hello welcome gmat tuesdays i got you guys a present you wanna see what it is
back solving today we're going to talk about back solving which is a great math strategy um
let's get this out of the way um and so this is one way to approach problems and it helps
you to avoid doing a lot of algebraic um uh algebraic problems in algebraic solving so
the key points to back solving are you need to make sure you have all answers
are numbers you need to make sure oh and this is an alternative to algebra which i just said and
uh start with c c is the best answer to start with because when you have um answer choices
that are listed on the gmat it's going to be from smallest to largest and so if you start with c
and you see then if it doesn't work you know oh if it's too big then you can eliminate c d and e
and start with b or a and if you know if it's too small then you can eliminate c b and a and
then you have two answer choices to work with so it's the most efficient way to approach things
but there is a caveat this is the gmat it's not always straightforward
also don't just be committed to see sometimes it's easier to start somewhere else so for example
if these were your answer choices here you can see one they're all really close together so i
can't really estimate um and two having to like deal with these very tough numbers is going to
be it's gonna be tough it's gonna be hard um but i can see b is a round number it's nice it's 15 000
that's very easy to deal with so in this case i would actually start with b just because you know
all these other answer choices are going to take me a lot more time um so start with c but start
with your easiest answer choice um ultimately okay let's take a look at what back solving really is
and so um with back solving you start with your answer choices plug them into your algebra and see
if it gives you the answer that you're looking for if it's not then you move on and so in
this case we have a question what is the smallest positive integer x for which x cubed plus 5x has a
value more than 80. so what this is saying is what number for x gives us x cubed plus 5 x and that is
greater than 80. and so instead of trying to like solve this algebraic equation it's crazy town why
not just use some of these numbers plug them in and just see what we end up with and so as i said
let's start with c so i'll plug in uh make four cubed plus five times four so four cubed is 64
and then five times four is 20 and that gives me 84. so i know now that 4 is an integer that does
give me a number greater than 80 when i plug it in so i know it's not going to be any of these it
might be c but i want to check and make sure that it's not three maybe three gets me even closer um
to 80 and so that would be the smallest integer to choose so let's just double check um so we'll do
three cubed plus five times 3 so 3 cubed is or 3 squared is 9 times 3 is 27 plus 15 that gives me
42 okay so that's not even close to 80 so then i know b is not the right answer and i will choose c
that's it so um remember back solving if you have numbers in the answer choices and you have
algebra in front of you think about plugging in numbers to arrive at an answer instead of
churning and burning through an algebra equation this can be a really efficient way
to get through some of the questions on the gmat all right uh did you like your present i hope so
um that's it for me today if you have any questions feel free to put them in
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