Two types of problems

Test Preparation SAT Preparation
1

<p>Hey I have been studying SAT for some time now and have got the hang of a lot of the math questions except for two types of them.</p>

<p>I don't know what is the best way to go about problems like this one:</p>

<p>A class of 29 students sponsored two field trips: one to a zoo and one to a museum. Every student attended at least one of the field trips, and 10 students attended both. If twice as many students went to the zoo as went to the museum, how many students went to the zoo.</p>

<p>or like this one:</p>

<p>2, -4, -8,....</p>

<p>In the sequence above, each term after the second is equal to the product of the 2 preceding terms. For example, the third term, -8, is the product of 2 and -4. How many of the first 100 terms of this sequence are negative.</p>

<p>If anyone could give me some tips to use on these type of questions I would greatly appreciate it.</p>

<p>thanks</p>

2

<p>The first one can be solved using the venn diagram.It is easy.
The second one.
2 , -4 ,-8,32,-256.-8192 ,20971…</p>

<p>You see that for every positive number ,there are two negative.So ,positive : negative = 2 :1
let the number of the first 100 positive terms is x ,so the number of the first 100 terms is 2x
You already know that the first term is 2 (it is possitive) ,so you dont need to include it in the following equation .So ,you need to think about the terms that are between 2 and 100 ==>they are 99.
number of positive terms + number of negative terms = 99 terms
x + 2x = 99
3x=99
x=33
In this sequence ,after the first term ‘‘2’’ ,there are 33 more positive and 33x2 = 66 more negative for the total of 1 +33 +66 = 200 terms.
YOur answer is 66</p>

3

<p>One way to think about the first one:</p>

<p>There were 29 kids. Everyone went at least somewhere. So that’s 29 trips. But 10 kids went both places. So that makes 39 trips. If you don’t feel like doing algebra, just look for two numbers in a 2:1 ratio that add up to 39. The numbers that work are 13 and 26. They want the one that more people went to…26.</p>

4

<p>For questions like no. 1, I think it’s easy if you draw a venn-diagram.</p>

5

<p>How would you solve that using algebra?</p>

6

<p>

</p>

<p>If you can’t think of a 2:1 ratio for 39 off the top of your head, like me. Just multiply it by .33 or .66 to get how many. .33 yields 12.87, but you would obviously round that one up to 13. </p>

<p>Just a little tip.</p>

7

<p>thanks for the help. Monoclide good tip.</p>

8

<p>I agree, it is a good tip. </p>

<p>But also, here is why it’s worth it to do LOTS of practice. As soon as I saw 39, I’m thinking – what a wierd number to put in an SAT problem. I wonder why they did that? The only thing useful about 39 is that it is 13 times 3. I bet I’m going to have to divide by 3…</p>

<p>And then sure enough, they hit you with that 2:1 ratio…</p>