Problem Solving

Can anyone just tell me how to decode the below into algebraic equation


total number of people in Town X is four times greater than the total number of people in Town Y

if Total no pf ppl in Town X = x
the total number of people in Town Y = y

IMO : x = 5y -- 5 is because the stmt says four time greater than..

Am I wrong in formulating the above equation?

gauravgundal wrote:Can anyone just tell me how to decode the below into algebraic equation


total number of people in Town X is four times greater than the total number of people in Town Y

if Total no pf ppl in Town X = x
the total number of people in Town Y = y

IMO : x = 5y -- 5 is because the stmt says four time greater than..

Am I wrong in formulating the above equation?

you must be corrected x=4y
your confusion comes from word "greater" and its association with the ">" sign like in inequality, right? try rewording: "smaller, older, younger" and you should see that "greater" functions here as relationship only.

total number of people in Town X ( a )
is ( equal )
four times greater than ( 4 )
the total number of people in Town Y ( b )

a=4b

I hope that helps..
e.g.
4 times greater than 9...
what is 4x9?
which then the answer is 36...

Thanks for bringing this up, Gaurav! This is a tricky statement, for sure, and because of that you'll see the GMAT feature this kind of setup a lot. I see it most frequently in percentage-based problems, such as:

Square A has a side of 1 and Square B has a side of 2. <Note, this question can be asked in two ways>

What percent greater is the area of Square B than the area of Square A?

Now, the area of square A is 1 and of square B is 4. But be careful - "greater than" in an equation means "in addition to" or "plus". So they're really asking:

Area of Square B = Area of Square A + X% (Area of Square A)

4 = 1 + 3(1)

so the area is 300% GREATER THAN the area of square A.

The area of Square B is what percent of the area of Square A?

Here they ask for the "percent of". 4 is 400% of 1, so the answer here is 400%.

_____________________________________________

It's a subtle distinction but extremely important on GMAT questions. In its base form, "greater than" as an addition term is probably best exemplified in an age problem:

Ben is four years older than Jim

would equate to

B = 4 + J

Note the direct tie between words and mathematical operations. "Is" means "=". "Older than" means "In addition to" or "+".

_______________________________________

So...to answer your question, Gaurav - you're right. I'd take an intermediate step just to clarify, though:

The population of Town X is four times greater than the population of Town Y.

X = 4Y + Y

X = 5Y


Had they said: The population of Town X is four times THAT OF Town Y, then we don't have to include addition, and it's just X = 4Y. But that "greater than" begs for an addition problem.

Thanks Brian for correcting ..