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We're on problem 185. Car x and car y traveled
the same 80 mile route. If car x took 2 hours-- so, x
went 80 miles in 2 hours, and that's 40 miles per hour-- and
car y travelled at an average speed that was 50% percent
faster than the average speed of car x. So, 50% faster. So y went 50% faster than x. 50% faster times 40
miles per hour. Well that's 40 plus 20. That's equal to 60
miles per hour. How many hours did it take car
y to travel the route? So, distance is equal
to rate times time. 80 miles is the distance. The rate is 60 miles an hour. So the time is equal to 80/60,
which is equal to 1 and 20/60. Which is equal to
1 and 1/3 hours. And that is what they
have there. They have choice c. I thought they might have 1 hour
and 20 minutes written. Next problem. 186. If the average of the four
numbers k, 2k plus 3, 3k minus 5, and 5k plus 1 is 63, what
is the value of k? So let's just average
the numbers. k, plus 2k plus 3, plus 3k
minus 5, plus 5k plus 1. And that was four numbers. So, divide by 4. That is equal to 63. Let's add up all the k's. I have 1k plus 2k is 3k. So, 6k. 8k. So, I get 8k. And then I get 3 minus 5 is
minus 2 plus 1 is minus 1. And if you multiply the 4
times the 63, if we just multiply both sides of this
equation by 4 you get 4 times 63 is 252. Let me think about that. 4 times 60 is 240 plus 12. Yeah, 252. And then 8k would be-- add
1 to both sides-- 253. And so k is equal to
253 divided by 8. Let's see what that is. 8 goes into 253-- 8 goes
into 25 three times. 24. Bring down-- equals one time. 1 times 8 is 8. You have a remainder of 5. So, it's 31 and 5/8 is k. And that is not one
of the choices. Let me see where I
made a mistake. So the average of k. 2k plus 3, 3k minus
5, and 5k plus 1. That's four numbers, right? What is the value of k? All right, so I add up the four
numbers, and I divide by 4 and they should
be equal to 63. So, maybe I just made a mistake
in the simplification. So, I have k plus 2k is
3k, 3k plus 3k is 6k. Oh, 6k plus 5k is 11k. I don't know what I
was-- that's 11k. And then you have 3 minus 5
which is minus 2 plus 1. Minus 1. So, 11k minus 1. So, this is 11k. So, k is equal to 253 divided by
11, which is-- 11 goes into 253 two times. 22, 33. Oh, that's nicer. It goes in exactly 23 times
and that's choice D. Sorry for the error. Next question. 187. If p is an integer, p is even. They're telling us q is odd. Which is the following must
be an odd integer? OK, so they give us
a bunch of things. So, an even times an odd. Well, by definition, that's
going to be even. Why is that? Well, you can view it as if you
multiply p times q, if p is even that means that p is
divisible by 2, right? So, if 2 is one of the factors
of p, it's definitely going to be one of the factors
of p times q. So, this one will not be odd. Let me think about it. If I add an even plus an odd,
that gives me an odd. So, let's see if any of
the choices are that. Let's see, p divided by q. An even divided by an odd does
not necessarily-- well, this is an interesting one. 2p plus q. That's choice c. Now if p is even-- well, it
doesn't matter whether p is even or not, but 2p is actually definitely going to be even. This is going to be even. And q, we already
know, is odd. So, this is an even
plus an odd. So, it's going to be odd. So, the choice is c. And we could even prove
it a little bit. If you say that p is equal
to 2 times some number k. Right? We don't know what that is. We say that q is equal to 2
times some number, I don't know, m plus 1, then what
does this simplify to? This simplifies to 2 times p,
which is 2 times some number k-- we don't know what k is--
plus q which is 2 times some number m plus 1. Some integer m. So, this becomes 4 times some
number k, plus 2 times some number m, plus 1. Well, 4 times some number k,
that's the same thing as 2 times some other number n. You know it's 2 times some other
integer where n is twice what k is, right? Plus 2m plus 1. And this is the same thing
as 2 times n plus m-- and remember, n, m k, these are all
just integers-- plus 1. And so, if n and m are integers,
then we could say, well, that's just equal to 2
times some other integer-- let's call it l-- plus 1. And this would be
an odd number. Because this is even. And then you're adding
1 to an even number. But you didn't have
to do that. You just had to recognize
that an odd plus an even is equal to an odd. Choice c. Next problem. 188. Drum x is 1/2 full of oil. So x is 1/2 full. And drum y, which has twice
the capacity of drum x, is 2/3 full. So y is 2/3 full and has
two times x capacity. If all of the oil in drum x is
poured into drum y, then drum y will be filled to what
fraction of its capacity? OK. So if x is 1/2 full. So x is equal to 1/2 of its--
well, let me think of the best way to write this
algebraically. x is 1/2 full and y
is twice as big. So, if you poured all of this
1/2 into y, it would contribute to 1/4
of y's capacity. I guess another way, we could
say capacity of x is equal to 1/2 the capacity of y. So, if we were to say 1/2 the
capacity of x, if we were to multiply both sides of this by
1/2, that's equal to 1/4 the capacity of y. So, this 1/2, that's equal to
1/2 the capacity of x which is equal to 1/4 the
capacity of y. So, if we add 1/4 of the
capacity of y to 2/3 of the capacity of y-- that's 2/3 full,
that's another way of saying 2/3 times the capacity
of y-- what do we get? We get 1/4 plus 2/3 which is
equal to-- get a common denominator 12--
3/4 plus 8/12. 3/12 plus 8/12, that's 2/3. You get 11/12. So, y would be 11/12 full
of its capacity. So, that is choice C. Problem 189. If x is greater than 0,
x/50 plus x/25 is what percentage of x? So, you get a common
denominator. This is equal to over 50. x/50 is x/50. x/25 is 2x over 50. So, that is equal to 3x over
50 which is the same thing as 3/50 x. And that's the same thing as--
since we want it as a fraction of 100, since we want to do a
percentage-- that's the same thing as if you multiply the
numerator and the denominator by 2, you get 6 over 100 x which
is equal to .06x which is equal to 6% of x. And that's choice A. Anyway. See you in the next video.