It is currently 11 Dec 2017, 08:25

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If y^k/y^5k = m, what is k?

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

Hide Tags

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42545

Kudos [?]: 135229 [1], given: 12674

If y^k/y^5k = m, what is k? [#permalink]

Show Tags

New post 03 Sep 2017, 06:21
1
This post received
KUDOS
Expert's post
7
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

32% (00:36) correct 68% (00:47) wrong based on 73 sessions

HideShow timer Statistics

Kudos [?]: 135229 [1], given: 12674

Expert Post
Math Expert
User avatar
D
Joined: 02 Aug 2009
Posts: 5336

Kudos [?]: 6088 [0], given: 121

Re: If y^k/y^5k = m, what is k? [#permalink]

Show Tags

New post 03 Sep 2017, 07:33
Bunuel wrote:
If \(\frac{y^k}{y^{5k}} = y^m\), what is k?

(1) m = 4
(2) y = 4




Hi..
All the terms are with base y and powers are k and m...
So m and k can be equated, requiring only value of m to find k..

\(\frac{y^k}{y^{5k}}=y^m........y^{k-5k}=y^m.....-4k=m.....k=-\frac{m}{4}\)

Let's see the statements
1) m=4
We will get the value of k
Sufficient

2) y=4
Nothing about k..
Insufficient

A
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 6088 [0], given: 121

Expert Post
Top Contributor
SVP
SVP
User avatar
G
Joined: 12 Sep 2015
Posts: 1899

Kudos [?]: 2733 [0], given: 362

Location: Canada
Re: If y^k/y^5k = m, what is k? [#permalink]

Show Tags

New post 03 Sep 2017, 08:35
Expert's post
Top Contributor
3
This post was
BOOKMARKED
Bunuel wrote:
If \(\frac{y^k}{y^{5k}} = y^m\), what is k?

(1) m = 4
(2) y = 4


Great question, Bunuel!!

Target question: What is k?

Given: \(\frac{y^k}{y^{5k}} = y^m\)
IMPORTANT: many people will mistakenly apply some exponent laws and conclude that -4k = m. HOWEVER, before we apply these exponent laws, we must be certain that the base does not equal 0, 1 or -1, in which case the exponent laws fly out the window.

Statement 1: m = 4
Let's TEST some values.

There are several values of y, k and m that satisfy statement 1. Here are two:
Case a: y = 1, k = 1 and m = 4. Plugging this into our given equation, we get \(\frac{1^1}{1^5} = 1^4\), which works! In this case, k = 1

Case b: y = 1, k = 2 and m = 4. Plugging this into our given equation, we get \(\frac{1^2}{1^{10}} = 1^4\), which works! In this case, k = 2

Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: y = 4
There are several values of x and y that satisfy statement 2. Here are two:
Case a: y = 4, k = 1 and m = -4. Plugging this into our given equation, we get \(\frac{4^1}{4^5} = 4^{-4}\), which works! In this case, k = 1

Case b: y = 4, k = 2 and m = -8. Plugging this into our given equation, we get \(\frac{4^2}{4^{10}} = 4^{-8}\), which works! In this case, k = 2

Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Since statement 2 tells us that y does NOT equal 0, 1 or -1, we can safely apply some exponent laws:
Given: \(\frac{y^k}{y^{5k}} = y^m\)
Simplify left side to get: \(y^{-4k} = y^m\)
So, -4k = m
Statement 1 tells us that m = 4
Plug this into our equation to get: -4k = 4. which means k must equal -1
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer:
[Reveal] Spoiler:
C


RELATED VIDEO

_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Kudos [?]: 2733 [0], given: 362

Expert Post
Math Expert
User avatar
D
Joined: 02 Aug 2009
Posts: 5336

Kudos [?]: 6088 [0], given: 121

Re: If y^k/y^5k = m, what is k? [#permalink]

Show Tags

New post 03 Sep 2017, 09:05
GMATPrepNow wrote:
Bunuel wrote:
If \(\frac{y^k}{y^{5k}} = y^m\), what is k?

(1) m = 4
(2) y = 4


Great question, Bunuel!!

Target question: What is k?

Given: \(\frac{y^k}{y^{5k}} = y^m\)
IMPORTANT: many people will mistakenly apply some exponent laws and conclude that -4k = m. HOWEVER, before we apply these exponent laws, we must be certain that the base does not equal 0, 1 or -1, in which case the exponent laws fly out the window.

Statement 1: m = 4
Let's TEST some values.

There are several values of y, k and m that satisfy statement 1. Here are two:
Case a: y = 1, k = 1 and m = 4. Plugging this into our given equation, we get \(\frac{1^1}{1^5} = 1^4\), which works! In this case, k = 1

Case b: y = 1, k = 2 and m = 4. Plugging this into our given equation, we get \(\frac{1^2}{1^{10}} = 1^4\), which works! In this case, k = 2

Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT




Hi...

I would differ on the coloured portion.
The Q is telling us that the equality is True. So if you have y as 0, the equation becomes undefined and the very basis of the Q falls flat..
Similarly for other values.
If I say - " if y/y =y, what is y? I CAN NOT take y as 0
What you have conveyed is surely TRUE of the Q asked :- " IS y^k/y^5k=y^m
..
So value of m is sufficient to tell about value of k.
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 6088 [0], given: 121

Expert Post
Top Contributor
SVP
SVP
User avatar
G
Joined: 12 Sep 2015
Posts: 1899

Kudos [?]: 2733 [0], given: 362

Location: Canada
Re: If y^k/y^5k = m, what is k? [#permalink]

Show Tags

New post 03 Sep 2017, 10:03
Expert's post
Top Contributor
chetan2u wrote:
I would differ on the coloured portion.
The Q is telling us that the equality is True. So if you have y as 0, the equation becomes undefined and the very basis of the Q falls flat..
Similarly for other values.
If I say - " if y/y =y, what is y? I CAN NOT take y as 0
What you have conveyed is surely TRUE of the Q asked :- " IS y^k/y^5k=y^m
..
So value of m is sufficient to tell about value of k.


The part about the base not equaling zero is a general comment.
For example, if we know that 0^x = 0^3, we can't conclude that x = 3

I don't agree your comments in blue.
All we know is that the equation must hold true.
My counterexamples for statement 1 satisfy the equation AND yield different answers to the target question. So, statement 1 cannot be sufficient.

Cheers,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Kudos [?]: 2733 [0], given: 362

Manager
Manager
User avatar
S
Joined: 27 Dec 2016
Posts: 194

Kudos [?]: 48 [0], given: 219

Concentration: Social Entrepreneurship, Nonprofit
GPA: 3.65
WE: Sales (Consumer Products)
Premium Member CAT Tests
Re: If y^k/y^5k = m, what is k? [#permalink]

Show Tags

New post 03 Sep 2017, 17:13
GMATPrepNow wrote:
Bunuel wrote:
If \(\frac{y^k}{y^{5k}} = y^m\), what is k?

(1) m = 4
(2) y = 4


Great question, Bunuel!!

Target question: What is k?

Given: \(\frac{y^k}{y^{5k}} = y^m\)
IMPORTANT: many people will mistakenly apply some exponent laws and conclude that -4k = m. HOWEVER, before we apply these exponent laws, we must be certain that the base does not equal 0, 1 or -1, in which case the exponent laws fly out the window.
Statement 1: m = 4
Let's TEST some values.

There are several values of y, k and m that satisfy statement 1. Here are two:
Case a: y = 1, k = 1 and m = 4. Plugging this into our given equation, we get \(\frac{1^1}{1^5} = 1^4\), which works! In this case, k = 1

Case b: y = 1, k = 2 and m = 4. Plugging this into our given equation, we get \(\frac{1^2}{1^{10}} = 1^4\), which works! In this case, k = 2

Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: y = 4
There are several values of x and y that satisfy statement 2. Here are two:
Case a: y = 4, k = 1 and m = -4. Plugging this into our given equation, we get \(\frac{4^1}{4^5} = 4^{-4}\), which works! In this case, k = 1

Case b: y = 4, k = 2 and m = -8. Plugging this into our given equation, we get \(\frac{4^2}{4^{10}} = 4^{-8}\), which works! In this case, k = 2

Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Since statement 2 tells us that y does NOT equal 0, 1 or -1, we can safely apply some exponent laws:
Given: \(\frac{y^k}{y^{5k}} = y^m\)
Simplify left side to get: \(y^{-4k} = y^m\)
So, -4k = m
Statement 1 tells us that m = 4
Plug this into our equation to get: -4k = 4. which means k must equal -1
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: [spoiler=]C[/spoiler

RELATED VIDEO


Wow :o :o :o
Intereseting, GMATPrepNow, I think we forget these exceptions. Thanks for remind us!
_________________

There's an app for that - Steve Jobs.

Kudos [?]: 48 [0], given: 219

Expert Post
Math Expert
User avatar
D
Joined: 02 Aug 2009
Posts: 5336

Kudos [?]: 6088 [0], given: 121

Re: If y^k/y^5k = m, what is k? [#permalink]

Show Tags

New post 03 Sep 2017, 20:59
GMATPrepNow wrote:
chetan2u wrote:
I would differ on the coloured portion.
The Q is telling us that the equality is True. So if you have y as 0, the equation becomes undefined and the very basis of the Q falls flat..
Similarly for other values.
If I say - " if y/y =y, what is y? I CAN NOT take y as 0
What you have conveyed is surely TRUE of the Q asked :- " IS y^k/y^5k=y^m
..
So value of m is sufficient to tell about value of k.


The part about the base not equaling zero is a general comment.
For example, if we know that 0^x = 0^3, we can't conclude that x = 3

I don't agree your comments in blue.
All we know is that the equation must hold true.
My counterexamples for statement 1 satisfy the equation AND yield different answers to the target question. So, statement 1 cannot be sufficient.

Cheers,
Brent



hi...

I do not have any doubt on the logic as I would surely use it when it would have said - IS ... = ...

I am sure I have seen few Qs earlier where the final equation boils down to something like \(y^2=y^k\)..
so if someone tells me that - If \(y^2+3y - (2y+2) = y^k +y-2\), what is k?
the equation boils down to \(y^2=y^k\).. here answer should be k=2 but the logic of y as 0, 1 or -1 will not give k as 2
I may have not come across the y as 0,1 etc in such situations, and it may actually be true and I may be wrong.
so would request if you have come across such use in actuals, it will surely help many who would go through this thread

But if someone tells me - Is \(y^2+3y - (2y+2) = y^k +y-2......y^2=y^k\).. we cannot answer as all those values of 1, -1 or 0 come in.
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 6088 [0], given: 121

Expert Post
Top Contributor
SVP
SVP
User avatar
G
Joined: 12 Sep 2015
Posts: 1899

Kudos [?]: 2733 [0], given: 362

Location: Canada
Re: If y^k/y^5k = m, what is k? [#permalink]

Show Tags

New post 04 Sep 2017, 17:00
Expert's post
Top Contributor
chetan2u wrote:
hi...

I do not have any doubt on the logic as I would surely use it when it would have said - IS ... = ...

I am sure I have seen few Qs earlier where the final equation boils down to something like \(y^2=y^k\)..
so if someone tells me that - If \(y^2+3y - (2y+2) = y^k +y-2\), what is k?
the equation boils down to \(y^2=y^k\).. here answer should be k=2 but the logic of y as 0, 1 or -1 will not give k as 2
I may have not come across the y as 0,1 etc in such situations, and it may actually be true and I may be wrong.
so would request if you have come across such use in actuals, it will surely help many who would go through this thread

But if someone tells me - Is \(y^2+3y - (2y+2) = y^k +y-2......y^2=y^k\).. we cannot answer as all those values of 1, -1 or 0 come in.


I'm not sure I understand what you mean by the "IS" distinction.
The target question asks "What IS the value of k"

ASIDE: If the question were...
What is the value of k?
(1) 1^3 = 1^k
...would statement 1 be sufficient?
_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Kudos [?]: 2733 [0], given: 362

Expert Post
Math Expert
User avatar
D
Joined: 02 Aug 2009
Posts: 5336

Kudos [?]: 6088 [0], given: 121

Re: If y^k/y^5k = m, what is k? [#permalink]

Show Tags

New post 05 Sep 2017, 08:27
GMATPrepNow wrote:
I'm not sure I understand what you mean by the "IS" distinction.
The target question asks "What IS the value of k"

ASIDE: If the question were...
What is the value of k?
(1) 1^3 = 1^k
...would statement 1 be sufficient?


Hi...

i meant by "IS....=.." :- Is \(x^7=x^k\)?
here I would surely check x for 0,1,-1 and other values

But if the Q says it - IF \(x^7+x^2+4x+4=x^k+(x+2)^2\), what is the value of k?
this will boil down to \(x^7=x^k\) and we should get k as 7..

1^3=1^k is a different matter as it is giving base as 1, but if there is a variable as x above, I have not seen a Q claiming it to be insufficient and substituting x as 0,1, and -1 .
as I said earlier, maybe I have not seen a Q, it could be that there are such Q in actuals. If so, it will help.
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 6088 [0], given: 121

Re: If y^k/y^5k = m, what is k?   [#permalink] 05 Sep 2017, 08:27
Display posts from previous: Sort by

If y^k/y^5k = m, what is k?

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


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.