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# GMAT: MathÂ 12

## Video transcript

We're on problem 65. They wrote 2, 4, 6, 8,
n, 3, 5, 7, and 9. And they tell us, in the list
above, if n is an integer between 1 and 10, inclusive--
so that means n could be 1, and it could be 10, or any
number inbetween, and it's an integer-- then the median must
be-- the median, right, not the mean, the median. So the median means the
middle number, right? Let's put all the other
numbers in order. So we have 2, 3, 4,
5, 6, 7, 8, 9. And they're essentially
saying that n could be anywhere in this. It could be a 1 here, it could
be right here, it could be another 2, it doesn't tell us. It could be any number, it could
be 2, could be another 3, could be 10. We don't know. But before we stick n in
here, let's figure out what the middle is. Right here we have eight
numbers, so the middle of the range is actually-- there is no
middle number-- but when we add n, there will be
a middle number. So let's just think about
it for a little bit. If n is 5 or less, so n goes
into this bucket, n goes someplace here, then
what happens? Then what becomes the
middle number? If n is 5 or less, then
we'll have n here. And n might be 5, n might
go right here. But what becomes the
middle number? Then we have 1, 2, 3, 4 on
this side of the middle number, and we have 1, 2, 3, 4
on that side of the number. So then, the median, which is
the middle number, becomes 5. That's if n is 5 or less. If n is less than or equal to
5, then we know that the median will be equal to 5. Now let's do the opposite
thought experiment. What if n is 6 or more? What if n is greater
than or equal to 6? So it goes someplace over
here, so n will go someplace here. Could be 6, I might have
to put it right there. But wherever I put it on the
side, I'll have 4 to the right of 6, and I'll have 4
to the left of 6. n isn't on this side anymore,
4 to the left of 6. So then the median would be 6. And either of these cases
have to be true for n. So the median is either 5 or
6, and that is choice B. Problem 66. I like this brownish color. Reminds me of when I was
in middle school math competitions. 4u7, n23, 162. And you add them all together,
you get one 1,222. And what they want to know is,
if n and u represent single digits in the correctly worked
computation above, what is the value of n plus u? So the best thing to do is to
try to work these out, and see what happens. So 7 plus 3 is 10,
plus 2 is 12. So you would write a 2 here,
which they already wrote, and carry a 1. And now we have 1 plus u-- let
me write this down-- 1 plus u plus 2 plus 6 is equal to, well,
it's either going to be equal to 2, or some
digit and a 2. So let's just think about
it a little bit. 1 plus u plus 2 plus 6, that's
equal to u plus 9. u plus 9 is going to have
to equal something. So if u is 9, and it has to be
something that ends with a 2. And remember, u can only
be between 0 and 9. It's a digit, it has to be an
integer, it has to be a digit. So let's think about
it a little bit. It has to be something
that ends in a 2. So the only next thing above
9 that ends as a 2 is 12. Because you can't get to 22. To get to 22, you would
have to add 13, and you can't be 13. So this has to be a 12, so
u has to be equal to 3. That's the only possibility
that'll give you something that ends in a 2. So if we assume that u is 3,
then we have 1 plus 3 plus 2 plus 6, which is 12, carry the
1, you get 1 plus 4 plus n plus 1 is equal to 12. So you get 1 plus 4 plus 1. That's 6, plus n is equal to 12,
and n would be equal to 6. And they want to know
what n plus u is. So n plus u, 6 plus 3. That's equal to 9. And that is choice B, 9. 67. Look at that, this is a dense
looking one, but let me write down the little equation they
wrote on top. r is equal to 400 times d plus s minus
p, all of that over p. If stock is sold three months
after it is purchased, the formula above relates p, d, s,
and r, where p is the purchase price of the stock. That's the purchase price. d is the amount of any
dividend received. Fair enough. s is the selling price of the
stock, and r is the yield of the investment as a percent. Fair enough. If Rose purchased $400 worth
of stock-- so p is equal to $400-- received a $5 dividend--
so d is equal to $5-- and sold the stock for
$420, for three months after purchasing-- so this formula
applies, because this is the formula for selling after three
months-- what was the yield of her investment,
according to the formula? Assuming she paid
no commissions. We just substitute in. So let's see. The yield would be equal to
400 times 5 plus 420 minus 400, p is 400, all
of that over 420. That is equal to 420 minus
400 is 20, plus 5 is 25. 400 times 25 over-- this
shouldn't be 420, this is p. The price you paid was 400. 25 over 400. I just substituted these values
into this equation. This cancels out, and I'm just
left with a yield of 25, and it's probably in terms
of percent. Yep, 25%. E. All right, problem 68. Let's switch colors. 68. The temperatures in degree
Celsius recorded at 6:00 in the morning in various parts of
a certain country were 10 degrees, I'm not going to write
all of it, 5, minus 2, minus 1, minus 5, and 15. What is the median of
these temperatures? The median just means
the middle. Don't confuse that with the
average, which is the mean. Or the mean, which
is the average. Median means middle, so let's
just put them in order and figure out the middle. So the smallest of
these numbers is minus 5, cross it out. Then we have minus
2, cross it out. Then we have minus
1, cross it out. Then we have 5, cross it out,
then we have 10, cross it out. Then we have 15. So this is interesting
about median. If there is no true middle
number, you have three on this side of negative 1, or negative
1 and less, and you have three on that side, so
there's no middle number, because we have an even
number of numbers. So what you want to do is, you
take the two middle numbers, which are negative 1 and 5,
and you average them. So it's negative 1 plus 5 over
2, which equals 4 over 2, which is equal to 2. 2 degrees Celsius, which
is choice C. Problem 69. If y times three 3x minus 5 over
2 is equal to y, and y does not equal 0, then
x is equal to what? Well the simplest thing, since
y doesn't equal 0, we can divide both sides of
this equation by y. You divide both sides by y.
y divided by y is 1, y divided by y is 1. So then we're left with 3x minus
5 over 2 is equal to 1. Multiply both sides by 2, you
get 3x minus 5 is equal to 2. Add 5 to both sides,
3x is equal to 7. And you get x is equal to 7
over 3, which is choice C. And I'm out of time, so I'll
see you in the next video.