GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Oct 2019, 22:54 GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  The variable x is inversely proportional to the square of the variable

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Intern  Joined: 20 May 2014
Posts: 12
The variable x is inversely proportional to the square of the variable  [#permalink]

Show Tags

36 00:00

Difficulty:   55% (hard)

Question Stats: 56% (01:19) correct 44% (01:39) wrong based on 482 sessions

HideShow timer Statistics

The variable x is inversely proportional to the square of the variable y. If y is divided by 3a, then x is multiplied by which of the following?

a. 1/9a

b. 1/9a^2

c. 1/3a

d. 9a

e. 9a^2
Veritas Prep GMAT Instructor G
Joined: 01 Jul 2017
Posts: 79
Location: United States
Concentration: Leadership, Organizational Behavior
Re: The variable x is inversely proportional to the square of the variable  [#permalink]

Show Tags

10
11
This is a classic question type that demonstrates a pattern common to many questions on the GMAT. Several of the approaches in this forum focus blindly on the math, but remember: the GMAT is a critical-thinking test. The tactics I will show you here will be useful for numerous questions, not just this one. For those of you preparing for the GMAT, my solution is going to walk through not just what the answer is, but how to strategically think about it. As a result, I will probably include some steps that I would normally just do in my head if it were the actual test, but I want to be as thorough as possible so you can see each step of the process. Ready? Here is the full "GMAT Jujitsu" for this question:

First, we need to make sure we understand the difference between the phrases "directly proportional" and "inversely proportional." Both of these terms describe relative relationships between two variables (or, potentially, relationships between entire chunks of equations.) For purposes of this discussion we will relate $$x$$ to $$y$$.

If $$x$$ and $$y$$ are "directly proportional", it means that the relationship between $$x$$ and $$y$$ can be represented by the equation $$x = Ky$$, where $$K$$ is a constant called the "coefficient of proportionality" or the "constant of variation." For example, the circumference of a circle is directly proportional to the circle's diameter ($$C = \pi d$$), with $$\pi$$ being the "coefficient of proportionality." Some people oversimplify this rule by saying, "when $$x$$ increases, so does $$y$$." However, that isn't always accurate. It is possible for $$K$$ to be negative, meaning that as $$x$$ increases, $$y$$ would actually decrease. (Picture a line drawn in coordinate space with a negative slope and you can visualize this quickly. Negative linear slopes are still directly proportional.)

If $$x$$ and $$y$$ are "inversely proportional", it means that the relationship between $$x$$ and $$y$$ can be represented by $$xy = K$$, with $$K$$ still serving as the "coefficient of proportionality." Notice that in this case, in order for the product $$xy$$ to always equal the constant, $$K$$, as $$x$$ increased, $$y$$ would have to decrease proportionally, in effect "cancelling out" the change in $$x$$. Another way to write this relationship would be $$x = K(\frac{1}{y})$$. With the equation in this form, you should be able to see why they call it "inversely proportional" instead of "negatively proportional." $$x$$ is proportional to the inverse of $$y$$ (in other words, $$\frac{1}{y}$$), not the negative of $$y$$. This relationship isn't linear, but is actually curved in coordinate space.

Now that we have the basics, let's take a look at this specific question. It states, "The variable $$x$$ is inversely proportional to the square of the variable $$y$$." This means that:

$$x(y^2)=K$$. Alternately, we can also visualize it as $$x = K(\frac{1}{y^2})$$.

The problem then states that we will be manipulating $$y$$ by dividing it by $$3a$$. This will make $$y$$ (and thus $$y^2$$) proportionally smaller. (Of course, we don't know what "$$a$$" is, but this is a good way to visualize what is happening.) Since $$x$$ and $$y^2$$ are inversely proportional, this means that anything we do to $$y^2$$, we must adjust $$x$$ in the proportionately opposite way to cancel out the change and keep $$x(y^2)$$ equal to the constant, $$K$$.

Thus, when we divide $$y$$ by $$3a$$, we change $$y^2$$ to:

$$(\frac{y}{3a})^2=\frac{y^2}{9a^2}$$

The "new" $$y^2$$ is now divided by $$9a^2$$. In order to reverse this change out, this means that $$x$$ would need to be multiplied by something so that $$x(y^2)$$ still equals the constant, $$K$$. For purposes of visualization, I will call that something "?". Here is what it would look like mathematically:

$$(x*?)*(\frac{y^2}{9a^2}) = x(y^2)$$

Solving for "$$?$$" allows us to cancel out $$x$$ and $$y^2$$ from both sides of the equation, and moves the $$9a^2$$ in the denominator over to the other side.

$$?=9a^2$$

Thus, the factor by which we must multiply $$x$$ by to maintain the "inversely proportional" relationship is $$9a^2$$. The answer is "E".
_________________
Aaron J. Pond
Veritas Prep Elite-Level Instructor

Hit "+1 Kudos" if my post helped you understand the GMAT better.
Look me up at https://www.veritasprep.com/gmat/aaron-pond/ if you want to learn more GMAT Jujitsu.
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9701
Location: Pune, India
Re: The variable x is inversely proportional to the square of the variable  [#permalink]

Show Tags

2
4
pmklings wrote:
The variable x is inversely proportional to the square of the variable y. If y is divided by 3a, then x is multiplied by which of the following?

a. 1/9a

b. 1/9a^2

c. 1/3a

d. 9a

e. 9a^2

Here is a post on inverse variation: the-variable-x-is-inversely-proportional-to-the-square-of-the-variable-205761.html

Now read the following:

x * y^2 = k

x' * (y/3a)^2 = k = x * y^2

x' * (y^2)/9a^2 = x * y^2

x' = x * 9a^2

_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
General Discussion
Manager  Joined: 23 Sep 2015
Posts: 81
Concentration: General Management, Finance
GMAT 1: 680 Q46 V38 GMAT 2: 690 Q47 V38 GPA: 3.5
Re: The variable x is inversely proportional to the square of the variable  [#permalink]

Show Tags

Tried this question

not sure how to set it up when the say inversely proportional

initially - did x= 1/y^2

But this yielded the wrong answer,

I then re examined the question and tried y^2/x =1

Which I then got y = SQR(X)

subbing into y/3a I got answer E)

not sure what is the correct way to do this. thanks!
Manager  Joined: 26 Nov 2014
Posts: 84
Re: The variable x is inversely proportional to the square of the variable  [#permalink]

Show Tags

3
Let , $$x = k *\frac{1}{y^2}$$ , Where K is constant.

$$x = k * \frac{1}{(3a)^2}$$ = $$k * \frac{1}{9a^2}$$

=> $$k = (9a^2)x$$

Ans E.
_________________
Consider Kudos for my post, if it is helpful.
TIA
Intern  Joined: 21 Mar 2014
Posts: 22
Re: The variable x is inversely proportional to the square of the variable  [#permalink]

Show Tags

GMATDemiGod wrote:
Tried this question

not sure how to set it up when the say inversely proportional

initially - did x= 1/y^2

But this yielded the wrong answer,

I then re examined the question and tried y^2/x =1

Which I then got y = SQR(X)

subbing into y/3a I got answer E)

not sure what is the correct way to do this. thanks!

hi, u missed a point, y is divided by 3a, i.e y^2 is divided by 9a^2.....
_________________
kinaare paaon phailane lage hian,
nadi se roz mitti kat rahi hai....
Intern  Joined: 21 Mar 2014
Posts: 22
Re: The variable x is inversely proportional to the square of the variable  [#permalink]

Show Tags

GMATDemiGod wrote:
Tried this question

not sure how to set it up when the say inversely proportional

initially - did x= 1/y^2

But this yielded the wrong answer,

I then re examined the question and tried y^2/x =1

Which I then got y = SQR(X)

subbing into y/3a I got answer E)

not sure what is the correct way to do this. thanks!

hi, u missed a point, y is divided by 3a, i.e y^2 is divided by 9a^2.....
_________________
kinaare paaon phailane lage hian,
nadi se roz mitti kat rahi hai....
Manager  S
Joined: 25 Mar 2013
Posts: 226
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5
Re: The variable x is inversely proportional to the square of the variable  [#permalink]

Show Tags

VeritasPrepKarishma wrote:
pmklings wrote:

Here is a post on inverse variation: the-variable-x-is-inversely-proportional-to-the-square-of-the-variable-205761.html

Now read the following:

x * y^2 = k

x' * (y/3a)^2 = k = x * y^2

x' * (y^2)/9a^2 = x * y^2

x' = x * 9a^2

Sorry I don't understand, Can anyone explain. Thanks
The variable x is inversely proportional to the square of the variable y ???
Why x*y^2 ??

I wrote as $$\frac{1}{x}$$ = y^2
_________________
I welcome analysis on my posts and kudo +1 if helpful. It helps me to improve my craft.Thank you
Intern  B
Joined: 05 Aug 2012
Posts: 18
WE: Project Management (Pharmaceuticals and Biotech)
Re: The variable x is inversely proportional to the square of the variable  [#permalink]

Show Tags

VeritasPrepKarishma wrote:

VeritasPrepKarishma Did you man to post another link? This is the problem being discussed.
Manager  G
Joined: 22 May 2015
Posts: 126
Re: The variable x is inversely proportional to the square of the variable  [#permalink]

Show Tags

1
Even i selected B as the answer.

When the question says "x is multiplied by" it seems to ask for the constant that is multiplies X to keep the inverse proportion valid, but it really is asking for by what factor does the new value of X differ from the previous one which is Option E.

xy^2 = K or X = K/y^2

Xy^2/9a = K

=> X(new) = 9a (K/y^2) from above = 9a(X(old)) = X(old) * 9a
i.e X (new) = X(old) * 9a => Option E

I have this problem of not understanding/misinterpreting the question sometimes :'( :'(
_________________
Consistency is the Key
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9701
Location: Pune, India
Re: The variable x is inversely proportional to the square of the variable  [#permalink]

Show Tags

raeann105 wrote:
VeritasPrepKarishma wrote:

VeritasPrepKarishma Did you man to post another link? This is the problem being discussed.

Oops! Yes, it is this one: https://www.veritasprep.com/blog/2013/0 ... inversely/
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9701
Location: Pune, India
Re: The variable x is inversely proportional to the square of the variable  [#permalink]

Show Tags

kanusha wrote:
VeritasPrepKarishma wrote:
pmklings wrote:

Here is a post on inverse variation: the-variable-x-is-inversely-proportional-to-the-square-of-the-variable-205761.html

Now read the following:

x * y^2 = k

x' * (y/3a)^2 = k = x * y^2

x' * (y^2)/9a^2 = x * y^2

x' = x * 9a^2

Sorry I don't understand, Can anyone explain. Thanks
The variable x is inversely proportional to the square of the variable y ???
Why x*y^2 ??

I wrote as $$\frac{1}{x}$$ = y^2

You can write it as

k/x = y^2
which is the same as k = x * y^2

Note that it is not necessary that constant is 1. k could take any value. So when you equate, you need to use k, not 1.
Check out the post for which the link is given above.
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Manager  D
Joined: 17 May 2015
Posts: 246
Re: The variable x is inversely proportional to the square of the variable  [#permalink]

Show Tags

kanusha wrote:
VeritasPrepKarishma wrote:
pmklings wrote:

Here is a post on inverse variation: the-variable-x-is-inversely-proportional-to-the-square-of-the-variable-205761.html

Now read the following:

x * y^2 = k

x' * (y/3a)^2 = k = x * y^2

x' * (y^2)/9a^2 = x * y^2

x' = x * 9a^2

Sorry I don't understand, Can anyone explain. Thanks
The variable x is inversely proportional to the square of the variable y ???
Why x*y^2 ??

I wrote as $$\frac{1}{x}$$ = y^2

Hi ,

The variable x is inversely proportional to the square of the variable y ???

The above statement can be written as follows:

$$x \propto \frac{1}{y^{2}} = \frac{k}{y^{2}}$$ , where $$k$$ is a proportionality constant.
or you can wtite it as
$$x y^{2} = k$$.

Hope this helps.
Senior Manager  G
Joined: 04 Aug 2010
Posts: 477
Schools: Dartmouth College
The variable x is inversely proportional to the square of the variable  [#permalink]

Show Tags

1
pmklings wrote:
The variable x is inversely proportional to the square of the variable y. If y is divided by 3a, then x is multiplied by which of the following?

a. 1/9a

b. 1/9a^2

c. 1/3a

d. 9a

e. 9a^2

x is inversely proportional to the square of y.
$$xy^2 = k$$, where $$k$$ is a constant.

Original values:
Let x=1 and y=6, with the result that $$k = 1*6^2 = 36$$.

New values:
Let a=2.
Dividing y by 3a, we get:
New $$y = \frac{6}{(3*2)} = 1$$.
Substituting y=1 and k=36 into $$xy^2 = k$$, we get:
$$x*1^2 = 36$$
New $$x = 36$$.

Since old x = 1 and new x = 36, the value of x is multiplied by 36.
Thus, the correct answer must yield 36 when a=2.
Only E works:
$$9a^2 = 9*2^2 = 36$$

_________________
GMAT and GRE Tutor
Over 1800 followers
GMATGuruNY@gmail.com
New York, NY
If you find one of my posts helpful, please take a moment to click on the "Kudos" icon.
Available for tutoring in NYC and long-distance.
Non-Human User Joined: 09 Sep 2013
Posts: 13411
Re: The variable x is inversely proportional to the square of the variable  [#permalink]

Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: The variable x is inversely proportional to the square of the variable   [#permalink] 09 Sep 2019, 05:46
Display posts from previous: Sort by

The variable x is inversely proportional to the square of the variable

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  