Find all School-related info fast with the new School-Specific MBA Forum

It is currently 19 Sep 2014, 00:20

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Alan’s regular hourly wage is 1.5 times Barney’s regular

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
2 KUDOS received
Intern
Intern
avatar
Joined: 31 Oct 2010
Posts: 33
Followers: 0

Kudos [?]: 11 [2] , given: 25

Alan’s regular hourly wage is 1.5 times Barney’s regular [#permalink] New post 01 Dec 2010, 05:34
2
This post received
KUDOS
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

31% (02:25) correct 69% (01:28) wrong based on 205 sessions
Alan’s regular hourly wage is 1.5 times Barney’s regular hourly wage, but Barney gets paid at twice his regular wage for any hours he works on Saturday. Both men work an integer number of hours on any given day. If Alan and Barney each worked for the same total non-zero number of hours last week, and earned the same total in wages, which of the following must be true?

I. Alan worked fewer hours Monday through Friday than did Barney.
II. Barney worked at least one hour on Saturday.
III. Barney made more money on Saturday than did Alan.

A.I only
B. II only
C. I and II only
D. I and III only
E. II and III only

I would just like to see the equation written out, so I can visualize the problem. I am having trouble conceptualizing the problem. I understand the a=1.5b but I would like to see how the second part is written when they have equal hours and equal pay. Thanks,
[Reveal] Spoiler: OA
Expert Post
3 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23471
Followers: 3500

Kudos [?]: 26400 [3] , given: 2710

Re: MGMAT CAT1 Question 11 [#permalink] New post 01 Dec 2010, 07:26
3
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
mmcooley33 wrote:
Alan’s regular hourly wage is 1.5 times Barney’s regular hourly wage, but Barney gets paid at twice his regular wage for any hours he works on Saturday. Both men work an integer number of hours on any given day. If Alan and Barney each worked for the same total non-zero number of hours last week, and earned the same total in wages, which of the following must be true?

I. Alan worked fewer hours Monday through Friday than did Barney.
II. Barney worked at least one hour on Saturday.
III. Barney made more money on Saturday than did Alan.

I only

II only

I and II only

I and III only

II and III only

I would just like to see the equation written out, so I can visualize the problem. I am having trouble conceptualizing the problem. I understand the a=1.5b but I would like to see how the second part is written when they have equal hours and equal pay. Thanks,


Although I don't think that algebraic way is the best for this problem, here you go:

Let Barney's regular hourly wage be x, then his Saturday wage will be 2x and Alan's hourly wage will be 1.5x;

Let the # of hours Barney worked Monday through Friday be m and on Saturday be n and the # of hours Alan worked Monday through Friday be p and on Saturday be q;

Given: xm+2xn=1.5x(p+q) and m+n=p+q.

xm+2xn=1.5x(p+q) --> m+2n=1.5(m+n) --> m=n --> Barney worked the equal # of hours Monday-Friday and on Saturday.

The above directly tells us that II must be true (as Barney worked total non-zero # of hours and he worked an integer # of hours on any given day then he must have been worked at least one hour on Saturday.)

As for I: Alan may have worked ALL his hours Monday through Friday so in this case this statement is not true (p=total>m). Alan also may have worked all his hours on Saturday. Or algebraically: there are any distribution possible between p and q, p=0 and q=total or p=total and q=0 or any other;

The above means that III is also not always true: if Alan worked all his hours on Saturday then he made all his money on Saturday thus he made more money on Saturday than Barney did.

Answer: B (II only).

But the above can also be done with much less algebra:

As Alan and Barney worked the same # of hours and earned the same amount of money, then their hourly average wages must have been the same: (average wage)=(total amount earned)/(# of hours worked). Now, Alan has constant hourly wage which is 1.5*x and Barney's average (\frac{xm+2xn}{m+n}) to be equal to this he must have been worked the equal # of hours Monday-Friday and on Saturday, so m=n.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

SVP
SVP
User avatar
Joined: 05 Jul 2006
Posts: 1542
Followers: 5

Kudos [?]: 76 [0], given: 39

Re: MGMAT CAT1 Question 11 [#permalink] New post 25 May 2013, 04:10
Bunuel wrote:
mmcooley33 wrote:
Alan’s regular hourly wage is 1.5 times Barney’s regular hourly wage, but Barney gets paid at twice his regular wage for any hours he works on Saturday. Both men work an integer number of hours on any given day. If Alan and Barney each worked for the same total non-zero number of hours last week, and earned the same total in wages, which of the following must be true?

I. Alan worked fewer hours Monday through Friday than did Barney.
II. Barney worked at least one hour on Saturday.
III. Barney made more money on Saturday than did Alan.

I only

II only

I and II only

I and III only

II and III only

I would just like to see the equation written out, so I can visualize the problem. I am having trouble conceptualizing the problem. I understand the a=1.5b but I would like to see how the second part is written when they have equal hours and equal pay. Thanks,


Although I don't think that algebraic way is the best for this problem, here you go:

Let Barney's regular hourly wage be x, then his Saturday wage will be 2x and Alan's hourly wage will be 1.5x;

Let the # of hours Barney worked Monday through Friday be m and on Saturday be n and the # of hours Alan worked Monday through Friday be p and on Saturday be q;

Given: xm+2xn=1.5x(p+q) and m+n=p+q.

xm+2xn=1.5x(p+q) --> m+2n=1.5(m+n) --> m=n --> Barney worked the equal # of hours Monday-Friday and on Saturday.

The above directly tells us that II must be true (as Barney worked total non-zero # of hours and he worked an integer # of hours on any given day then he must have been worked at least one hour on Saturday.)

As for I: Alan may have worked ALL his hours Monday through Friday so in this case this statement is not true (p=total>m). Alan also may have worked all his hours on Saturday. Or algebraically: there are any distribution possible between p and q, p=0 and q=total or p=total and q=0 or any other;

The above means that III is also not always true: if Alan worked all his hours on Saturday then he made all his money on Saturday thus he made more money on Saturday than Barney did.

Answer: B (II only).

But the above can also be done with much less algebra:

As Alan and Barney worked the same # of hours and earned the same amount of money, then their hourly average wages must have been the same: (average wage)=(total amount earned)/(# of hours worked). Now, Alan has constant hourly wage which is 1.5*x and Barney's average (\frac{xm+2xn}{m+n}) to be equal to this he must have been worked the equal # of hours Monday-Friday and on Saturday, so m=n.

Hope it's clear.


Bunuel , u humble anyone's approach to logical and or mathematical problems. respect :)
SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1666
Location: United States
Concentration: Finance
GMAT 1: 710 Q48 V39
WE: Corporate Finance (Investment Banking)
Followers: 12

Kudos [?]: 164 [0], given: 274

GMAT ToolKit User
Re: MGMAT CAT1 Question 11 [#permalink] New post 14 Jan 2014, 10:24
Bunuel wrote:
mmcooley33 wrote:
Alan’s regular hourly wage is 1.5 times Barney’s regular hourly wage, but Barney gets paid at twice his regular wage for any hours he works on Saturday. Both men work an integer number of hours on any given day. If Alan and Barney each worked for the same total non-zero number of hours last week, and earned the same total in wages, which of the following must be true?

I. Alan worked fewer hours Monday through Friday than did Barney.
II. Barney worked at least one hour on Saturday.
III. Barney made more money on Saturday than did Alan.

I only

II only

I and II only

I and III only

II and III only

I would just like to see the equation written out, so I can visualize the problem. I am having trouble conceptualizing the problem. I understand the a=1.5b but I would like to see how the second part is written when they have equal hours and equal pay. Thanks,


Although I don't think that algebraic way is the best for this problem, here you go:

Let Barney's regular hourly wage be x, then his Saturday wage will be 2x and Alan's hourly wage will be 1.5x;

Let the # of hours Barney worked Monday through Friday be m and on Saturday be n and the # of hours Alan worked Monday through Friday be p and on Saturday be q;

Given: xm+2xn=1.5x(p+q) and m+n=p+q.

xm+2xn=1.5x(p+q) --> m+2n=1.5(m+n) --> m=n --> Barney worked the equal # of hours Monday-Friday and on Saturday.

The above directly tells us that II must be true (as Barney worked total non-zero # of hours and he worked an integer # of hours on any given day then he must have been worked at least one hour on Saturday.)

As for I: Alan may have worked ALL his hours Monday through Friday so in this case this statement is not true (p=total>m). Alan also may have worked all his hours on Saturday. Or algebraically: there are any distribution possible between p and q, p=0 and q=total or p=total and q=0 or any other;

The above means that III is also not always true: if Alan worked all his hours on Saturday then he made all his money on Saturday thus he made more money on Saturday than Barney did.

Answer: B (II only).

But the above can also be done with much less algebra:

As Alan and Barney worked the same # of hours and earned the same amount of money, then their hourly average wages must have been the same: (average wage)=(total amount earned)/(# of hours worked). Now, Alan has constant hourly wage which is 1.5*x and Barney's average (\frac{xm+2xn}{m+n}) to be equal to this he must have been worked the equal # of hours Monday-Friday and on Saturday, so m=n.

Hope it's clear.


Hi Bunuel,

I believe the best approach is a mixture of conceptual and number picking, but I'm having a hard time getting to make work fast in under 2 minutes. Would you please show us how you deal with this problem in such way?

Much appreciated!

Cheers
J :)
1 KUDOS received
SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1666
Location: United States
Concentration: Finance
GMAT 1: 710 Q48 V39
WE: Corporate Finance (Investment Banking)
Followers: 12

Kudos [?]: 164 [1] , given: 274

GMAT ToolKit User
Re: Alan’s regular hourly wage is 1.5 times Barney’s regular [#permalink] New post 04 Feb 2014, 08:07
1
This post received
KUDOS
Statement I. Alan worked fewer hours Monday through Friday than did Barney, well let's see. Maybe Alan did work fewer hours and then worked those missing hours on Saturday, or maybe not, we really can't tell the split of Alan's hours.

Statement II, what we do know is that Barney must have worked at least 1 hour on Saturday, how else then could he compensate for a lower salary if they work the same number of total hours?

Statement III what if Barney worked fewer hours during the week and then worked on Saturdays, then Alan could compensate by working more hours during the week, and maybe just working a smaller number of hours on Saturday (>=1). In that case we leave the possibility open of Barney earning a salary that is lower than Barney's but still making more money than Barney on Saturday. This can be possible because of the higher amount of hours worked by Alan.

Hence B is the correct choice

Is this clear enough?
Cheers
J
Senior Manager
Senior Manager
avatar
Joined: 15 Aug 2013
Posts: 282
Followers: 0

Kudos [?]: 11 [0], given: 23

Re: MGMAT CAT1 Question 11 [#permalink] New post 10 May 2014, 11:04
Bunuel wrote:
mmcooley33 wrote:
Alan’s regular hourly wage is 1.5 times Barney’s regular hourly wage, but Barney gets paid at twice his regular wage for any hours he works on Saturday. Both men work an integer number of hours on any given day. If Alan and Barney each worked for the same total non-zero number of hours last week, and earned the same total in wages, which of the following must be true?

I. Alan worked fewer hours Monday through Friday than did Barney.
II. Barney worked at least one hour on Saturday.
III. Barney made more money on Saturday than did Alan.

I only

II only

I and II only

I and III only

II and III only

I would just like to see the equation written out, so I can visualize the problem. I am having trouble conceptualizing the problem. I understand the a=1.5b but I would like to see how the second part is written when they have equal hours and equal pay. Thanks,


Although I don't think that algebraic way is the best for this problem, here you go:

Let Barney's regular hourly wage be x, then his Saturday wage will be 2x and Alan's hourly wage will be 1.5x;

Let the # of hours Barney worked Monday through Friday be m and on Saturday be n and the # of hours Alan worked Monday through Friday be p and on Saturday be q;

Given: xm+2xn=1.5x(p+q) and m+n=p+q.

xm+2xn=1.5x(p+q) --> m+2n=1.5(m+n) --> m=n --> Barney worked the equal # of hours Monday-Friday and on Saturday.

The above directly tells us that II must be true (as Barney worked total non-zero # of hours and he worked an integer # of hours on any given day then he must have been worked at least one hour on Saturday.)

As for I: Alan may have worked ALL his hours Monday through Friday so in this case this statement is not true (p=total>m). Alan also may have worked all his hours on Saturday. Or algebraically: there are any distribution possible between p and q, p=0 and q=total or p=total and q=0 or any other;

The above means that III is also not always true: if Alan worked all his hours on Saturday then he made all his money on Saturday thus he made more money on Saturday than Barney did.

Answer: B (II only).

But the above can also be done with much less algebra:

As Alan and Barney worked the same # of hours and earned the same amount of money, then their hourly average wages must have been the same: (average wage)=(total amount earned)/(# of hours worked). Now, Alan has constant hourly wage which is 1.5*x and Barney's average (\frac{xm+2xn}{m+n}) to be equal to this he must have been worked the equal # of hours Monday-Friday and on Saturday, so m=n.

Hope it's clear.


Hi Bunuel,

I'm having a hard time figuring out why statement III is wrong when NOT done algebraically.

I approached this problem conceptually: II is correct is rather easy to see. When it comes to III, the statement says that Barney made more money on Saturday than Alan. Correct?

Doesn't that HAVE to be true? What I mean by that is -- if Barney worked AT LEAST 1 hour on saturday, his salary is 2x vs. Alan's which is 1.5x, so doesn't that inherently make III true?

I would go even further and say that Barney would need to make a ton more money on Saturday to compensate for his lack of pay during the week.

What am I missing here?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23471
Followers: 3500

Kudos [?]: 26400 [0], given: 2710

Re: MGMAT CAT1 Question 11 [#permalink] New post 11 May 2014, 04:27
Expert's post
russ9 wrote:
Bunuel wrote:
mmcooley33 wrote:
Alan’s regular hourly wage is 1.5 times Barney’s regular hourly wage, but Barney gets paid at twice his regular wage for any hours he works on Saturday. Both men work an integer number of hours on any given day. If Alan and Barney each worked for the same total non-zero number of hours last week, and earned the same total in wages, which of the following must be true?

I. Alan worked fewer hours Monday through Friday than did Barney.
II. Barney worked at least one hour on Saturday.
III. Barney made more money on Saturday than did Alan.

I only

II only

I and II only

I and III only

II and III only

I would just like to see the equation written out, so I can visualize the problem. I am having trouble conceptualizing the problem. I understand the a=1.5b but I would like to see how the second part is written when they have equal hours and equal pay. Thanks,


Although I don't think that algebraic way is the best for this problem, here you go:

Let Barney's regular hourly wage be x, then his Saturday wage will be 2x and Alan's hourly wage will be 1.5x;

Let the # of hours Barney worked Monday through Friday be m and on Saturday be n and the # of hours Alan worked Monday through Friday be p and on Saturday be q;

Given: xm+2xn=1.5x(p+q) and m+n=p+q.

xm+2xn=1.5x(p+q) --> m+2n=1.5(m+n) --> m=n --> Barney worked the equal # of hours Monday-Friday and on Saturday.

The above directly tells us that II must be true (as Barney worked total non-zero # of hours and he worked an integer # of hours on any given day then he must have been worked at least one hour on Saturday.)

As for I: Alan may have worked ALL his hours Monday through Friday so in this case this statement is not true (p=total>m). Alan also may have worked all his hours on Saturday. Or algebraically: there are any distribution possible between p and q, p=0 and q=total or p=total and q=0 or any other;

The above means that III is also not always true: if Alan worked all his hours on Saturday then he made all his money on Saturday thus he made more money on Saturday than Barney did.

Answer: B (II only).

But the above can also be done with much less algebra:

As Alan and Barney worked the same # of hours and earned the same amount of money, then their hourly average wages must have been the same: (average wage)=(total amount earned)/(# of hours worked). Now, Alan has constant hourly wage which is 1.5*x and Barney's average (\frac{xm+2xn}{m+n}) to be equal to this he must have been worked the equal # of hours Monday-Friday and on Saturday, so m=n.

Hope it's clear.


Hi Bunuel,

I'm having a hard time figuring out why statement III is wrong when NOT done algebraically.

I approached this problem conceptually: II is correct is rather easy to see. When it comes to III, the statement says that Barney made more money on Saturday than Alan. Correct?

Doesn't that HAVE to be true? What I mean by that is -- if Barney worked AT LEAST 1 hour on saturday, his salary is 2x vs. Alan's which is 1.5x, so doesn't that inherently make III true?

I would go even further and say that Barney would need to make a ton more money on Saturday to compensate for his lack of pay during the week.

What am I missing here?


We got that Barney worked the same number of hours from Monday to Friday and on Saturday. Thus his wage is split into two parts 1 part is for the work done from Monday to Friday and 1.5 parts for the work done on Saturday.

Now, if Alan worked all his hours on Saturday then he made all his money on Saturday thus he made more money on Saturday than Barney did.

Does this make sense?
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Senior Manager
Senior Manager
avatar
Joined: 15 Aug 2013
Posts: 282
Followers: 0

Kudos [?]: 11 [0], given: 23

Re: MGMAT CAT1 Question 11 [#permalink] New post 15 May 2014, 15:35
Bunuel wrote:
russ9 wrote:
Hi Bunuel,

I'm having a hard time figuring out why statement III is wrong when NOT done algebraically.

I approached this problem conceptually: II is correct is rather easy to see. When it comes to III, the statement says that Barney made more money on Saturday than Alan. Correct?

Doesn't that HAVE to be true? What I mean by that is -- if Barney worked AT LEAST 1 hour on saturday, his salary is 2x vs. Alan's which is 1.5x, so doesn't that inherently make III true?

I would go even further and say that Barney would need to make a ton more money on Saturday to compensate for his lack of pay during the week.

What am I missing here?


We got that Barney worked the same number of hours from Monday to Friday and on Saturday. Thus his wage is split into two parts 1 part is for the work done from Monday to Friday and 1.5 parts for the work done on Saturday.

Now, if Alan worked all his hours on Saturday then he made all his money on Saturday thus he made more money on Saturday than Barney did.

Does this make sense?


Absolutely. Thanks.
Intern
Intern
avatar
Joined: 09 Jan 2014
Posts: 3
GPA: 3.48
Followers: 0

Kudos [?]: 1 [0], given: 10

GMAT ToolKit User
Re: Alan’s regular hourly wage is 1.5 times Barney’s regular [#permalink] New post 01 Aug 2014, 08:06
Let total no.of hours worked by each of them be = x

For Mon-Fri :
Hourly wage of B(Barney) = p
Thus Hourly wage of A(Alan) = 1.5p
Total hours worked by A = x-y
Total hours worked by B = x-z

On sat :
Hourly wage of B = 2p while that of A remains same ie = p
Hours worked by A = y
Hours worked by B =z

Now given:
(x-z)p + (z)2p = (x)(1.5p)
On solving we get z=x/2

Since hours worked on saturday(x/2) is non zero and an integer; x/2=2,4,6 & so on ............... (i)

Statement 1:
it says x-y < (x/2)
ie x< 2y
we have not obtained any such relation among x & y above. Thus cannot be true always

Statement 2:
(x/2)>=1
From (i) we know that this is correct always

Statement 3:
it says (x/2)2p > (y)(1.5p)
ie x>1.5y
we have not obtained any such relation among x & y above. Thus cannot be true always

Thus only statement 2 is true always. Hence answer is (B)
Re: Alan’s regular hourly wage is 1.5 times Barney’s regular   [#permalink] 01 Aug 2014, 08:06
    Similar topics Author Replies Last post
Similar
Topics:
An employee is paid 1.5 times the regular hourly rate for ajit257 5 07 Apr 2011, 16:40
An employee is paid 1.5 times the regular hourly rate for xmagedo 3 28 Jul 2010, 06:44
3 Experts publish their posts in the topic An employee is paid 1.5 times the regular hourly rate for ea lionslion 9 18 Mar 2010, 17:24
An employee is paid 1.5 times the regular hourly rate for sludge 2 09 Jun 2007, 18:55
An employee is paid 1.5 times the regular hourly rate for pesquadero 6 23 May 2006, 18:29
Display posts from previous: Sort by

Alan’s regular hourly wage is 1.5 times Barney’s regular

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.