All right, problem 42.
So say for the system of equations given, and this is
the system of equations they give, they say x minus 4 is
equal to z.
They say y minus x is equal to 8, and that 8 minus
z is equal to t.
So they say for the system equation, what is
the value of z?
So we're trying to figure out z in this.
Statement number one: they tell us that x is equal to 7.
Well, if we know x is equal to 7, we can solve for z right
here because x is 7 and 7 minus 4 is z, so 7 minus 4 is
3, so z is equal to 3.
That was pretty straightforward.
So one alone is sufficient just using this first equation
in the system.
So let's see if two is of any use.
t is equal to 5.
Well, this is an easy one, too.
You put t is equal to 5 right here and then you could easily
solve for z, right?
You get 8 minus z is equal to 5 and you can solve for it,
but I'm not even going to do it.
You just have to know that you can.
So this alone is sufficient as well.
So the answer is D.
Each statement alone is sufficient.
Problem 43.
Is x equal to 5?
In statement number one, they say x is greater
than or equal to 5.
Well, that doesn't tell me whether x is equal to 5.
It just says it's greater than 5.
Statement number two tells us x is less than or equal to 5.
Once again, that does not tell me whether x is 5, but if I
told you that both of these are true, x is greater than or
equal 5, and-- not or-- and x is less than or equal to 5,
well, actually, that still-- well, the only x that
satisfies that equation, that satisfies both of
these, is 5, right?
I mean, you put 3 in, 3 will not satisfy this one.
If you put 7 in, 7 will not satisfy this one.
So the only thing that satisfies this is 5, so you
need both of these.
So the answer is both statements together are
sufficient, C.
That one's confusing because it's so simple on some level.
44.
The table above shows that this-- let me see if I can
draw this table.
And they write R, S T, U, and R, S, T, and U.
They have a bunch of things.
I don't even know what these are yet.
I haven't read the question, but let's see, 0, y, x, 62, y,
0, 56, 75, x, 56, 0, 69.
And then 62-- that's a 6-- 62, 75, 69, and 0.
And what are they going to ask?
They're saying the table above shows the distance in
kilometers by the most direct route between any two of the
four cities.
For example, the distance between city R
and city U is 62.
Or if you said between U and R, it's going to be 62 as
well, right?
That's the same thing.
Fair enough.
What is the value of x?
So the value of x is the distance between T and R.
Let me circle that.
They want to know what the value of x is.
It's the distance between T and R, so it's that one.
And another way to look at distance between T and R,
that's this one so, these are both x.
Fair enough.
OK.
So statement number one tells us, by the most direct route,
the distance between S and T, so we could say the distance
between S and T, I'll just say it's line segment ST, is equal
to twice the distance between S and R.
It's equal to two times SR. So let's see, do we
know what SR is?
SR is equal to y, right?
And ST is equal to 56.
So 56 is equal to 2 times SR. The distance between S and R
is y, so it equals 2y.
And so we can solve for y.
y is equal to 28.
And we didn't have to solve it, but let's see.
I'm just trying to see where this goes.
But that still doesn't help me figure out the distance
between R and T.
That just tells me solve for y. y is 28.
Statement number two, see where this is going.
By the most direct route the distance between T and U is
1.5 times the distance between R and T.
So the distance between R and T, this is the interesting
thing, because R and T is x, right?
So they're saying the distance between T and U is equal to
1.5 times x.
And what's this between T and U?
The distance between T and U is 69, right?
You don't even have to solve it.
You just know that you can usually solve for x if you
know statement number two.
So statement number two alone helps you
figure out what x is.
Statement number one is fairly useless.
So the answer is B.
Statement two alone is sufficient.
Let me draw a line here.
I don't want to--
OK, problem number 45.
What is the value of the two-digit integer x?
So 2-dig integer x equals, who knows?
All right.
Statement number one: The sum of the two digits is 3.
So let's that x is equal to the number AB where this is
the tens digits and this is the ones digit.
So statement number one says the sum of the two digits is
3, so A plus B is equal to 3.
Well, that doesn't help us.
There's a lot of-- well, you know that these are going to
be positive numbers, but we don't know whether they're two
different numbers.
Two: x is divisible by 3.
x is divisible at 3.
Well, I don't know if you learned that trick in school,
but any number that is divisible by 3, the sum of
their digits are also divisible by 3.
So once again, that just means that A plus B is equal to some
multiple of 3.
Well, if you keep adding them, they eventually add up.
So if you had a two digit number, so
this is-- let's see.
Let's think.
Just A plus B is equal to 3.
This could be a couple of different things.
It could be a two-digit number.
It could be 30.
It could be 1.
It could be 12.
It could be 21.
I think those are all of the possibilities that we can have
just off of statement number one.
And x is divisible by three, well, all of these are
divisible by 3, so really, both statements give you no
information.
So the answer is E, that both statements combined still give
me nothing.
But all of these are possibilities.
And actually, this one leads to many, many more
possibilities that x is divisible by 3 because then
you could have things like-- I don't know.
This would have been a valid number as well.
This would actually give a lot more.
This is a little bit more strict.
But anyway, either way, we can't figure out what x is.
It could be 30.
It could be 12.
It could be 21.
It could be anything.
All right.
Problem 46.
What is the tenth digit in the decimal representation of a
certain number?
So the tenth, that's the number right behind the
decimal point.
So the number-- let's just call it x-- so statement
number one says x is less than 1/3.
And two says that x is greater than 1/4.
So this is enough to figure out what the tenth digit is.
So what's the number that's less than 1/3?
Let me to think of a couple of them.
Well, 1/3 is like 0.333 repeating, so if I just write
0.32 that satisfies one and it satisfies 2, right?
0.32 is greater than 1/4.
But what's another?
And then in this case, a tenth digit would be a 3, but let me
try to find another one that would satisfy these both.
Well, let's see, greater than 1/4, what about 0.26?
0.26 is definitely greater than 1/4 and is definitely
less than 1/3, but both of these have different tens.
One has a 2, one has a 3 there.
So even both statements combined still do not allow me
to solve the problem.
There's not enough information given.
So once again, E, together I'm still not getting enough
information.
Oh, I'm almost at 10 minutes.
Anyway, I'll see you in the next video.