SSAT explanations to the practices-- Smart people help please~?

tiger_max22 · December 28, 2008, 3:36pm

I’m doing the SSAT practice and one of the books just don’t explain how they get their answers, which infuriates me because I paid ( actually my parents did :D)more for the book than the Kaplan book, which costs less and actually explains the answers.

Could anyone help explain how to solve/ why these answers are right?

–Program:Computer as Direction: Assembler ( ??? What’s the relationship)

<hr>

For all real numbers f & p, f@p= (f+p) + (f x p)
ex: 3@5= (3+5) + (3x5) = (8+15)

<li>N@4= 54, then N= ?
– the answer is 10
-------------------------</li>
<li>Figure 2 represents a square piece of cardboard. If a smaller square is cut, in whole inch increments from each corner and the cardboard is folded and taped to make a box whose base perimeter measures 20 inches, which of the following could be the area of the original square piece of cardboard?</li>
</ol>

<h2>( Basically, there was a picture of a square and all 4 corners had a dotted outline of a smaller square.) The answer was 81.</h2>

<li>The average weight of 3 boys is 120 lbs & the average weight of 2 girls is 105 lbs. What is the average weight, in pounds, of all 5 children?
– 114 lbs
----------------------------</li>
<li>Mr. Ed paid $8,000 for a rectangular lot 250ft wide by 400 ft long. What was his cost per square foot?
– I think the answer was $.08
-----------------------------</li>
<li>If p+q is divisible by 3, which of the following is also divisible by 3?
– answer is (2 x P) + (2 x Q) but why is p+q / 3 incorrect??
---------------------------------</li>
<li>What is the greatest possible number of points of intersection of two circles if one has a radius that is twice the radius of the other?
– answer is 2.
---------------------------------</li>
<li>A list consists of 1000 consecutive even integers. What is the difference between the greatest number in the list and the least number in the list?
– 1998.</li>
</ol>

So, this practice test was online;

I’m struggling with the algebra part…

[Practice</a> Questions - Help your Exam Score with free Practice Test Questions](<a href=“http://www.testprepreview.com/modules/percentandratios.htm]Practice”>http://www.testprepreview.com/modules/percentandratios.htm)

I need help with the first few on solving percentages… I want to know the algebraic way to solve backwards.

Thanks, if you can help answer at least some of my questions!

P.S. I would’ve posted this at some tutoring forum, but I guess the SSAT is more relavent on this board, and many people on this board have fantastic scores, so they may have more experience

italianboarder · December 28, 2008, 5:13pm

–Program:Computer as Direction: Assembler ( ??? What’s the relationship)

I believe that the reasoning behind this would be that a computer runs and follows a program. Directions are completed and followed during assembly. Sort of like a schematic?

<hr>

For all real numbers f & p, f@p= (f+p) + (f x p)
ex: 3@5= (3+5) + (3x5) = (8+15)

<ol>
<li>N@4= 54, then N= ?
– the answer is 10</li>
</ol>

Okay, this is a “work it out” problem(I’m assuming you can’t do it mentally or you don’t want to take the chance).
Set up the equation by subbing N for F and 4 for P.
(f+p) + (f x p)=F@P

N@4= (N+4) + (Nx4)=54
(Nx4)=54-N-4
(Nx4)=50-N
N=(25/2)-(.25N)
1.25N=(25/2)
2.5N=25
N=10

<hr>

<ol>
<li>Figure 2 represents a square piece of cardboard. If a smaller square is cut, in whole inch increments from each corner and the cardboard is folded and taped to make a box whose base perimeter measures 20 inches, which of the following could be the area of the original square piece of cardboard?</li>
</ol>

( Basically, there was a picture of a square and all 4 corners had a dotted outline of a smaller square.) The answer was 81.

OKAY: Don’t burn time at this one… You need to post the multiple choice options. Basically you need to strike some away.

<h2>I wish I had a white boarding, but basically what you need to realize is that the base is 4 sides. So each side is 5 inches(20/4). So the smaller square has sides of 5 inches… The original square’s sides would be larger than 5 inches. So take the area and find the length of one side(Sqroot) I’m assuming the other options would be impossible. </h2>

.4(y)=15
Y=15/.4
Y=37.5

SO:
.2(2Y)=?
.2(2(37.5))=?
.4(37.5)=15
NOW WAIT! This will save time… Work with the outside first. You’ll realize that COMMON SENSE saves you some time. You don’t even have to do the work(I did it for your benefit). IT is basically saying:
If one portion(40%) of y is 15. Then half of a portion of 2y should be 15. You are doubling the sample(the sample is Y) and you are halving the portion.

<hr>

<ol>
<li>The average weight of 3 boys is 120 lbs & the average weight of 2 girls is 105 lbs. What is the average weight, in pounds, of all 5 children?</li>
</ol>

Boys(Note, X1 is the first boy’s weight, X2 the second boy’s weight, ect)=
(X1+X2+X3)/3=120
(Y1+Y2)/2=105

Find the sums of the weights, and then add them together. Then divide them by the number of children.

(X1+X2+X3)=360
(Y1+Y2)=210
SUM: 570
570/5=114

<hr>

<ol>
<li>Mr. Ed paid $8,000 for a rectangular lot 250ft wide by 400 ft long. What was his cost per square foot?
– I think the answer was $.08</li>
</ol>

Dude… If you missed this one then I honestly think you just let pressure get to you. Keep calm and SHOW YOUR WORK. It keeps your thought process solid and lets you double check it.

250(400)=Width(Length)=Area=10,000sq(feet)

<h2>So, take the cost(8,000) and divide it by the area. It’ll give you .08$</h2>

<ol>
<li>If p+q is divisible by 3, which of the following is also divisible by 3?
– answer is (2 x P) + (2 x Q) but why is p+q / 3 incorrect??</li>
</ol>

IF you double the parts, the sum will be doubled. A doubled sum will still be divisible, BUT remember the quotient will be doubled.
((P+Q)/3) is not necessarily divisible by 3. ((P+Q)/3)/3 may not equal a whole number.
AN EXAMPLE:
8+7=15
15/3=5
THAT WORKS OUT!

((P+Q)/3)/3=?
((15)/3)/3=1.66666667
THAT DOESN’T

<hr>

<ol>
<li>What is the greatest possible number of points of intersection of two circles if one has a radius that is twice the radius of the other?
– answer is 2.</li>
</ol>

<h2>This is a common geometric theorum. Know your theorums man. No math behind it, you should draw them and think about it.</h2>

<ol>
<li>A list consists of 1000 consecutive even integers. What is the difference between the greatest number in the list and the least number in the list?
– 1998.</li>
</ol>

Know your definitions. X is the first consecutive even interger. X+1998 is the last.(Consecutive intergers go up by two each term. So 999 terms later, you have an increase of 1998.)

neatoburrito · December 28, 2008, 5:25pm

I remember my son working through this problem.

italian’s first step is the same as son’s. The perimeter was twenty so the length of the side after it’s cut is 5.

The problem tells you two things:

<ol>
<li> It’s a square</li>
<li> The area cut away was in even units</li>
</ol>

I got the book out and the choices were 25, 24, 50, 81, and 99

I remember making my son reason this one out loud. Here was his logic…

If it’s cut in whole increments, then the area cut away will be even. Looking at the answers, 25 is the area of the bottom of the box. None of the others are perfect squares except 81. Square root is 9. They must have cut away 2 inches from each side. (5 + 4 = 9) 9 x 9 = 81 as a quite check to make sure the answer is correct.

I love this problem. It’s a great example of mathmatical reasoning.

mpicz · December 28, 2008, 7:04pm

For the stuff you cant do algebraically or by using geometry use some trivial techniques. For example.

<h1>4 : If you look in your princeton book about averages it will tell you to draw a little cirle. You cut up the circle into 2 fourths and 1 half. It will tell you to to put the average in one box and number of items in the other fourths box. In between your lines in the diagram are multiplication signs. So once you fill out the diagram for boys and girls you can see that you have to multiple 120 by 3 and 105 by 10. After that obviously you add them up and divide it by how many children. So if your not good simple algebra or geometry use easy techniques.</h1>

Again, Look at #6. If you don’t understand it, simply use a plug in technique that comes in very useful.

If you plug in 29 and 1 as p and q you will get 30 which is divisible by 3. Now 30/3=10…10 is not divisible 3 and theres one answer gone. Do it for the other ones until you have your answer.

Simply different explanations of what italian was trying to say, incase you didn’t understand him. These are simple techniques that are you can easily remember during the test.

italianboarder · December 28, 2008, 7:19pm

Hey mpicz, thanks man for helping. And in all honesty, I think my way would probably put you over the time limits. One thing, #6 would be a tricky devil to solve by using plug ins. Some plug ins would work and some wouldn’t.

Lets say you picked 89 and 1. 90/3=30 and 30 is divisible by 3.

mpicz · December 28, 2008, 7:47pm

Hmmm ya your right. Ok that was a bad pick for me…but I know from experience in certain types of questions plugg ins works really well. Not this one obviously cuz italian just found a flaw.

To tell you the truth tiger, in the test I would have gone with p+q/3 or maybe something else (or atleast come back to it if I had time)…so dont feel stupid about that one. I would look at (2 x P) + (2 x Q), and not want to spend the extra 30 seconds lol

neatoburrito · December 28, 2008, 8:08pm

on #6 again, I asked my son. He plugged in 1 and 2

A) (p x q) + 3 = 5 NO
B) p + (3 x q) = 7 NO
c) (3 x p) + q = 5 NO
d) (2 x p) + (2 x q) = 6 YES
and for the sake of argument
e) p + q / 3 = 1 NO

always plug in the simplest numbers. The math is really simple enough to do in your head. You’d probably have enough time to double check with another set of numbers…like 2 and 4. They would give you:

A) 11
B) 14
C) 10
D) 12
E) 2

Again…D is the only choice that works.
The ssat is not trying to trick you.

89 and 1 work just as well, but he says only to pick different numbers if you get either nothing that will work or more than one that will work. Stay away from picking zero and it’s really better to avoid 1 as well.

As to number 7… It seems to me that the great possible points of intersection of ANY two circles is two.

For average problems. Use algebra. A= total / number of terms

remember that the middle term of consecutive integers is the average.

Same for percent problems (all percentages in decimal form)

% = part / whole
part = % times whole
whole = part / percent

when figuring how much something costs after a discount, save yourself a step and find the percent that you’ll be paying for.

tiger_max22 · December 28, 2008, 9:23pm

Thanks guys with all the problems.
I’m still not sure if I understand the first one.
On Italian’s method, on step # 4:
You divide both variables on the right side by 4 to isolate N. And then you bring the .25N back again to the other side, which makes it 1.25N? Then you divide to isolate N again… Wow… This is so confusing; I hope I’m understanding it right.

And for the box one, it has to be a perfect square because well, it’s a square, right? And both sides need to be the same…
And it definately needs to be more than 25… Ok, I get it now.

And for the consecutive numbers one. Is it like,

0 -2000 are the first 1000 even numbers, so 2000-2 = 1998 ??
If that’s right, I don’t know why I went on thinking it more difficult than it really was.
As for the other “easy” problems, I did the division parts wrong. I get confused with dividing the decimals with another decimals. Like with Mr. Ed’s problem.

Thanks a lot again, esp. Italian. I probably have more questions later, but right now I’m just tired of studying night-day. I’m almost finished with the upper level tests on my book, but really don’t feel like doing the ISEE nor lower level tests. Which seems like a complete waste… :B

mpicz · December 28, 2008, 9:26pm

Ya your sons right and I knew that…but I was just saying italian succeeded in finding an exemption. But of course if you try a simpler one and it works go with that(even though when plugging in number in most cases you should be able to use everything; the more complicated number ususally just make it more complicated to solve at the end, not disprove your workings). Dont try and disprove your self.

And tiger, if I were you I would put all my time into math and hope the other 2 sections come. Get familiar with simple nuances and it will definitely improve your score. And dont skip over the “easy” stuff it will help :).

tiger_max22 · December 28, 2008, 9:31pm

Haha, I’ll try… Math is black and white, but it’s hard to figure out sometimes.
Esp. the algebra and word problems.

As for the reading and vocab, I’m focusing more on the verbal part than reading.
I’ve made a list of flash cards with Kaplan’s reference words on them.

Reading is pretty much easier since most of the answers are in the short passages.

mpicz · December 28, 2008, 9:37pm

Lol ya cool…did you understand all the explanations?

neatoburrito · December 28, 2008, 9:42pm

On the first one, if you’re insecure about algebraic operations, all your really need to know is how to make the substitution. You only 60 seconds for each problem so you can save yourself second guessing your alegbra skills by looking at the answer choices and doing the rather simple arithmetic in your head.

(N + 4) + (N x 4) = 54

A) 9 + 16 No
B) 14 + 40 Bingo you don’t need to check the others because you’ve got the one that works.

But, when I opened the book to look at the answer choices, I saw my son’s scratch work and it was different from italian’s and would probably take less time than checking the answers first. This is what he has:

(N + 4) + (N x 4) = 54
N + 4 + 4N = 54
4 + 5N = 54
5N = 50
N = 10

He just killed the parenthesis and combined like terms.

Remember, they are more like puzzles than anything. The solutions are almost always really simple. They are testing logic, not math.

neatoburrito · December 28, 2008, 9:43pm

Also, some advice I gave my son. If the math starts getting complicated, you’re probably on the wrong track.

mpicz · December 28, 2008, 9:48pm

I think either way you can get through it pretty quick, I personally would skip it and come back when im done so I’ll probably have a good 5 minutes.

tiger_max22 · December 28, 2008, 9:54pm

Wow, that method was so much easier!
Thanks!

neatoburrito · December 28, 2008, 10:22pm

Yeah, he has a way of finding the simplest solution. His teacher HATES it and sometimes refuses to give him any credit if he doesn’t set up the problem the way she has taught it. There was one test question that said, “If a square has an area of 25, what is the perimeter?” He promptly wrote 20 and moved on because, to him, it was a simple math fact like 2 + 3. She wrote “show work” and “-10.” He’s not trying to be cheeky, it was just obvious to him. She wanted him to write out formulas and such. It was all I could do not to tell him to start showing ALL work, like making tally marks when adding. That would be hysterical!

mpicz · December 28, 2008, 10:47pm

What grade is he in? I mean if its not 8th grade then that was a pretty stupid question to put on a math test lol. But you can’t really fault the teacher, atleast write something stupid lol 5x5=25…5+5+5+5=20…there ya go stupid teacher lol…what logical formula would you write out for that?

tiger_max22 · December 28, 2008, 11:34pm

uhm, I ran into another problem.
I don’t like the study guide, 'cuz it doesn’t show how they get their answers…

In a class, 1/8 of the boys and 1/4 of the girls play the piano, and 3 times as many girls as boys play the piano. If there are 100 boys and girls in the class, how many boys play the piano?

A. 3
B. 5
C. 12
D. 24
E. 25

Is there a way I can really perk up my alg. and reasoning skills?

Also, does this make sense?

Which figure CANNOT be drawn without lifting the pencil or retracing it?

It sounds like a double negative to me… Kinda confusing to understand.

The answer is a figure where you can draw in one fluid motion.
So a simplified question would be: Which figure can be drawn without lifting the pencil or retracing it? or maybe not…?

Wow… help plz. So much math this week… I’m starting to think so deeply about every problem, even simple problems, thinking the SSATB are trying to trick me. D:

mpicz · December 28, 2008, 11:59pm

This is pretty simple just staring at it but ill kind of work it out for you. On these type start with disregarding the 1/8 and 1/4 part. Plug in from the answers.

Start with C , theres 3 times more girls than boys. Soooo 12 x 3 =36…36+12 is 48…not 100.

So you know it has to be something higher. When I look at this I just stare at 25…25x3 = 75. …75+25= 100…Your answer. You cant really improve in the time you have

neatoburrito · December 29, 2008, 12:04am

He’s in 7th grade.

I asked him and we figured it out. It’s tricky, but we’ll try to explain it.

<ol>
<li> Three times as many girls play piano as boys.</li>
</ol>

Try out the answer choices!

A) If 3 boys play piano then 3 = 1/8 so there are 24 boys in the class (3x8=24)
AND 9 would = 1/4 so there would be 36 girls(9x4). 24 + 36 does not = 100 WRONG!

B) If 5 boys play piano then 5 = 1/8 and there are 40 boys in the class
AND 15 = 1/4 (remember, three times as many girls play as boys) so there are 60 girls
in the class. 40 + 60 = 100 BINGO! look no further.

Hope this helps.

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