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GMAT: Math 31

161-162, pg. 174. Created by Sal Khan.

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Video transcript

We're on problem 161. The positive integer n is divisible by 25. If the square root of n is greater than 25, which of the following could be the value of n divided by 25? So what could be a valid value for n divided by 25? So let's see if we can manipulate this a little bit. If we square both sides, we get n, right-- the square of the square root of n is n-- is greater than 625. And then if we divide both sides by 25, we get n/25 is greater than 25. So a valid value for n/25 has to be greater than 25. If we look at all the choices, there's only one value that's greater than 25, and that's E, 26. Problem 162. It looks they want to make sure we know how to deal with fractions. 1 over 1 plus 1 over 2 plus 1/3. Let's just drive through this math. That equals 1 over 1 plus 1 over-- let's see, 2 is the same thing as 6/3 right-- 6/3 plus 1/3 is 7/3. So this is equal to 1 over 1 plus-- 1 over 7/3 is the same thing as 3/7-- so that's equal to 1 over 7/7 plus 3/7, so it's 10/7. Which is equal to 7/10, which is choice B. Let's switch colors. 163. A fruit salad mixture consists of apples, peaches, and grapes in the ratio-- so the so the apples to peaches to grapes-- is equal to 6 to 5 to 2, respectively by weight. If 39 pounds of the mixture is prepared, the mixture includes how many more pounds of apples than grapes? So they want to figure out the apples minus the grapes. OK, so they tell us that the apples plus the peaches plus the grapes is equal to 39 pounds. When you're dealing with a ratio, it's useful to say well each of these is going to be equal to, I guess you'd call it their ratio number times some number, right? Let me explain what I'm saying. Let's just say that apples are equal to 6 times some number x, right? Well if apples are equal to 6 times some number x, then peaches are going to be equal to 5 times that number x, right? Because the ratio of the apples to the peaches is a 6 to 5, right? So if you did 6x over 5x, you'd get 6 to 5. And by the same logic, then the grapes would be 2 times that same number x. And all the ratios would work out. So we can substitute all of these back into that equation. And you get 6x plus 5x plus 2x is equal to 39. 6 plus 5 is 11, plus 2-- Well actually I have a phone call that I was expecting. So let me continue this in the next video.