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

It is currently 18 Oct 2018, 04:43

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

If f(x,y) = [m][fraction]10x/(x+2y)[/fraction]+[fraction]20y/(2x+y)[/f

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

Hide Tags

Senior DS Moderator
User avatar
D
Joined: 27 Oct 2017
Posts: 875
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
If f(x,y) = [m][fraction]10x/(x+2y)[/fraction]+[fraction]20y/(2x+y)[/f  [#permalink]

Show Tags

New post 06 Oct 2018, 10:29
3
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

18% (01:01) correct 82% (01:57) wrong based on 33 sessions

HideShow timer Statistics

Weekly Quant Quiz #3 Question No 7



If f(x,y) = \(\frac{10x}{(x+2y)}+\frac{20y}{(2x+y)}\), where 0<x<y, which of the following could be the value of f(x,y)?

A. 9
B. 10
C. 19
D. 20
E. 23

_________________

Win Tests/ Prep Courses- Weekly Quant Quiz Contest
SC: Confusable words

All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts
Combination Concept: Division into groups
Question of the Day (QOTD)
Free GMAT CATS

Senior DS Moderator
User avatar
D
Joined: 27 Oct 2017
Posts: 875
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
Re: If f(x,y) = [m][fraction]10x/(x+2y)[/fraction]+[fraction]20y/(2x+y)[/f  [#permalink]

Show Tags

New post 06 Oct 2018, 10:29
2

Official Explanation



From f(x, y) = 10x/(x+2y)+20y/(2x+y), there are 2 variables (x, y), so it is difficult to find the value of f(x, y). If so, you have to use 0<x<y,
① if x=0, f(0, y) = (10(0))/(0+2y)+20y/(2(0)+y) = 20y/y = 20.
② if x=y, f(x, x) = 10x/(x+2x)+20x/(2x+x) = 10x/3x+20x/3x = 30x/3x = 10.

However, from 0<x<y, x is the range between 0 and y, excluding 0 and y, so f(x, y) also becomes the range between 10 and 20, excluding 10 and 20. In other words, the only option that satisfies 10 < f(x, y) < 20 is C, 19. The answer is C.
_________________

Win Tests/ Prep Courses- Weekly Quant Quiz Contest
SC: Confusable words

All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts
Combination Concept: Division into groups
Question of the Day (QOTD)
Free GMAT CATS

PS Forum Moderator
User avatar
P
Joined: 16 Sep 2016
Posts: 313
GMAT 1: 740 Q50 V40
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
Re: If f(x,y) = [m][fraction]10x/(x+2y)[/fraction]+[fraction]20y/(2x+y)[/f  [#permalink]

Show Tags

New post 06 Oct 2018, 10:47
The answer could be A.

please find solution attached.

Best,
G
Attachments

Q7.jpeg
Q7.jpeg [ 107.5 KiB | Viewed 364 times ]

Manager
Manager
avatar
B
Joined: 16 Sep 2011
Posts: 73
GMAT ToolKit User Reviews Badge
Re: If f(x,y) = [m][fraction]10x/(x+2y)[/fraction]+[fraction]20y/(2x+y)[/f  [#permalink]

Show Tags

New post 06 Oct 2018, 11:17
0<x<y
f(x,y) =10x/(x+2y) + 20 y /(2x+y)


f(x,y) = 10x(2x+y) + 20y*(x+2y) /(x+2y)*(2x+y)

f(x,y)= 20x2+ 30xy+40y2 /(2x^2 + 5xy +2Y^2)
=limiting case will give 10 if x= y

and hence for y>x, only A could be the answer

A
RC Moderator
User avatar
P
Joined: 24 Aug 2016
Posts: 400
Location: Canada
Concentration: Entrepreneurship, Operations
GMAT 1: 630 Q48 V28
GMAT ToolKit User Reviews Badge CAT Tests
Re: If f(x,y) = [m][fraction]10x/(x+2y)[/fraction]+[fraction]20y/(2x+y)[/f  [#permalink]

Show Tags

New post 06 Oct 2018, 12:08
f(x,y) = 10x/(x+2y)+20y/(2x+y)= 10(a+b)

where a = x/(x+2y) & b=2y/(2x+y)

if x= y ; a=1/3 & b= 2/3
hence 10 a = 3.3 & 10 b= 6.6
as x<y.... a<3.3 & b > 6.6.... ofcourse value of a & b are interdependent on x & y
10a+10b is closest to value 10......... will go with 10 Ans B
_________________

Please let me know if I am going in wrong direction.
Thanks in appreciation.

Senior Manager
Senior Manager
avatar
P
Joined: 31 Jul 2017
Posts: 477
Location: Malaysia
Schools: INSEAD Jan '19
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
Re: If f(x,y) = [m][fraction]10x/(x+2y)[/fraction]+[fraction]20y/(2x+y)[/f  [#permalink]

Show Tags

New post 07 Oct 2018, 11:54
gmatbusters wrote:

Weekly Quant Quiz #3 Question No 7



If f(x,y) = \(\frac{10x}{(x+2y)}+\frac{20y}{(2x+y)}\), where 0<x<y, which of the following could be the value of f(x,y)?

A. 9
B. 10
C. 19
D. 20
E. 23


Hi chetan2u, Bunuel

Can you please advise as to what is wrong with below method -

f(x,y) = 10 - \(\frac{20xy}{(2x^2 + 5xy + 4y^2)}\) - which means the value of f(x,y) is always less than 10. Only option A is correct.
_________________

If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6958
Re: If f(x,y) = [m][fraction]10x/(x+2y)[/fraction]+[fraction]20y/(2x+y)[/f  [#permalink]

Show Tags

New post 07 Oct 2018, 19:06
1
rahul16singh28 wrote:
gmatbusters wrote:

Weekly Quant Quiz #3 Question No 7



If f(x,y) = \(\frac{10x}{(x+2y)}+\frac{20y}{(2x+y)}\), where 0<x<y, which of the following could be the value of f(x,y)?

A. 9
B. 10
C. 19
D. 20
E. 23


Hi chetan2u, Bunuel

Can you please advise as to what is wrong with below method -

f(x,y) = 10 - \(\frac{20xy}{(2x^2 + 5xy + 4y^2)}\) - which means the value of f(x,y) is always less than 10. Only option A is correct.


You have missed out on one term in your method ..
So \(\frac{20x^2+30xy+40y^2}{2x^2+5xy+2y^2}\)=\(\frac{20x^2+50xy-20xy+20y^2+20y^2}{2x^2+5xy+2y^2}\)
=\(\frac{10(2x^2+5xy+2y^2)+(2y^2-2xy)}{2x^2+5xy+2y^2}\)=\(10-\frac{2y(y-x)}{2x^2+5xy+2y^2}\)
2y(y-x) is always positive as y>X so answer becomes -- 10+(something positive)
Thus 9 or 10 can never be the answer.

Hope it clarifies where you went wrong..
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

GMAT Club Bot
Re: If f(x,y) = [m][fraction]10x/(x+2y)[/fraction]+[fraction]20y/(2x+y)[/f &nbs [#permalink] 07 Oct 2018, 19:06
Display posts from previous: Sort by

If f(x,y) = [m][fraction]10x/(x+2y)[/fraction]+[fraction]20y/(2x+y)[/f

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.