  $1200  $1300  $1300  $1700 $1200  $1200  $1300  $1300  $1700 $1200  $1200  $1300  $1300  $1700 

Almost there, right? Remember, for each $1200 you list, you have to cross off one $1300. How many more can you list before there’s only one $1300 left?

$1200  $1200  $1200  $1300  $1300  $1700 $1200  $1200  $1200  $1300  $1300  $1700 $1200  $1200  $1200  $1300  $1300  $1700               $1200  $1200  $1300  $1300  $1700  

Count up your $1200s. There are 11 of them.

[pwnthesat]

Blue book, Test 11, Section 8, Question 14

Note that if n represents the number of pails in the stack, then the 2 must represent the height added to the stack every time a new pail is added. Therefore, the 2 must represent c, the distance between the tops of two stacked pails.

[pwnthesat]

Could you please explain question 14 in section 8 from the DVD / test 11?

Yeah, this one is a brainbender. Here’s the key: The “n” in h(n) = 2n + 8 represents the number of cups, so the “2” must represent whatever gets added to the height of the stack every time another cup is added. 

Every time you add another cup to the stack, you’re adding height c from the diagram. That’s why the answer is (C).

[pwnthesat]

Thanks. Can you also do the patterns question #6 on Jan. 2008

Sure. The sequence is basically the integers, starting with 1. The only twist is that the signs alternate, so all the even numbers are negative and all the odd numbers are positive.

So the 50th term, according to the pattern, will be -50. The 51st term will be 51. So the sum of the terms will be:

-50 + 51 = 1