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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 4

20-23, pgs. 154-155. Created by Sal Khan.

## Want to join the conversation?

- #33. ( I don't have text of the book, so correct me if I misunderstood something) Shouldn't it be (7;5) since the vertical axis is depicted downwards? I mean we were taught that numbers on the line increase from the cross in the direction of the axis, so now I'm confused with the question(4 votes)
- In quadrant I, (X,Y) X and Y are both positive. In quadrant II, (-X,Y) X is negative and Y is positive. In quadrant III, (-X,-Y) X and Y are both negative. In quadrant IV, (X,-Y) X is positive and Y is negative. Coordinates of V is in quadrant IV, (X,-Y) V = (7,-5). Y going above 0 is going to be positive and Y going below 0 is going to be negative. I think the arrow is what confuses you, disregard the arrow going in the down direction and answer by which quadrant the coordinate is placed. V is on quadrant IV.(4 votes)

- As I look at the book... The answer is (A) -2, because the point on the number line associated with E is not quite pointing at 2, somewhere between 1 and 2. The point on the number line associated with A is clearly pointing at -2. Look closely :)(4 votes)
- I get what you mean but in the GMAT textbook any edition, What if they gave you a chance to make problem? How would you decipted the axis anyway you like? How would you distribute the data n your own way? Will it be complex? Easy? I'm just saying. I think I'm the only one thinking about it...Well bye.(0 votes)

- If there was more than seventy two numbers (20) or seventy one, and the (for the seventy one) what will it happen if the number to find is in the middle of it?

Show me a example or a tell me a reason.(2 votes) - Time4:30Question 22.

Is there a trick to doing this question that isn't covered in this video. If one has to do that much long division in the exam it would really waste time. At an average of around 2 minutes per question, this would be really tough to squeeze in!

Any help on tricks or methods for this kind of question would be appreciated!(1 vote)- Well, working with numbers a lot tends to help. Two options are clearly off the table because we hopefully know that the repeating pattern resulting when dividing by 3 is every number (1/3 and 2/3). Dividing by 9s is famous for being every number repeated, such as 8/9 is 0.88888...

I was just doing some math dividing by 11, so I found it interesting that it alternated: 2/11 is 0.181818...

3/11 is 0.272727

By logic then, I guessed that the 41/99 was going to be alternating pattern of two digits because a divisor of 99 is actually dividing by 9 x 11. And, in fact it is the numerator repeated, which is kind of cool: 41/99 is 0.41414141

8/99 is 0.080808

So that leaves the last possibility by process of elimination.

One other thing I know from working a lot with numbers is that numbers ending in 7 as a divisor tend to be messy. So that helps confirm that 23/37 is a good choice. Then, if you feel you need to make**sure**, as a last resort you can DIVIDE it.

Indeed it ends up 0.621 621 621

If you ever are given this question with an option divided by 7, choose that one.

58/7 = 8.285714 285714 which is a reliable l-o-n-g repeat

10/7 = 1.428571 428571

39/7 = 5.571428 571428

16/7 = 2.285714 285714 hmmm, like 58

All of them contain the same sequence of numbers, but start at different places in the sequence, depending on what (oh well, you don't need to know WHY, only that there is a long repeat)

It helps to know the divisibility rules also, and practicing long division before a test like this can make sure you don't trip on the mechanics if you cannot find a way to eliminate the alternatives.(2 votes)

- Are gmat questions this easy ?(0 votes)
- Is this test for high school students or younger?(1 vote)
- Which book (edition) is being used here?(1 vote)
- where can I get the pdf material from the questions being resolved in here ? Thanks(1 vote)
- Sal works through problems in the 11th edition of the official GMAC GMAT Review (ISBN Number: 0-9765709-0-4 published in 2005). You should take the practice tests on your own, grade them and then use these videos to understand the problems you didn't get or to review. Have fun!(1 vote)

- Vote for me

and math is hard for thanks for this series(1 vote) - what is the name of the book your using for question I would like to purchase so I can follow along(1 vote)

## Video transcript

We're on problem 20. Of the 5 coordinates associated
with points A, B, C, D and E on the number line
above, which has the greatest absolute value? OK. Let me just draw the number
line that they drew. And they say from 0 to 1. 0, 1, 2. And then they say minus
1, minus 2. And then they say these are
choices A, B, C, D, and E. Of the 5 coordinates associated
with the points A, B, C, D, and E on the number
line above, which has the greatest absolute value? So you can view absolute value
as the distance from zero So the greatest distance from
zero is going to happen in two places. It's going to happen
here at A. It's also going to
happen here at E. Can you have more than
one right answer? Because both of those
are choices. Let's see. Indicate the best of the
answer choices given. I'm looking up the thing. Is it possible to have more
than one right answer? Because this doesn't seem quite
right that I can have two possible answers
for this one. The answer is A. The coordinate A is the
farthest from zero. This has the greatest
absolute value. I disagree with that. It could be choice E as well. The absolute value of the
number x is the distance between x and 0 on
the number line. The coordinate of point A is the
farthest from 0, and thus has the greatest
absolute value. That's false. I mean, that's true, but
E is just as far. I don't know, I think
they made a mistake. I think this could be choices
A or E, because the absolute value of either of those is 2. I think they made a mistake. And they say the choice is A,
which I agree with, but it could just as easily
be choice E. So I don't know. Write a letter to GMAT. I mean, this seems pretty
straightforward. Of the 5 coordinates associated
with choices A, B, C, D, and E on the number line,
which has the greatest absolute value? The absolute value of
this point is 2. The absolute value of
this point is 2. They're equal. Anyway. Next problem. I think it should be A or E. It's surprising that they would
let a question like that get through their screen. Or at least they should
get rid of choice E. If x and y are prime numbers,
which of the following cannot be the sum of x and y? x plus y cannot equal what? So statement 1: 5. Well, I can immediately say
2 plus 3 is equal to 5. So that doesn't work. Cannot equal, so B. 9, I could do 2 plus
7 is equal to 9. This was A. This is B. Let's see what C is. So it's not B. C is 13. So let me think. What could it be? 11 plus 2 is equal to 13,
so it's not choice C. D. 16. The sum. So let me see, 16. 9 and 7. No. 11 and 5. 11 plus 5 is equal to 16. So without even looking at E,
it's probably going to be E. E , 23. Let me see if I can come up with
two prime numbers that add up to 23. 19 and 4. No. Let's see. 2 and 21. No. First of all, we found examples
for all of these, so if you don't want to waste time
on the GMAT, you should already have chosen E and moved
on by this point, but we could just look through a bunch
of prime numbers and think if they can add up to 23,
but I can't think of any right at the moment. And I feel pretty good that E
is the answer, because I was able to find prime numbers that
added up to all of the other four choices. Next question. 22. I'll switch colors just
to ease the monotony. If each of the following
fractions were written as a repeating decimal, which would
have the longest sequence of different digits? Are they going to sit here and
make us-- so let me write all the choices down. Maybe we can do some
cancellation from the get-go. 2/11. B is 1/3. And we already know
that that's just going to be 0.33 repeating. Longest sequence of
different digits. So it's not going to be choice
B because choice B doesn't have different digits. It just keeps being a 3, so it's
not going to be choice B, so we don't have to
worry about that. Choice C. 41/99. Choice D is 2/3. We know that that's 0.666. It just keeps going. So it's not going to be that. It's the same digit that
just keeps repeating. And choice E is 23
divided by 37. So 2 divided by 11 repeats. Let's just try it, though. 11 goes into 2.000 one time. 1 times 11 is 11. You get a 90. 11 goes into 90 eight times. 88. It's 20. I already see the pattern. 11 goes into 20 two times. Sorry, it goes into
20 one time. 1 times 11 is 11. Then you get a 90. It goes into it eight times,
so it's just 0.181818. It's just going to keep
repeating 0.18. So that's 2/11. 41/99. Let me do it in a different
color just so I don't get too messy. 99 goes into 41.0000. So 99 goes into 410
four times. 4 times 99 is what? 396. 4 times 9 is 6. 3. 4 times 9 is 36. Yep, 396. This is equal to 140. 99 goes into 140 one time. 1 times 99 is 99. This becomes 41. Already started repeating,
right? 99 goes into 410. That's just like that. So it's going to be 0.41
repeating over and over again because we got the same
number again. We're going 99 into
41 four times. We're going to get
396 and it's just going to keep happening. Then we're going to get 396. And then we're going
to get 140 again. It's 41, 41. So it's 41 repeating. So if I had to guess, it's
already going to be choice E, without having to do any work
because these just have the same numbers repeating
from the get-go. Choices A and C have the
same two numbers repeating from the get-go. So I'm guessing that this
one has a lot more. So if you just wanted to worry
about time, you could just pick E and move on. But let's do it just to
prove to ourselves. So 37 goes into 23. I don't remember when I took
the GMAT having to do this much decimal division or
decimal multiplication. So 37 goes into 230. I don't know. Does it go into it six times? No, probably five times. 5 times 7 is 35. 5 times 3 is 15, so
it's 18, plus 3. OK. 30. 85. Actually, this would have
gone six times. Let me change that to 6. Let me to it in a
different color. I don't want to make
it too messy. 6 times 7 is 42. 6 times 3 is 18, plus 4 is 22. 80. 37 goes into 80 two times. 2 times 37 is what? 74, right? 60 plus 14. 74. You get a 60. 30 is going to go into 60. So already we haven't even
started repeating and we're already three digits into it. So this is going to have
the longest sequence of different digits. We don't have to keep going. We've answered our question. The choice is definitely E. Next question. They've drawn something there. In the figure above the
coordinates of point V are-- well, this is just kind
of a reading the graph type of problem. I'm just going to draw this 4th
quadrant just so that I can show you how I
think about it. OK, so let me just count: one,
two, three, four, five; one, two, three, four, five. They tell us that each of those
slashes are 1, because they do it in a couple
of places. They go one, two, three, four,
five, and then they say this is negative 5. So that's information that
you actually need. You have to know that each
of those slashes are definitely 1. But then on this, they
go one, two, three, four, five, six, seven. So they go one, two, three,
four, five, six, seven, so this is point 7. And you have to just count
it on your paper. So this is one, two,
three, four, five. And this is point one, two,
three, four, five. This is minus 5. And this is where V is. So they're just testing
to see if you know how to graph a point. So this is x is 7. And y is minus 5. So it's 7 minus 5. And actually, that's
interesting. You don't even have to count the
points, because you say, you know what? This is in the 4th quadrant. x is positive. y is negative. And if you look at all the
choices, there's only one choice where x is positive
and y is negative, and that's choice E. So you really didn't even have
to count it, although I think this wouldn't have taken much
time to count it, so that's not like a huge shortcut. Anyway, see you in
the next video.