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## Problem solving

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# GMAT: Math 18

## Video transcript

We're on problem 96. It says 1/2 plus, open brackets,
2/3 times 3/8 divided by 4 minus 9/16. Do you know order of operations,
and can you deal with fractions? 2/3 times 3/8, the 3's cancel
out, and the 2 and the 8 become 1/4. 1/4 divided by 4, let me write
this, 1/2 plus 1/4 divided by 4, that's the same thing as
times 1/4, minus 9 over 16. So that is equal to 1/2
plus 1/16 minus 9/16. And now it doesn't matter what
order we do it in, but since everything's in 1/16ths, so let
me write this in 1/16ths. So this is 8/16 plus
1/16 minus 9/16. So that's equal to 8 plus 1
minus 9 all over that 16. That's 9 minus 9,
that equals 0. Choice E, all that
work to get to 0. Next problem, 97. Water consists of hydrogen and
oxygen, and the approximate ratio by mass of hydrogen to
oxygen is equal to 2:16. Approximately how many grams
of oxygen are there in 144 grams of water? OK, 144 grams of water, that
means that the oxygen and hydrogen is equal to 144. They say 144 grams of water,
not when you have 144 grams of hydrogen. So when you add these together,
you have 144. And then they tell us that
the ratio of hydrogen to oxygen is 2:16. Or another way to write it,
you can say hydrogen over oxygen is equal to 2/16, which
is another way of saying 1/8. And they want to know how many
grams of oxygen, so we want to solve for oxygen, so we want
to substitute for hydrogen. So we could say hydrogen is
equal to 1/8th the oxygen. I just multiplied both
sides times oxygen. So if hydrogen is equal to 1/8
oxygen, you have oxygen plus 1/8 oxygen, let me make
sure that's right. Yeah, hydrogen to oxygen
is equal to 144. And if you view this as 8/8, 1
oxygen is the same thing as 8/8, so you get 9/8 oxygen
is equal to 144. So you get oxygen is equal
to 144 times 8 over 9. Does 9 go into 144? I think it should, let me see
how many times does 9-- 3 definitely does. This is 12 times 12, so 3 will
go into 144 48 times. 9 goes into 144 1,
9, 54, 16 times. So this is equal to 16 times
8 over 1, which is what? That's equal to 250-- no,
that can't be right. No, you can't have more grams of
oxygen than you do-- let me see, I've made a mistake
someplace. Hydrogen to oxygen is equal
to 2:16, which is 1:8. Oxygen plus hydrogen is equal
to 144, you get 9/8. Oh, I see my mistake. That's good. I've been making a lot of
careless mistakes, maybe I need to take a rest. 9/8 oxygen
is equal to 144, so oxygen is equal to 144 times
9 over 8-- sorry, times 8 over 9. I was doing it right, so
where was my mistake? So 144 times 8 over 9, that's
equal to-- oh, I just made a mistake at the very last step. 9 goes into 144 16 times. 16 times 8 isn't
256, it's 128. That was my mistake. So there's 128 grams
of oxygen. I just made a mistake right
at that last step. All right. And that's choice D. Question 98. If x times 2x plus 1 is equal
to 0, and they also tell us that x plus 1/2 times 2x minus
3 is equal to 0, then x is equal to what? So this is interesting. x times 2x plus 1 is equal to 0,
that means that either x or 2x plus 1 has to
be equal to 0. So one of these has
to be equal to 0. But then x plus 1/2 times 2x
plus 3, this tell us that one of these have to
be equal to 0. So if x is equal to 0, then this
has to be the one that's equal to 0. So either this and that
is equal to zero, or-- do you see that? Well I guess both of these
could be equal to 0. Let me multiply them out. Maybe I'm going down
the wrong path. If I multiply these out,
I get 2x squared plus 2 is equal to 0. If I multiply these out, I get
x times 2x, which is 2x squared, x times minus 3
minus 3x, 1/2 times 2x, so it's plus x. And then 1/2 times minus
3 minus 3/2 is equal to 0, so I get what? 2x squared minus 2x. 3x plus x is minus 2x, minus
3/2 is equal to 0. Actually I think I made a
mistake, x times 2x plus 1, that's not right. That's 2x squared plus
x is equal to 0. Fair enough. We know 2x squared, so we can
just write that 2x squared is equal to minus x, and
then substitute this information in here. So we get minus x, 2x squared
is equal to minus x. Minus x minus 2x minus
3/2 is equal to 0. So you get minus 3x, let's
add 3/2 to both sides, is equal to 3/2. And then divide both sides by
minus 3, you get x is equal to 3/2 times minus 1/3, so that
equal to minus 1/2. And that is choice B. Next problem, 99. On a scale that measures the
intensity of a certain phenomenon, a reading of n
plus 1 corresponds to an intensity that is 10 times the
intensity corresponding to a reading of n. So n plus 1 is equal
to 10 times the reading of just an n. On that scale, the intensity
corresponding to a reading of 8 is how many times as great as
the intensity corresponding to reading of 3? So if you call a reading
of 3, I don't know, let's call that a 1. A reading of 4 is going to be
10 times the reading of 3. A reading of 5 is going to
be 10 times that, so 100. A reading of 6 is going to be
10 times that, or 1,000. A reading of 7 is going to be
10 times that, or 10,000. And then a reading of 8 would be
10 times that, so it would be 100,000. Which is not one
of the choices. Let me make sure I'm
reading that. On a scale that measures the
intensity of certain phenomenon, a reading of n
plus 1 corresponds to an intensity that is 10 times the
intensity corresponding to a reading of n. So a reading of 4 is 10 times
the intensity of a reading of 3, and a reading of 5
is 10 times that. Fine. On that scale, the intensity
corresponding to a reading of 8 is how many times as great as
the intensity corresponding to a reading of 3? A reading of 4 would be 10 times
as great, a reading of 5 would be 100 times as great, a
reading of 6 would be 1,000 times as great. Oh yeah, 100,000, which
is 10 to the fifth. 10 to the fifth power. Five 0's, so that is choice C. Confusing myself unnecessarily, and I'm out of time. See you in the next video. Let me stop this one.