Stupid question, simplification of an expression

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Thu Feb 17, 2011 6:45 pm

oxfordbound wrote:Hi all,

first post, but really stupid question I can't wrap my head around. The problem below, I understand the entire logic of it, but don't understand why it was solved THIS way.

Question: Rectangluar floors X and Y are equal in area. If floor X is 12 feet by 18 feet and floor Y is 9 feet wide, what is the length of floor Y in feet?

I have seen the solution as:
(assuming l represents length of floor Y)

area of X = 12 * 18
area of Y = 9 * l

Therefore, 12 * 18 = 9l

--Here's where I get confused, normally I would just multiply the 12 by 18 and look for a divisble number by 9. But in a video i saw of this problem, the individual says "lets just take 9 out from both sides" and divides the 18 by the 9 but not the 12....why?????

In my mind, he would have to do 12/9 * 18/9.

(The answer is 24; he got this by multiplying 12 by 2. I would've gotten it by 162/9).

Clarifications please!

Oxforrd Bound

Area of X is 12*18 = 216.
Area of Y is 9*l where l is the length.
Or 9*l = 216.
Or l = 216/9 = 24.

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Source: Beat The GMAT — Problem Solving | Thu Feb 17, 2011 6:45 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Feb 17, 2011 8:14 pm

oxfordbound wrote:
Therefore, 12 * 18 = 9l

--Here's where I get confused, normally I would just multiply the 12 by 18 and look for a divisble number by 9. But in a video i saw of this problem, the individual says "lets just take 9 out from both sides" and divides the 18 by the 9 but not the 12....why?????

We should always look for opportunities to change larger values into smaller values.

Given 12*18 = 9L, rather than multiply 12*18 -- which will result in a large product -- we should divide each side of the equation by 9 so that the numbers become smaller:

12*18/9 = 9L/9.
12*2 = L
24 = L.

Much easier and quicker than if were to multiply 12*18 first and then divide by 9.

Hope this helps!

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Fri Feb 18, 2011 12:22 am

oxfordbound wrote:Hi all,

first post, but really stupid question I can't wrap my head around. The problem below, I understand the entire logic of it, but don't understand why it was solved THIS way.

Question: Rectangluar floors X and Y are equal in area. If floor X is 12 feet by 18 feet and floor Y is 9 feet wide, what is the length of floor Y in feet?

I have seen the solution as:
(assuming l represents length of floor Y)

area of X = 12 * 18
area of Y = 9 * l

Therefore, 12 * 18 = 9l

--Here's where I get confused, normally I would just multiply the 12 by 18 and look for a divisble number by 9. But in a video i saw of this problem, the individual says "lets just take 9 out from both sides" and divides the 18 by the 9 but not the 12....why?????

In my mind, he would have to do 12/9 * 18/9.

(The answer is 24; he got this by multiplying 12 by 2. I would've gotten it by 162/9).

Clarifications please!

Oxforrd Bound

No one has expected hence no one really took notice what your actual doubt was. You meant that if 12*18 is divided by 9, then each component of the product should have been divided by 9, so that 12*18 is divided by 9 = (12/9)*(18/9), which is a wrong perception I am sorry. When an expression like x + y - z is divided by say m, it can be written like x/m + y/m - z/m since the expression is a polynomial whose each term needs to be divided by m in order to divide x + y - z by m; but if the expression is like x y z to be divided by say n, we take x y z as a single term because x y z is a monomial with x y z as its valid factors, and in working (x y z)/n out, we do common factor cancellation in order to reduce the fraction to its lowest where the solution becomes easier to get.

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