Math Problems

Test Preparation SAT Preparation
1

<p>6) 7,10,13... In the sequence above, each term after the first is 3 more than the previous term, how much greater is the 104th term than the 100th term?</p>

<p>13) 2 consec. post even integers are x and y where x is less than y. The square of the smaller number is subtracted from the product of x and y. Which of the following represents the difference?
answer is 2x but the answer i got was -2x?</p>

<ol>
<li>There are 17 numbers. If the 5 smallest are decreased by 1 each and the 3 greatest are increased by 2 each, which of the followin statements is true?
a. median does not change
b.med decreases
c. median increases
d.avg decreases
e.avg does not change</li>
</ol>

2

<p>6) let the 100th term be X
101st term is then x+3, 102nd is 101st + 3 or (x+3)+3 = x+6, 103rd is x+6+3 or x+9, and 104th term is x+9+3 = x+ 12. Take away the original x for the 100th term, and you know the 104th term is 12 greater.</p>

<p>130) x<y
xy - x^2 = ?
since they are positive consec. even integers, y= x+2.
(x+2)x - x^2 =?
x^2 + 2x -x^2 = 2x.</p>

<p>17) let your 17 numbers be:
a b c d e f g h i j k l m n o p q
after making your changes you have:
a-1 b-1 c-1 d-1 e-1 f g h i j k l m n o+2 p+2 q+2
since you are taking one away from the bottom five and adding two to the greatest 3 you have a net change of +1. This means your average must increase. Notice that while you are adding and taking away from some of the terms, there order does not change. This means the median will be unchanged.</p>

3

<p>akelle is correct for #6, #130, and #17.</p>

<p>Just some pointers for #6, #130, and #17.</p>

<p>Tips:</p>

<p>CollegeBoard loves to put sequences on there where they will give you the few numbers in the sequence. They’ll tell you the pattern and then ask for the nth number, usually the nth number is something ridiculous like in this case #100. Most if not all SAT questions can be answered in less than a minute so never take the long route. Try to find the “trick” in solving the question correctly in the shortest amount of time.</p>

<p>In this question it is key to realize the 100th term is going to be a large number and the 104th term is also going to be a large number, but a number that is only slightly bigger than the 100th term. See akelle’s post for the math.</p>

<p>130.) It seems you had the right idea, after all you got -2x instead of 2x.</p>

<p>17.) When I mentally did this problem I conceptually thought about this problem before I started. If the bottom five numbers each are subtracted by 1 and the top three numbers have 2 added to them. Then I know the average has gone up since 6 - 5 = 1. I also know only 8 numbers were affected, but all 8 numbers didn’t affect the other numbers. The “outliers” just become more extreme.</p>

<p>If you want to do it numerically just plugin:
1,2,3,4,5 … 6,6,6,6,6,6,6,6,6 … 7,8,9
0,1,2,3,4 … 6,6,6,6,6,6,6,6,6 … 9,10,11 (-1 to bottom and +2 to top 3)</p>

<p>The median is unchanged.
The average has gone up by 1/17 = .0528.</p>

<p>If you ever don’t stand a SAT problem conceptually just plug numbers in. Trust me. You’ll get quite a few more answers correct!</p>