Learn for the GMAT: Math 16 Video

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Learn for the GMAT: Math 16

Were on problem 87, machine a produces parts twice as fast as machine b does, so machine a produces a 100 parts twice as fast as machine b, well I'm just keep reading. Machine b produces a 100 parts in 40 minutes, so b produces 100 parts in 40 minutes, so that’s equal to what 100 divided by 40 that’s 2.5 parts per minute. And they told us a produces twice as fast, so a is going to be twice that, so a is going to be five part per minute. Five parts per minute, okay, if each machine produces parts at a constant rate, how much, how many parts does machine a produce in six minutes. So five parts per minute so times six minutes, six minutes is equal to what and this cancels out, six times five is 30 parts, choice A. 88, a necklace is made by string and individual beads together in the repeating pattern red bead, green bead, white bead, let's see so red, green, white, and blue and then yellow. And they keep repeating, if the necklace begins with the red bead and ends with a white bead and then end could be equal too. So let's think about it, it starts with the red bead, all right. It starts with the red bead and ends with the white bead. So let's think about this, if it's exactly a multiple of five, right. If n is equal to, if n is equal to exactly the number of beads in this pattern and then it always end with a yellow right. So if n is equal to some multiple of five right, you know, it could be five, it could be 10 or whatever and then you're going to end with a yellow bead, right that makes sense. If you had 10 you just have the pattern twice. If n is equal to five some multiple of five plus one and then you're always going to complete the cycle completely and then you're going to have one more and then you're going to end with the red bead, right. I think you see the pattern here, if n is equal to some multiple of five and then it has two left over or when it's divided five has reminder of two you're going to end with the green bead, right. You're going to multiple of five parts you're going to complete all the video and then you're going to have one or two left and so if n is equal to a multiple of five, plus three and then you're going to end with the white bead. So multiple of five plus three is essentially any, any number that ends with either an eight or a three. Right, because the multiple of five ends with either a five or a zero. So let's see what choices they give us, they give us 16 doesn’t, not a multiple five plus three. 32 none multiple five plus three, 41 is not, 54 is not, 68 that is a multiple of five plus three. 65 plus three, right, 65 is 13 times five that’s equal to 13 times five plus three. So the choice is E. Problem 89, in the x y coordinates system. If a,b, a,b and a plus three b plus k are two points on the line defined by the equation x is equal to 3y minus seven and then k id equal to what? Okay, well I think an easier thing to do an easier thing to do, is to well actually we could just stay. Well, I let's just define y in terms of x. So you get x plus seven is equal to three y, y is equal to one third x plus seven over three. Okay, let's see what we could do? So the slope of this line is one third, right, that’s if you remember from algorithms mx plus b form but this is, yeah, this is how fast the line goes up or down. This one third, right every move to the right in x by one you are moving up on y by one third. So what's the slope if you give me two points what's the slope. What's the change in y over the change in x and I’ll—so I call this y one and this is y two. So or .1 and .2, so you could say change in y is b plus k. The later y point minus the first y point over a plus three minus a right and what does this reduce too. So b plus k minus b, b is cancel out a plus three minus a, a is cancel out. I'm left with k over three and that equals a slope where you know that the slope is equal to one third, k over three is equal to one third. So k is equal to one it is choice D. Problem 90, at the rate of m meters per second. So m meters per second, how many meters does a cyclist travel in x minutes, so x minutes. So remember this is tricky there are said x meters per second right, how meters does a cyclist travel in x minute so let's x in terms of seconds. So x minute is just going to be 60 x seconds, right? It is because you have 60 seconds per minute. So 60 x seconds and distance is equal to rate times time, hopefully that’s a little bit of intuition to you for, now but the rate is equal to m meters per second and he’s traveling for x seconds, so you get m times 60x which is 60mx seconds times meters per second that’s meter. So 60mx meters, 60mx and let's see, how many meters does a cyclist travel in x minutes. X minutes, right, x minutes is 60 x seconds at the rate. How many meters does the recycle travel. Right, rate times time and the rate of m meters per second. I think, they have made a, I think they made a boo-boo here because they have time to 60, 60m. Oh! I see the mistake I made, they say, okay, let me redo it, my bad. They said at the rate of m meters per s seconds, so the cyclist rate is actually m over s meters per second and that’s confusing because they say that s seconds and I thought they said, “Oh, m meters per second but it's a rate of m meters per s seconds. How many meters does the cyclist travel in x minute which we know is 60, which we know is 60 if it x minute is x seconds. So you multiply the rate times the time and you get 60mx, right. Mx over s which is choice e. and it save me that my original answer wasn’t anywhere near at the choices. Problem 21, if Sam were twice as old as he is, he would be 40 years older than Jim, so two times Sam, so time were twice as old as he is, so Sam s is Sam current age. If Sam were twice as old as he is, he would be 40 years older than Jim. So he would be Jim plus 40, if Jim is 10 years younger than Sam how old is Sam. So Sam, Jim is 10 years younger than Sam. So we could say Sam is Jim plus 10, we could have also said Sam minus 10 is equal to Jim same thing. Let's see what we could do here. Let's see if how, how best we can solve this equation they want to know how old Sam is. So let's we want to solve for s so let's do something, let's subtract to this equation from that equation so two s minus s is s, j minus j is zero, 40 minus 10 is 30, so Sam is 30 and we’re done and there's lot of ways you could have done that, you could have substituted, you could have solve for j and substitute in here and then solve, it would take me a little bit more time but we just subtracted this equation from then and you get s is equal to 30 which is choice B. Choice B and I think I'm about out of time, so I’ll continue into the next video. See you soon.

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Were on problem 87, machine a produces parts twice as fast as machine b does, so machine a produces a 100 parts twice as fast as machine b, well I'm just keep reading. Machine b produces a 100 parts in 40 minutes, so b produces 100 parts in 40 minutes, so that’s equal to what 100 divided by 40 that’s 2.5 parts per minute. And they told us a produces twice as fast, so a is going to be twice that, so a is going to be five part per minute.

Five parts per minute, okay, if each machine produces parts at a constant rate, how much, how many parts does machine a produce in six minutes. So five parts per minute so times six minutes, six minutes is equal to what and this cancels out, six times five is 30 parts, choice A.

88, a necklace is made by string and individual beads together in the repeating pattern red bead, green bead, white bead, let's see so red, green, white, and blue and then yellow. And they keep repeating, if the necklace begins with the red bead and ends with a white bead and then end could be equal too.

So let's think about it, it starts with the red bead, all right. It starts with the red bead and ends with the white bead. So let's think about this, if it's exactly a multiple of five, right. If n is equal to, if n is equal to exactly the number of beads in this pattern and then it always end with a yellow right. So if n is equal to some multiple of five right, you know, it could be five, it could be 10 or whatever and then you're going to end with a yellow bead, right that makes sense.

If you had 10 you just have the pattern twice. If n is equal to five some multiple of five plus one and then you're always going to complete the cycle completely and then you're going to have one more and then you're going to end with the red bead, right. I think you see the pattern here, if n is equal to some multiple of five and then it has two left over or when it's divided five has reminder of two you're going to end with the green bead, right. You're going to multiple of five parts you're going to complete all the video and then you're going to have one or two left and so if n is equal to a multiple of five, plus three and then you're going to end with the white bead.

So multiple of five plus three is essentially any, any number that ends with either an eight or a three. Right, because the multiple of five ends with either a five or a zero. So let's see what choices they give us, they give us 16 doesn’t, not a multiple five plus three. 32 none multiple five plus three, 41 is not, 54 is not, 68 that is a multiple of five plus three. 65 plus three, right, 65 is 13 times five that’s equal to 13 times five plus three. So the choice is E.

Problem 89, in the x y coordinates system. If a,b, a,b and a plus three b plus k are two points on the line defined by the equation x is equal to 3y minus seven and then k id equal to what? Okay, well I think an easier thing to do an easier thing to do, is to well actually we could just stay. Well, I let's just define y in terms of x. So you get x plus seven is equal to three y, y is equal to one third x plus seven over three. Okay, let's see what we could do? So the slope of this line is one third, right, that’s if you remember from algorithms mx plus b form but this is, yeah, this is how fast the line goes up or down. This one third, right every move to the right in x by one you are moving up on y by one third. So what's the slope if you give me two points what's the slope. What's the change in y over the change in x and I’ll—so I call this y one and this is y two. So or .1 and .2, so you could say change in y is b plus k.

The later y point minus the first y point over a plus three minus a right and what does this reduce too. So b plus k minus b, b is cancel out a plus three minus a, a is cancel out. I'm left with k over three and that equals a slope where you know that the slope is equal to one third, k over three is equal to one third. So k is equal to one it is choice D.

Problem 90, at the rate of m meters per second. So m meters per second, how many meters does a cyclist travel in x minutes, so x minutes. So remember this is tricky there are said x meters per second right, how meters does a cyclist travel in x minute so let's x in terms of seconds. So x minute is just going to be 60 x seconds, right? It is because you have 60 seconds per minute.

So 60 x seconds and distance is equal to rate times time, hopefully that’s a little bit of intuition to you for, now but the rate is equal to m meters per second and he’s traveling for x seconds, so you get m times 60x which is 60mx seconds times meters per second that’s meter. So 60mx meters, 60mx and let's see, how many meters does a cyclist travel in x minutes. X minutes, right, x minutes is 60 x seconds at the rate.

How many meters does the recycle travel. Right, rate times time and the rate of m meters per second. I think, they have made a, I think they made a boo-boo here because they have time to 60, 60m. Oh! I see the mistake I made, they say, okay, let me redo it, my bad. They said at the rate of m meters per s seconds, so the cyclist rate is actually m over s meters per second and that’s confusing because they say that s seconds and I thought they said, “Oh, m meters per second but it's a rate of m meters per s seconds. How many meters does the cyclist travel in x minute which we know is 60, which we know is 60 if it x minute is x seconds. So you multiply the rate times the time and you get 60mx, right. Mx over s which is choice e. and it save me that my original answer wasn’t anywhere near at the choices.

Problem 21, if Sam were twice as old as he is, he would be 40 years older than Jim, so two times Sam, so time were twice as old as he is, so Sam s is Sam current age. If Sam were twice as old as he is, he would be 40 years older than Jim. So he would be Jim plus 40, if Jim is 10 years younger than Sam how old is Sam. So Sam, Jim is 10 years younger than Sam. So we could say Sam is Jim plus 10, we could have also said Sam minus 10 is equal to Jim same thing. Let's see what we could do here. Let's see if how, how best we can solve this equation they want to know how old Sam is.

So let's we want to solve for s so let's do something, let's subtract to this equation from that equation so two s minus s is s, j minus j is zero, 40 minus 10 is 30, so Sam is 30 and we’re done and there's lot of ways you could have done that, you could have substituted, you could have solve for j and substitute in here and then solve, it would take me a little bit more time but we just subtracted this equation from then and you get s is equal to 30 which is choice B. Choice B and I think I'm about out of time, so I’ll continue into the next video. See you soon.

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