So we're at problem 76.
Which of the following ratios is most nearly equal to the
ratio of 1 plus the square root of 5 to 2.
And then they give us a bunch of integer choices, so this is
really just a problem of approximating what the square
root of 5 is.
So let's think about this a little bit.
So 2 is equal to the square root of 4, or 2 squared is
equal to 4.
3 is equal to the square root of 9.
So the square root of 5 is going to be a lot closer to 2.
What's 2.1 squared?
2.1 times 2.1 you get 21.
0, 2 times 21 is 42.
So then you get, 4.41 So 2.1 is equal to
square root of 4.41.
2.2 times 2.2, 2 is 44, 0, 44, this gets pretty close to 5.
8, 4.
So 2.2 is I think about as close as we're going to get.
If we approximate the square root of 5 is 2.2, and this is
just an approximation, we just have to figure out which
choice is closest, 1 plus 2.2 over 2, that's equal to 3.2
over 2, and that's not one of the choices, because this
really isn't an integer choice.
But let's see if I can just express this,
this is equal to 1.6.
It'd give you 1.6:1.
So we just have to find which of the choices are roughly
equal to 1.6:1.
So choice A, 8:5.
Well what is that?
That's 1 and 3/5.
Well that's exactly 1.6.
So that's the choice I'm going to go with.
Let me look at the other ones.
6:5 is going to be a lot closer to 1, 6:5 is 1.2, 5:4
is 1.25, 2:1 is 2.
So choice A is the best choice.
Next question.
Problem 77.
Let me scroll down a little bit.
7 over 1/5 plus 5 over 1/7 is equal to-- 7 divided by 1/5 is
equal to 7 times 5, plus 5 divided by 1/7 is
equal to 5 times 7.
When you divide by a fraction, it's the same thing as
multiplying by its reciprocal.
So 5 times 7.
So this is equal to 35 plus 35, which is equal to 70, and
that's choice D.
78.
From January 1, 1991, to January 1, 1993, the number of
people enrolled in health maintenance organizations
increased by 15%.
The enrollment on January 1, 1993 was 45 million.
How many million people, to the nearest million, were
rolled in health maintenance organizations
on January 1, 1991?
OK, so let's just call this x.
That's what they want to know, they want to know how many
million people were enrolled in 1991.
So when x increased by 15%, you got to 45 million.
So remember, not 15% of x is 45 million, x
increases by 15%.
So let me write an extra step that I normally don't do.
So you could view it as x plus 15% x, right?
This is x, and then you're increasing it by 15% of x, is
going to be equal to 45 million.
And then this is 1x plus 0.15x, so that's 1.15x is
equal to 45 million.
And you could also just go straight to this step.
In fact, you usually can once you get used to it.
You can say, 15% increase, that's the same thing as
multiplying by 1.15.
So x is equal to 45 divided by 1.15, and we're going to have
to do a little bit of division to figure this out.
115 divided by 45, add a couple of 0's So it's 1.15
divide by 45, so that's the same thing as 115, take the
decimal place, go 2 to the right, going to 4,500.
115 goes into 450 how many times?
Does it go into it 4 times?
No, that'd be 460, so it goes into it 3 times.
3 times 115 is 345.
This difference is 105, bring down a 0.
115 goes into 1,050 how many times?
If I did 8, 800, I think it's 8 times, because 9 would be--
actually 900 plus 90 plus 45, actually it would be 9 times.
9 times 5 is 45.
9 times 1 is 9 plus 4 is 13.
9 times 9 is 1-- I'm sorry, is 9, plus 1 is 10.
You have a remainder 15, bring down the 0, that goes 1 time.
So we already have the decimal point.
And all their choices are in integers.
So this is closest to B, 39.
And I wanted to get that last decimal point, because maybe
that was 39.9, in which case 40 would
be the closest choice.
Sometimes they get tricky like that.
Next question.
79.
R is the set of positive odd integers less than 50.
And S is equal to squares of R, squares of the
numbers in that set.
How many elements does the
intersection of R and S contain?
OK, so we have to say, positive odd
editors less than 50.
So we have to think, how many positive odd integers less
than 50 are squares of other positive odd
integers less than 50.
It doesn't take a long time to figure out all of the squares
between 1 and 50.
It's 1, 2, 4, 9, 16, 25, they start increasing
pretty fast, 36, 49.
Now we know that they have to be positive,
these are all positive.
We know they have to be odd, because we're looking for
things that are both squares and they're in set R.
They're squares, and they're squares of other
things in set R.
So let's take out all the even numbers.
Can't be 36, can't be 2, can't be 4, can't be 16.
1 is 1 squared.
So 1 is in set R, it's a positive odd integer less than
50, and it is a square of another positive odd integer
less than 50, a square of itself.
So 1 counts.
9 is 3 squared.
9 itself is a positive odd integer less than 50, and it's
also the square of 3, which is another positive odd integer
less than 50.
So 9 counts.
25, same logic.
It's a positive odd integer less than 50, it's the square
of 5, which is the same.
And 49, same thing.
Square of 7, both 49 and 7 are positive odd
integers less than 50.
So I found four.
So that's C.
Question 80.
A retail appliance store priced a video recorder at 20%
above the wholesale cost of $200.
We could just go, 20% above 200, that's going to
be 1.2 times 200.
If a store employee applied the 10% employee discount to
the retail price to buy the recorder, how much did the
employee pay for the recorder?
So this is the retail price.
This was the wholesale price, that's what the store bought
it for, this is what a non-employee would have to
pay, 1.2 times 200.
And then the employee got a 10% discount.
So essentially the employee paid the
retail price times 0.9.
So what's 1.2 times 200?
200 times 1.2.
Let's just do it out.
2 times 200 is 400.
Add a zero.
1 times 200 is 200.
And we have one point behind the decimal-- well let's add
them up, you get 2400.
We have one digit behind the decimal, so it's 240.
So the retail price is 240, and we have to multiply that
times 0.9 to figure out what the employee paid.
They got a 10% discount, which is another way of saying they
played 90% of the retail price.
So 240 times 0.9.
9 times 0 is zero, 9 times 4 is 36, 9 times 2
is 18 plus 3, 21.
We have one number behind the decimal point, so the employee
paid $216, which is choice B.
Now I'm out of time, I'll continue
this in the next video.