SAT Prep: Test 2 Section 3 Part 4 Video

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SAT Prep: Test 2 Section 3 Part 4

We’re now on Problem #15 on page 463. Let’s see. They have a chart and it says city and noon temperature in Fahrenheit. So, I’ll just write temperature. And City A is 50°, B is 33°, C is 27°, D is t°, E is 68°, F is 44° and G is 40°. Now, the question says, the table above shows the noon temperature for seven cities. If the median noon temperature is 40%, then the noon temperature for city D could be any of the following except. So, the median means what? It means the middle number. It means the middle number. It means, if we were to rearrange all of these numbers from smallest to highest, the 40 would be the middle. So, let’s rearrange all the numbers except for t from smallest to highest because we don’t what t is. So, let’s see. The smallest is 27. Then we go to 33. We have 40. Then we have 44. Then we have 50 and then we have 68. And they’re saying the median is 40. So, in order for the median to be 40, this needs to be the middle number, that means there need to be just as many numbers smaller than 40 as there are numbers larger than 40. Jus the way I drew it right now, it doesn’t look like the median because there are only two numbers less than it and there are three numbers greater than it. So, I think you see where this is going. t has to be some place here. t has to be some place less than 40° in order for 40 to be the median number. So, let’s see. And actually, t could be less than or equal to 40 because even if we had another 40 here, then 40 would still be the median because if you put all the numbers in order. You have seven numbers. The fourth highest number would still be 40. So, t has to be less than or equal to 40. So, if we look at the choices, A is 29. Well, that satisfies it. B is 35; that satisfies it. C is 39; satisfies it. D is 40, and then if we look at E. E is 42. So, that does not satisfy it. So, our choice is E. Problem #14. So, let me see if I can draw this. A line on the top and then I have a line that goes straight down like that. And then this thing goes like this, something like this. I think it goes something like this. I’ll draw this right. I'm trying to see even. Close enough I think to what they have on drawing. Let me fill in all the information. So it says, these are right angles, this is 6, the length of this is 6, length of this is 6, and then it tells us that these are 30°. And it says, what is the perimeter of the figure above? So, in order to figure out the perimeter, we know this side. We know this side. We know this side. We need to figure out these two sides. So, once we know those and then we’re set. And you could do some fancy things here if you wanted to go in the wrong direction but you’d get the right answer. You could make 30-60-90 triangle here and here and figure out this side and then figure out the hypotenuse, etcetera. But the real trick of this is just kind of seeing the negative image here. Trying to see kind of what hasn’t been drawn. And I’ll show you what I mean. Let’s just draw a little line here. And I think now you’ll start to see what I am doing. If there was a line here, what’s this angle? Well, this whole thing is a right angle. It’s 90°, so this angle would be 60 and so with this angle. This angle would also 60° and so with this angle because they have to add up to 180 and if two of them were 60, the third one is going to be 60. So, what do we know about this triangle right here? Well, it’s an equilateral triangle. All the sides are the same because all the angles are the same. Well, we know one of the sides. We know this side we made up because it’s going to be the same length as this side up here. So, this is going to be 6. Well, if that side is 6, then all of the sides of this equilateral triangle we made are going to have to be 6. And then we’re done. Now, we just have to add up all the sides. So, it’s 6 + 6 + 6 + 6 + 6, we ignore this one. This isn’t part of the perimeter. The perimeters are the purple side. So, it’s 5 × 6 = 30. Choice D. Problem #15. m is the greatest prime factor of 38. n is the greatest prime factor of a 100. What is the value of m + n? Well, without knowing the trick here and the trick hasn’t just jump into my head. Let’s just try to factor them, do the prime factorization. We want to get the greatest prime factor and this one is actually pretty easy because you have 2 and then it’s 2 times what? 2 × 19, we’re done. That was pretty easy. 2 × 19, 19 is the greatest prime factor of 38. 100 might take us a little bit more time because it’s 2 × 50. 100 is 2 × 50. 50 is 2 × 25. 25 is 5 × 5. Actually, that didn’t take us much time either. I thought there might be a trick here but this is just a straight prime factorization problem. So, the greatest prime factor of a 100 is 5. We add them together, 19 + 5 = 24. And that is choice C. Okay. Let’s see if I have time to fit in Problem #16. Otherwise, I’ll do it in the next video. Line l has a positive slope. Let me draw a coordinate axis. So, that’s my y-axis, that’s my x-axis, and I'm going to draw another line in another line in a different color. It has a positive slope, so that means it’s going to go from the bottom left to the top right. And it goes through the point (0, 0). So, this is line l. Line l looks something like that. So, this is line l. If line K is perpendicular to line l, which of the following must be true? So, it intersects at a perpendicular angle. So, line K is going to look something like this. It’s perpendicular. And I have a feeling that this is going to go into something that you just need to know, if you know the slope of something, let’s say line l’s slope. Let’s say that this is y = mx + b but we know it goes to the intercept, so it’s actually just mx. Then, we know that line K right here is going to have the negative inverse of the slope of line l. So, it’s going to be -1/mx and then plus b. This could intersect right here. We don’t know because they didn’t tell us, it goes through the origin. So, we don’t know what b is, b could be zero. Well, the bottom line is, the only we do know is that if this number is positive, this number is going to be negative. And they told us that this is positive. And let’s see. Choice A, line K passes through (0, 0). It’s C, choice C, line K has a negative slope. And that’s all we know. See you in the next video.

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We’re now on Problem #15 on page 463. Let’s see. They have a chart and it says city and noon temperature in Fahrenheit. So, I’ll just write temperature. And City A is 50°, B is 33°, C is 27°, D is t°, E is 68°, F is 44° and G is 40°. Now, the question says, the table above shows the noon temperature for seven cities. If the median noon temperature is 40%, then the noon temperature for city D could be any of the following except.

So, the median means what? It means the middle number. It means the middle number. It means, if we were to rearrange all of these numbers from smallest to highest, the 40 would be the middle. So, let’s rearrange all the numbers except for t from smallest to highest because we don’t what t is.

So, let’s see. The smallest is 27. Then we go to 33. We have 40. Then we have 44. Then we have 50 and then we have 68. And they’re saying the median is 40. So, in order for the median to be 40, this needs to be the middle number, that means there need to be just as many numbers smaller than 40 as there are numbers larger than 40. Jus the way I drew it right now, it doesn’t look like the median because there are only two numbers less than it and there are three numbers greater than it.

So, I think you see where this is going. t has to be some place here. t has to be some place less than 40° in order for 40 to be the median number. So, let’s see. And actually, t could be less than or equal to 40 because even if we had another 40 here, then 40 would still be the median because if you put all the numbers in order. You have seven numbers. The fourth highest number would still be 40. So, t has to be less than or equal to 40.

So, if we look at the choices, A is 29. Well, that satisfies it. B is 35; that satisfies it. C is 39; satisfies it. D is 40, and then if we look at E. E is 42. So, that does not satisfy it. So, our choice is E.

Problem #14. So, let me see if I can draw this. A line on the top and then I have a line that goes straight down like that. And then this thing goes like this, something like this. I think it goes something like this. I’ll draw this right. I'm trying to see even. Close enough I think to what they have on drawing. Let me fill in all the information. So it says, these are right angles, this is 6, the length of this is 6, length of this is 6, and then it tells us that these are 30°. And it says, what is the perimeter of the figure above?

So, in order to figure out the perimeter, we know this side. We know this side. We know this side. We need to figure out these two sides. So, once we know those and then we’re set. And you could do some fancy things here if you wanted to go in the wrong direction but you’d get the right answer. You could make 30-60-90 triangle here and here and figure out this side and then figure out the hypotenuse, etcetera.

But the real trick of this is just kind of seeing the negative image here. Trying to see kind of what hasn’t been drawn. And I’ll show you what I mean. Let’s just draw a little line here. And I think now you’ll start to see what I am doing. If there was a line here, what’s this angle? Well, this whole thing is a right angle. It’s 90°, so this angle would be 60 and so with this angle. This angle would also 60° and so with this angle because they have to add up to 180 and if two of them were 60, the third one is going to be 60. So, what do we know about this triangle right here? Well, it’s an equilateral triangle. All the sides are the same because all the angles are the same.

Well, we know one of the sides. We know this side we made up because it’s going to be the same length as this side up here. So, this is going to be 6. Well, if that side is 6, then all of the sides of this equilateral triangle we made are going to have to be 6. And then we’re done. Now, we just have to add up all the sides. So, it’s 6 + 6 + 6 + 6 + 6, we ignore this one. This isn’t part of the perimeter. The perimeters are the purple side. So, it’s 5 × 6 = 30. Choice D.

Problem #15. m is the greatest prime factor of 38. n is the greatest prime factor of a 100. What is the value of m + n? Well, without knowing the trick here and the trick hasn’t just jump into my head. Let’s just try to factor them, do the prime factorization. We want to get the greatest prime factor and this one is actually pretty easy because you have 2 and then it’s 2 times what? 2 × 19, we’re done. That was pretty easy. 2 × 19, 19 is the greatest prime factor of 38. 100 might take us a little bit more time because it’s 2 × 50. 100 is 2 × 50. 50 is 2 × 25. 25 is 5 × 5. Actually, that didn’t take us much time either. I thought there might be a trick here but this is just a straight prime factorization problem. So, the greatest prime factor of a 100 is 5. We add them together, 19 + 5 = 24. And that is choice C.

Okay. Let’s see if I have time to fit in Problem #16. Otherwise, I’ll do it in the next video. Line l has a positive slope. Let me draw a coordinate axis. So, that’s my y-axis, that’s my x-axis, and I'm going to draw another line in another line in a different color. It has a positive slope, so that means it’s going to go from the bottom left to the top right. And it goes through the point (0, 0). So, this is line l. Line l looks something like that. So, this is line l. If line K is perpendicular to line l, which of the following must be true?

So, it intersects at a perpendicular angle. So, line K is going to look something like this. It’s perpendicular. And I have a feeling that this is going to go into something that you just need to know, if you know the slope of something, let’s say line l’s slope. Let’s say that this is y = mx + b but we know it goes to the intercept, so it’s actually just mx.

Then, we know that line K right here is going to have the negative inverse of the slope of line l. So, it’s going to be -1/mx and then plus b. This could intersect right here. We don’t know because they didn’t tell us, it goes through the origin. So, we don’t know what b is, b could be zero.

Well, the bottom line is, the only we do know is that if this number is positive, this number is going to be negative. And they told us that this is positive. And let’s see. Choice A, line K passes through (0, 0). It’s C, choice C, line K has a negative slope. And that’s all we know. See you in the next video.

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