Oh hello
I'm coming to you from Magoosh and we are going to talk about a math question um this
was actually a question that a student asked they left a comment on a previous uh video that I made
and they wanted to know how to solve this problem so let's just dive in and do it I need a pair
let's use a green one um so the question says if x y and z are three different prime numbers which
of the following can not be a multiple of any of x y and z all right so that's kind of uh read that
first you're like what so sometimes it's useful just go back through and kind of like pull out
the important details so we know we've got prime numbers that we're dealing with
and they want to know which one which of these cannot be a multiple of any of x
y or z so cannot be divided by x y or z so for these types of questions you can
dive in and just plug in numbers for x y and z although there is a crucial insight
which I will get to which will save you a lot of time so if you know your properties of numbers
you can definitely save a lot of time on the test but let's just take a look at how you would solve
this if you didn't know this crucial insight but what you will know at the end of the video
um so as you can see I met x y and z here we can just choose prime numbers for
to plug into our answer choices and find which one of these answers is not a multiple
multiple of x y or z so let's say that this is 5 three and two so uh x plus y five plus three
that equals eight is eight a multiple of one of these numbers yes it's a multiple of two
so we can eliminate it y minus z y three minus two equals one and
is one of multiple these numbers it's a multiple of all these numbers so we can eliminate it
x y plus one so x times y plus one so five times three
it's 15 plus 1 equals 16 is 16 a multiple of one of these numbers
excuse me is one of these numbers a multiple of 16 I've been saying this wrong uh yes it's two
so we can eliminate x y plus one now we have x y z plus one so it'll be five times three which
is fifteens times two thirty plus one is thirty one are any of these numbers a multiple of 31
no all right so this is looking good that's supposed to be a star it's a bad star
um all right one more answer for choice to check x squared plus y squared so 5 squared is 25
plus 9 because 3 times 3 is 9 and that gives us 34
are any of the or any of these numbers a multiple of 34 yes two is so we can eliminate it so
this approach can get you to the right answer I actually cheated a little bit because I
was very smart with the numbers that I chose if you were to do these opposite 2 3 and 5 you'd end
up having these two which means you'd have to plug in more numbers again to see which of these two is
actually not a multiple so that's going to be time consuming on the test and the GMAT rewards you for
finding shortcuts for knowing stuff about numbers and one thing that you should know now walking
away from this video is what a co-prime is and what that means so here's the crucial insight two
consecutive integers are co prime which means that their only common positive factor is one okay so
how does that help us if you were to look at these answer choices and know about co primes and know
about multiples you would know that x y and z if you were to just have the that answer choice you
would definitely have to eliminate it because x y and z is a multiple of x times y times z but
x times y times z plus one is the next consecutive number so in this case x y and z would have been
30 and then the next consecutive number would have been 31. looking at these two numbers you
would know because of coprime that one is the only common factor thus that means that x y and z are
exceeding x y z plus one 31 cannot be a multiple of x y or z so there is the longer way to get to
the answer and then there's always going to be some sort of shortcut they're going to reward
you for doing your due diligence spending a lot of time understanding uh your integer properties
understanding the very uh very fundamental basics of uh integers and number properties so
now when you approach a problem like this you can remember co-prime means that there are only
there's only one common factor one positive common factor between two consecutive numbers and if you
knew this going into this question you wouldn't have to fuss around with plugging in all these
numbers you could just go directly to d and choose it all right uh if you have any questions about
any of this please feel free to put comments down below here they're gonna be down there
somewhere um we'd like to hear from our students like this came from a student so feel free to ask
us questions and we'll make videos about them be excellent to the universe and I'll see you soon