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## Problem solving

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# GMAT: Math 31

## 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.