The mathematical reasoning section on the
GED is going to test your ability on solving algebraic equations. Here is an example of
a question that you might have to solve when you take the GED. “If ’10x’ plus two equals
seven, what is the value of ‘2x’?” Well, let’s first start with solving this algebraic equation
of “10x” plus two equals seven. Because if we can figure out what “x” is, then we can
figure out what “2x” is. The first thing we need to do is subtract two from both sides
to get rid of this plus two. So, that leaves us with “10x” equals five. Now to solve for
“x”, we undo the ten times “x” by dividing both sides by ten. Ten divided by ten is one.
So this is “x” equals, and you can simplify five-tenths to a half, or five-tenths. Now
be careful. Because they didn’t ask what is the value of “x”. They didn’t ask you just
to solve for “x”, and they’re expecting you not to pay attention. See this first answer?
They’re expecting you to solve for “x” and go “Oh great there is my answer”. So pay attention
to what they’re asking. They want “2x”, which means two times a half. And two times a half
is one. So, this answer would be C. So, this is something that you’re going to have to
know how to do when you take the GED. The GED will test your knowledge of functions
and patterns. Here is an example of the type of problem you’ll see when you take the GED.
“Which of the following equations satisfies the five sets of numbers shown in the above
table?” You could start by seeing if you can figure out the pattern. Meaning, what do you
do to “x” to get “y”. So, just starting with the first set, you could multiply negative
two times two to get negative four. But it doesn’t work on your next set of numbers.
Three times two is not thirty-one. You could also subtract two from negative two to get
negative four. But you can’t subtract two from three to get thirty-one. So, it may be
more difficult to find the pattern in the table. Luckily though, you have options. Since
you have multiple-choice options, you can use these answer choices to test them against
your table of values. That’s the way we’re going to approach this problem. Let’s start
with the first answer. “y” equals “2x” squared plus seven. Now we just need to pick one set
of numbers to substitute into this equation to test and see if that, if this equation
does satisfy our set of numbers. So, let’s just take two and twelve. You could pick any
set you wanted, but I usually like to pick one that looks a little easier, like two and
twelve. The “y” is twelve, so replace “y” with twelve. We’re checking to see if it equals
two times the “x”, which is two, squared plus seven. Now it’s really important that you
follow the order of operations when simplifying this right side. And there’s a cute little
way to remember the order of operations which you may have heard, and that is PEMDAS. The
P stands for parenthesis. The E stands for exponents. The M stands for multiplication,
I’ll just use the times dot. The D stands for division. The A stands for addition. And
the S stands for subtraction. So, that’s the order that we have to simplify expressions.
On this equation, we’re going to start then with our exponents. Because, even though you
see parenthesis there, that’s not actually what that P means. What is actually
means is grouping symbols, and we have nothing grouped inside the parenthesis. So in this
case, the parenthesis are actually just a multiplication sign. So, we start right here
with two squared. And we have does twelve equal two times four plus seven. Now we have
multiplication and addition. Multiplication comes before addition. So, does twelve equal
eight plus seven? And lastly, we add and we see that twelve does not equal fifteen, which
means this is not our answer. Because that equation does not satisfy our set of numbers.
Now let’s try B; “y” equals “x” cubed plus four. So that was A, let’s try B. And we can
just use the same “x” and “y”. So, I’m going to replace the “y” again with twelve, and
replace the “x” again with two. Follow your order of operations, which means exponents
first. Two cubed is two times itself three times. So, two times two times two, which
is eight. And again we are checking to see if these are equal. Eight plus four is twelve.
So, twelve equals twelve. That doesn’t necessarily mean that that’s our answer though. Just because
it worked on one set of numbers, doesn’t mean it will work on all of our sets of numbers.
So, we need to keep testing answers. Let’s try C; “y” equals “2x”. Same “x” and “y”.
So, replace “y” with twelve and see if that equals two times “x” which is two. Well twelve
does not equal four, which means we can eliminate that as a possible answer choice. Now let’s
try D; “y” equals “3x” plus one. Same “x” and “y”. So, twelve equals three times two
plus one. Continue to follow your order of operations, so multiply first. We want to
see does twelve equal six plus one. Twelve does not equal seven; therefore, that is also
not our answer. Let’s try E now; “y” equals “6x”. Again “y” is twelve. We want to see
if that equals six times two. Twelve does equal twelve. So, this is what I was talking
about. Because you can have more than one equation that works on one set of numbers.
So, to determine which one is the correct answer, we need to test another ordered pair.
So, let’s just pick another set of numbers. Um again, you want to keep it easy. You don’t
want it to be too hard. How about negative two and negative four. So, I’m going to try
the same equation again but using another set of numbers. So, this time the “y” is negative
four. We want to see if that equals negative two cubed plus four. Still following the order
of operations, which means exponents first. Negative two times negative two times negative
two is negative eight plus four. And negative eight plus four is negative four. So, we weren’t
sure if it equaled each other until it didn’t, um in the end. So, this has helped confirm
that B is our answer. But we’re not quite ready to circle it yet, until we determine
that E definitely isn’t the answer. So, we’re going to plug in the same ordered pair into
this answer choice E. So, again your “y” is negative four and we want to see if that equals
six times negative two. Does negative four equal negative twelve? No. So that right there
confirms that B is the correct answer because E did not work when we tried another set of
numbers. There you have an example of a problem using functions or patterns that you could
see when you take the GED. If you’re about to take the GED, then you
need to be prepared for word problems. Here I have an example of the type of problem that
you’ll see when you take the GED. “A number N is multiplied by three. The result is the
same as when N is divided by three. What is the value of N?” Well, I’m going to start
by taking all these words and turning them into an equation. So, first we have N multiplied
by three. And you would just write that as “3N” because that means three times N. Then
they say “the result is the same as”. Well, that’s just saying equal to. So, equals, when
N is divided by three. And that is written as N divided by three. Then they ask, what
is the value of N. Well, a couple of ways to do this. Since you have the multiple-choice
answers, you could use those. Replace N with each answer, and figure out which value of
N makes this equation true. For example if you try one, you have three, replace N with
one, times one equals, and you should put a question mark there because we’re not sure
if it’s equal yet, one divided by three. Three times one is three. And we want to know does
three equal a third. Well, no. Three wholes and one-third of one whole are not the same.
So, since these aren’t equal, that means one is not the value of N. And you can do that
with each answer choice until you find the one that does make the equation true. Or you
can solve the equation. And there’s more than one way to solve the equation. You could divide
both sides by three, but then that might look kind of weird, since you already have N divided
by three. So, what I’ll do is undo dividing N by three by multiplying both sides by three.
So, three times “3N” is “9N”. And that’s equal to, these threes cross-cancel, just N. Now,
you have variables on both sides. So, we want to get all of our variables on one side. And
you can do that by subtracting N from both sides. You have nine Ns minus an N leaves you with
eight Ns equals, N minus N is zero. Now, to solve for N, we just divide both sides
by eight. So, N is equal to zero divided by anything is zero. So, there you have N is
zero. Let’s test that out by plugging it back into our equation. So again, our equation
is “3N” equals N divided by three. And since we solved our equation, and got that N was
zero, we’re going to replace both of these Ns with zero. So, three times zero, and we
want to see if it equals zero divided by three. Zero times anything is zero. And zero divided
by anything is zero. And zero does equal zero. So, we found our answer, that N is zero. There
you have one example of the type of problem you’ll see when you take the GED.
If you’re taking the GED, you need to be prepared to answer word problems. And you’re going
to have to have some knowledge of percentages as well. Here’s a problem that combines both
of those skills: word problem, it’s a word problem, and you have to be able to use percentages
to solve it. “A long distance runner does a first lap around a track in exactly fifty
seconds. As she tires, each subsequent lap takes twenty percent longer than the previous
one. How long does she take to run three laps?” Well first of all, if it takes her fifty seconds
for the first one, and she’s running three, then that means fifty times three. It’s going
to take her, at least, a hundred fifty seconds. You can already eliminate answer choice D.
And since it’s taking her longer for the other ones, meaning more than fifty seconds, that
means it’s going to take more than fifty times three, or more than one hundred fifty seconds.
So, we can eliminate E as well. We’ve already narrowed it down. So, our chances of getting
this correct are even better now. So, let’s lay out what we know. The first lap took her
fifty seconds. The second lap took twenty percent longer than that. So, the second lap
took her the fifty seconds, like the first lap did, and twenty percent of fifty seconds.
Okay, we’re going to have to do a little bit of translating here. We don’t use percentages
when we’re calculating things. So, we leave this fifty, but we’re going to change this
percent into a decimal. And the way to do that is to take the decimal in twenty percent
and move it two places to the left. So, it’s two-tenths. And then “of” tells you to multiply.
So, we’re going to multiply that two-tenths times fifty. So, we have fifty plus, two times
fifty is a hundred, and then there’s one number behind the decimal. So, it took her ten seconds
longer. Because twenty percent of fifty is ten, and it took her ten seconds longer than
the fifty seconds for the first lap. So, her second lap took her sixty seconds. The third
lap we’ll do similarly. It took, again, twenty percent longer than, and this is key here,
than the previous one. So, it’s not going to be another sixty second lap. It took her
sixty seconds and twenty percent of sixty seconds. So, sixty plus, again change that
to a decimal, so it’s two-tenths, “of” tells you to multiply, so times sixty. So, sixty
seconds plus, two times sixty is one hundred twenty, and there’s one number behind the
decimal. So, sixty plus twelve, or seventy-two seconds. Now, since we’re finding how long
it took her to run all three laps, we need to take each one of these times and add them
together. So, we have fifty for the first lap, sixty for the second lap, and seventy-two
for the third. That’s two, seven plus six is thirteen, plus five is eighteen. So, it
took her one hundred eighty-two seconds to do all three laps, answer B. So, this is just
one example of the type of problem you’re going to see when you take the GED.
If you’re taking the GED, be prepared for a lot of word problems, like this one. “John
buys a hundred shares of stock at a hundred dollars per share. The price goes up by ten
percent and he sells fifty shares. Then, prices drop by ten percent and he sells his remaining
fifty shares. How much did he get for the last fifty?” Okay so, here’s what we’re focused
on, just the last fifty. But we need to figure out what the price was of those last fifty
he sold. So, it started at a hundred dollars per share, which we see right there. Then
it increased by ten percent, it went up by ten percent. So, we’re going to add ten percent
to this hundred dollars. And ten percent of a hundred dollars is ten dollars. So, the
new price, after it went up, was a hundred ten dollars. Um, and let me show you, first,
how to find the ten percent of a hundred dollars. This is how I find ten percent of anything.
Basically, ten percent of a number is just dividing that number by ten. And you can divide
a number by ten by taking the decimal and moving it one place to the left. So, that’s
your ten dollars. And you can do that with any number, just move the decimal one place
to the left and that’s ten percent of that number. Okay so, this was the price after
it increased by ten percent, but then, the prices dropped by ten percent. So, ten percent
of a hundred ten dollars, again we find it the same way, just take that decimal, move
it one place to the left, and that’s ten percent of a hundred ten. Since it dropped, we subtract
the eleven dollars from the hundred ten dollars, which is ninety-nine dollars. Now, we can
finally find how much he sold those fifty shares for. He sold each share for ninety-nine
dollars. So, it’s ninety-nine times fifty, which is four thousand nine hundred fifty
dollars. So, there you have one example of the kind of word problems you’re going to
see when you take the GED. Good luck!