GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 03 Jul 2020, 22:53

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

Variations on the Gmat i.e varying jointly

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

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
B
Joined: 28 Feb 2015
Posts: 3
Variations on the Gmat i.e varying jointly  [#permalink]

Show Tags

New post 28 May 2020, 16:26
Hi

I am asking for help in explaining a case from the thread "variations-on-the-gmat-all-in-one-topic" BY VeritasPrepKarishma ( i cannot use hyperlinks yet)

"How will you write the joint variation expression in the following cases?

4. x varies directly with y^2 and y varies directly with z.

\(x/y^2=k\)

\(y/z=k\) which implies that \(y^2/z^2=k\)

Joint variation: \(x*z^2/y^2=k\)"

According to this logic, in the case above for instance If both y and z get doubled, x become unchanged, while it should be 16 times bigger. Please help
Intern
Intern
avatar
B
Joined: 14 Oct 2017
Posts: 38
Concentration: Finance, Real Estate
GPA: 3.2
Re: Variations on the Gmat i.e varying jointly  [#permalink]

Show Tags

New post 28 May 2020, 16:50
in the joint vacation. are you sure there is no typo in adding k^2 VeritasKarishma
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 10622
Location: Pune, India
Re: Variations on the Gmat i.e varying jointly  [#permalink]

Show Tags

New post 29 May 2020, 01:22
1
toy9575 wrote:
in the joint vacation. are you sure there is no typo in adding k^2 VeritasKarishma


k represents a constant, any constant. k^2 will be a constant too. Basically, its value does not change when x, y or z change. It is like (1/2) in this relation:
Area of triangle = (1/2) * b*h
If b or h or area change, (1/2) stays as it is.

Now whether the value of that constant is 1/2 or 1/4 or 200, it doesn't matter.

Replace k by "Constant" and you might feel better about it.
_________________
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
User avatar
V
Joined: 16 Oct 2010
Posts: 10622
Location: Pune, India
Re: Variations on the Gmat i.e varying jointly  [#permalink]

Show Tags

New post 29 May 2020, 01:37
1
steppenwolf111 wrote:
Hi

I am asking for help in explaining a case from the thread "variations-on-the-gmat-all-in-one-topic" BY VeritasPrepKarishma ( i cannot use hyperlinks yet)

"How will you write the joint variation expression in the following cases?

4. x varies directly with y^2 and y varies directly with z.

\(x/y^2=k\)

\(y/z=k\) which implies that \(y^2/z^2=k\)

Joint variation: \(x*z^2/y^2=k\)"

According to this logic, in the case above for instance If both y and z get doubled, x become unchanged, while it should be 16 times bigger. Please help


If y is doubled, z is doubled too. So y becomes 2y and y^2 becomes 4y^2. Similarly, z becomes 2z and z^2 becomes 4z^2.
So 4 in numerator gets cancelled with 4 in the denominator and x remains the same.
_________________
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 >
Intern
Intern
avatar
B
Joined: 28 Feb 2015
Posts: 3
Variations on the Gmat i.e varying jointly  [#permalink]

Show Tags

New post 29 May 2020, 03:25
VeritasKarishma wrote:
steppenwolf111 wrote:
Hi

I am asking for help in explaining a case from the thread "variations-on-the-gmat-all-in-one-topic" BY VeritasPrepKarishma ( i cannot use hyperlinks yet)

"How will you write the joint variation expression in the following cases?

4. x varies directly with y^2 and y varies directly with z.

\(x/y^2=k\)

\(y/z=k\) which implies that \(y^2/z^2=k\)

Joint variation: \(x*z^2/y^2=k\)"

According to this logic, in the case above for instance If both y and z get doubled, x become unchanged, while it should be 16 times bigger. Please help


If y is doubled, z is doubled too. So y becomes 2y and y^2 becomes 4y^2. Similarly, z becomes 2z and z^2 becomes 4z^2.
So 4 in numerator gets cancelled with 4 in the denominator and x remains the same.


Unfortunatelly I still don't understand. In case 2. x varies directly with y and y varies inversely with z. The formula is as followed \(x/yz=k\) which means that when y is doubled and z is doubled x is four times bigger. In case 4 "x varies directly with y^2 and y varies directly with z" means that when z is doubled y is doubled and when y is also doubled all in all it means (2*2)^2=16
GMAT Tutor
avatar
P
Joined: 24 Jun 2008
Posts: 2276
Re: Variations on the Gmat i.e varying jointly  [#permalink]

Show Tags

New post 29 May 2020, 03:35
1
steppenwolf111 wrote:
Hi

I am asking for help in explaining a case from the thread "variations-on-the-gmat-all-in-one-topic" BY VeritasPrepKarishma ( i cannot use hyperlinks yet)

"How will you write the joint variation expression in the following cases?

4. x varies directly with y^2 and y varies directly with z.

\(x/y^2=k\)

\(y/z=k\) which implies that \(y^2/z^2=k\)

Joint variation: \(x*z^2/y^2=k\)"

According to this logic, in the case above for instance If both y and z get doubled, x become unchanged, while it should be 16 times bigger. Please help


Most of the above is not mathematically correct.

First, if x varies directly with y^2, then x = ky^2, where k is some constant.

If y varies directly with z, then y = mz, where m is some constant. There is no reason that this constant should be equal to the "k" we used above, so we need to use a new letter (you can't use k again, as someone did in the quoted portion of your post).

If x = ky^2, and y = mz, then by substitution, x = k(mz)^2 = km^2 z^2. Since km^2 is just some new constant number, we can replace it with a single letter, say p, so

x = p * z^2

where p is some constant (equal to km^2).

I haven't followed how you arrived at your direct variation equation, but it is not correct.

Further, it doesn't make much sense to ask what happens "If both y and z get doubled" in this situation. We know y varies directly with z. Their values are related, and can't change independent of each other. Any time z is doubled, y is doubled automatically. So in the sentence "if both y and z get doubled", half of the information is redundant -- the only actual information here is that z doubles. And if z doubles, then from our variation equation x = pz^2, the value of x will quadruple.
_________________
GMAT Tutor in Montreal

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com
GMAT Club Bot
Re: Variations on the Gmat i.e varying jointly   [#permalink] 29 May 2020, 03:35

Variations on the Gmat i.e varying jointly

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





cron

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