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## GMAT

### Course: GMAT > Unit 1

Lesson 1: Problem solving- GMAT: Math 1
- GMAT: Math 2
- GMAT: Math 3
- GMAT: Math 4
- GMAT: Math 5
- GMAT: Math 6
- GMAT: Math 7
- GMAT: Math 8
- GMAT: Math 9
- GMAT: Math 10
- GMAT: Math 11
- GMAT: Math 12
- GMAT: Math 13
- GMAT: Math 14
- GMAT: Math 15
- GMAT: Math 16
- GMAT: Math 17
- GMAT: Math 18
- GMAT: Math 19
- GMAT: Math 20
- GMAT: Math 21
- GMAT: Math 22
- GMAT: Math 23
- GMAT: Math 24
- GMAT: Math 25
- GMAT: Math 26
- GMAT: Math 27
- GMAT: Math 28
- GMAT: Math 29
- GMAT: Math 30
- GMAT: Math 31
- GMAT: Math 32
- GMAT: Math 33
- GMAT: Math 34
- GMAT: Math 35
- GMAT: Math 36
- GMAT: Math 37
- GMAT: Math 38
- GMAT: Math 39
- GMAT: Math 40
- GMAT: Math 41
- GMAT: Math 42
- GMAT: Math 43
- GMAT: Math 44
- GMAT: Math 45
- GMAT: Math 46
- GMAT: Math 47
- GMAT: Math 48
- GMAT: Math 49
- GMAT: Math 50
- GMAT: Math 51
- GMAT: Math 52
- GMAT: Math 53
- GMAT: Math 54

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# GMAT: Math 3

12-19, pgs. 153-154. Created by Sal Khan.

## Want to join the conversation?

- I have the 12th edition book which does not have no. 14 and 16 problem. Can someone please give the questions? Thanks(4 votes)
- 14. Which Cannot be a value of 1/1-x?

16. What is the combined area, in square inches, of the front and back of a rectangular sheet of paper measuring 8.5 by 11 inches.

I have a PDF version of the 11th edition. I'd be happy to email it to you if you like.(8 votes)

- Sorry, in problem number 16, Why is 187 the answer? should´t it be 187*2 in order to be both areas combined?(4 votes)
- i am in 6th grade soorry but could you put a little more slower problems(1 vote)

- At the beginning of question 13, Sal talks about the Khan application, is he referring to an iphone application? If so, which one?(3 votes)
- For problem 15, is the answer 4 rolls or 4 dozens? The questions was about rolls.(2 votes)
- question number 15 says how many dozens of rools are remain after one half plus 80% of one half arer sold which means half of 40 dozens is 20 and 80 percent of the remaining 20 is 16 so 4 dozen rolls remain not 4 rolls.(3 votes)

- Is this correct:

1/0-1 = -1

Zero minus 1 = negative one. Negative one into one equals negative one.(2 votes)- The question focuses on the value of the expression, not value of X.

Is there an X that can result in the expression to be equal to -1? Yes, when X=0, expression is -1. So this is not our answer. Move to next option.

Is there an X that can result in the expression to be equal to 0? No. Because this can happen only when X is infinity which cannot be written as a number. So 0 is a value that the expression can never have, hence this is the right answer.(4 votes)

- on number 17 you said 30 then 36(3 votes)
- #15-Shouldn't the answer be 48, since (I think) the question asked for the number of rolls and not the number of rolls as a dozen?(2 votes)
- Just to clarify, the expression 1/(x-1). The denominator can not equal 0 because it would result would be undefined (1/0). if this is the case, then x could not = 1 because 1-1=0 in the denominator. So is the question asking what x can not be equal to or is it asking what will make the equation undefined? Thank you.(1 vote)
- I understand you're trying to go fast like it is a test setting but we are trying to learn these steps. Going slower and more elaboration would be very helpful.(1 vote)
- How do we use the distrusted property of multipction(1 vote)

## Video transcript

We're on problem 12. 0.1 plus 0.1 squared plus
0.1 to the third. So that's the same
thing as 0.1. What's 0.1 squared? It's 1 times 1 with 2 numbers
to the right of the decimal, so it's 0.01. And then to the third power. You're just going to end
up 1/10 of that, right? 0.01 times 0.1. Well that's 1 with 3 numbers
to the right of the decimal point. If I'm going to add them
all up, I get 1, 1, 1. And that is answer B. They're making sure you can
multiply your decimals. Problem 13. If you have trouble with
decimals, you might want to get on the Kahn Academy-- the
actual application, it's free-- and just work through the
basic arithmetic, because we have actually a bunch of
things on multiplying decimals and stuff. You have to start at 1 plus 1,
but it makes sure you don't have any holes in
your knowledge. It eventually gets to algebra
and trigonometry and calculus. You might find that useful. Anyway, question 13. A carpenter constructed a
rectangular sandbox with a capacity of 10 cubic feet. If the carpenter were to make a
similar box twice as long-- 2 times length-- twice as wide--
2 times width-- and twice as high as the first
sandbox, what would be the capacity in cubic feet of
the second sandbox? So you might want to visualize
it, right? The best way to visualize it
is probably how many of the old ones could fit? So if this was one of the old
ones, and now I'm going to make a new one that's
2 times the size in every dimension, right? That's 2 times the height. So essentially, I could increase
the width by 2. Increase the depth by 2, or
whatever you want to call it. Right? And then I'm going to increase
the height by 2. And I'm going to have
trouble drawing. So how many of the original
sandboxes-- that's what they want to know-- how many of the
original sandboxes essentially could fit into the new one? Well, 2 in 1 direction
times 2 times 2. So 2 times 2 times
2 is equal to 8. So another way to think of it,
you could view the old sandbox as almost a unit, like one
cubic unit sandbox. And now we're going to go
2 in every direction. So we could fit 8 of the old
sandboxes into the new one. And the old one had
a capacity of 10. So 8 times that is equal to 80
cubic feet, which is choice D. Question 14. And these, at least so far,
I think these are on the easier end. They'll probably get harder,
but so far they're a lot faster than the data
sufficiency ones. Which of the following cannot
be a value of 1 over x minus 1? And I think this is one of the
ones where we have to look at the choices. 1. Negative 1. So can we pick x so this
is negative 1? Well sure, if x is equal to 0,
1 divided by negative 1 is negative 1. So it's not negative 1 because
that can be a value for that. 0. Well, this is interesting. How can we ever make
this equal to 0? The only way we can get this
close to 0 is if the denominator becomes a really
huge number, right? But it'll never be equal to 0. It'll just be a really, really,
really small fraction. This approaches 0 as x
approaches infinity. But this will never equal 0. So the answer is B. All of the other things are
completely possible. You just have to realize, you
should just see choice B, and is like, how could this
ever equal 0? Because the numerator
is never equaling 0. This can only approach 0 if the
denominator gets really, really, really big. It will just become a really
small fraction. But it'll never, ever equal 0. And you could even try. 1 over x minus 1
is equal to 0. You can try to solve it. If you multiply both sides
by x minus 1, you get 1 is equal to 0. It's impossible. Undefined. 15. A bakery opened yesterday
with a daily supply of 40 dozen rolls. Half of the rolls were
sold by noon. 1/2 by noon. And 80% of the remaining rolls
were sold between noon and closing time. 80% remaining, noon
and closing. How many dozen rolls had not
been sold when the bakery closed yesterday? OK, half sold by noon. So 20 sold by noon. And 20 left. Right? And they said 80% of the
remaining rolls were sold between noon and closing time. So we could view it two ways. If you wanted to do it really
fast, you're like, OK, 20% of the remaining rolls
will not be sold. Right? So you could say 20% of the
remaining rolls-- so times 20-- don't get sold, right? If 80% get sold, 20%
don't get sold. And that equals what? We could say 20 times
20 is 400. Two spaces behind the
decimal point. And that makes sense. 20% is 1/5. So 1/5 of 20 is 4. So 4 rolls don't get sold
when it closed. You could do it the
other way around. You could say, OK, how many sold
between, at this time, 80% of 20 is 16 more sell. 16 sell. And then you can say, OK, how
many total were sold? Well, 20 plus 16, 36. And then 40 minus
36 is also 4. It takes a little bit more
time, but it gets you the same answer. Eventually time is what you'll
have to focus on. Once you are confident
that you can get every problem right. What is the combined area in
square inches of the front and back of a rectangular sheet of
paper measuring 8.5 by 11? So it's essentially going to
be 2 times 8.5 times 11. If you just multiplied 8.5 times
11, that would give you the area of one side. So we want the area
of both sides. It's going to be 2 times that. And I want to do this first,
just so I can get rid of this mixed number. So 8.5 times 2. That's 17, times 11, which
is going to be what? 17 times 11 is 170. Because that's 17 times
10, plus 17. So that's 187. That's choice E. Let's do problem 17. 150 is what percent of 30? So 150 is equal to x percent
of 30 times 30. Or another way we could write
that is-- well, let me just write it as a variable. Let's figure it out
as a decimal. And then once you know
a decmial, it's easy to convert that. So 150 is equal to
x of 36 or 36x. This is some number times 36. Divide both sides by 36. You get x is equal to 150/36. Let's see, I think we can divide
the top and the bottom. Definitely we can divide
them by 6. 6 goes into 150 25 times. And it goes into 36 6 times. Right? Oh wait, what am I doing? It's 30. My own handwriting
got me caught up. This is a much easier problem
than what I was doing. They're saying 150 is what
percent of 30, right? So it's x times 30. This is easy. You divide both sides by 30. I mistakenly wrote 36 there. Divide both sides by 30, you
get 5 is equal to x, right? If you wanted to write 5 as a
percentage, you just multiply both sides by 100. So you could say x
is equal to 500%. And that makes sense. 150 is 5 times 30. 100% of 30 is 30. 200% of 30 is 60. And so forth. So 500% of 30 is 150. That took me too long I think. E. Got to make sure your
handwriting is good. Next question. 18. The ratio 2:1/3 is equal to--
Well, 2 divided by 1/3 is equal to 2 times 3/1, which
is equal to 6/1. So 2:1/3 is the same thing
as the ratio of 6:1, which is choice A. Right? 2:1/3 is equal to 6:1. Another way to think about
it is 2 is 6 times 1/3. And 6 is 6 times 1. Same thing. So 18 is A. Next question. 19. Running at the same constant
rate, 6 identical machines can produce a total of 270
bottles per minute. At this rate, how many bottles
could 10 such machines produce in 4 minutes? OK, so how much does each
produce per minute? So 1 machine will produce
270 divided by 6 bottles per minute. Right? That's one machine. I just divided both
sides by 6. 6 machines produce that. So 10 machines would produce 10
times as many per minute. So 10 times this is
2,700 divided by 6 bottles per minute. And if they want to know how
much 10 machines are going to produce in 4 minutes, you just
multiply this times 4. So this is how much they produce
in 1 minute, so the answer's going to be 2,700
times 4 divided by 6. So let me see if I can do
this math fast. So 6 is equal to 2 times 3. If you divide 2,700
by 3, that's 900. And 3 divided by 3 is 1. And then 4 divided by 2 is 2. So 900 times 2 is
equal to 1,800. And that is choice B. And I'm all out of time. See you in the next video.