It is currently 26 Jun 2017, 10:52

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# positive integer

Author Message
Manager
Joined: 24 Apr 2009
Posts: 93

### Show Tags

21 Jul 2009, 12:36
1
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

If x and y are positive integers, and x<y, which of the following could be the value of (x/x+y)*10+(y/x+y)*20?
(a) 10
(b) 14
(c) 16
(d) 21
(e) 30
Current Student
Joined: 18 Jun 2009
Posts: 356
Location: San Francisco

### Show Tags

21 Jul 2009, 13:48
1
KUDOS
(x/x+y)*10+(y/x+y)*20 = K

solving above we get 10(x+2y)/(x+y)

we need to find K

from the answer choices we see that K is a positive integer

This can happen only if x+y which is the denominator is a factor of 10

Factors of 10 are 1,2,5

We cannot get 1 and 2 from x+y as x and y are +ve integers and x<y

so lets take 5 where x=2 and y = 3

we substitute these values we get

10(x+2y)/(x+y) = 10(2+6)/2+3 = 2(8) = 16 so answer is C

The other possible value of x and y is x=1 and y =4, we see that we wont get any of the given answers, this is not needed as we got the solution already but just gave as an extra step.

Manager
Joined: 03 Jul 2009
Posts: 106
Location: Brazil

### Show Tags

21 Jul 2009, 15:06
Good explanation gmanjesh, I did the same method.
Manager
Joined: 27 Jun 2008
Posts: 157

### Show Tags

21 Jul 2009, 20:55
1
KUDOS
gmanjesh wrote:
(x/x+y)*10+(y/x+y)*20 = K

solving above we get 10(x+2y)/(x+y)

Can you please tell us how did you solve the equation.
Current Student
Joined: 18 Jun 2009
Posts: 356
Location: San Francisco

### Show Tags

21 Jul 2009, 21:08
(x/x+y)*10+(y/x+y)*20 = K

take x+y as the common denomintor

10x+20y/(x+y)

take common factor 10 out

10(x+2y)/(x+y)

hope that helps
Manager
Joined: 27 Jun 2008
Posts: 157

### Show Tags

21 Jul 2009, 23:37
Duh! I read * as ^. I should call it a day. Thanks gmanjesh for your patient elaboration.
Manager
Joined: 24 Apr 2009
Posts: 93

### Show Tags

22 Jul 2009, 02:18
OA given is A i.e. 10.. i am not sure how..
Also, factors of 10 are 1, 2, 5, and 10.
By the method explained above in a post answer comes to be 16 but OA is 10..
please lemme know, is there any other method to solve this question..
Current Student
Joined: 18 Jun 2009
Posts: 356
Location: San Francisco

### Show Tags

22 Jul 2009, 06:13
sorry I missed 10, but yeah still the answer would be 16 which matches one of the answers.

I guess OA was wrong or a typo.
Manager
Joined: 27 Jun 2008
Posts: 157

### Show Tags

22 Jul 2009, 09:15
well if you consider the final equation

10(x+2y)/(x+y)
or 10((X+y)+Y/X+Y)
= 10(1+(Y/X+Y))
i.e. 10+(10Y/X+Y)

In all probability it should be more than 10.
Director
Joined: 23 May 2008
Posts: 806

### Show Tags

22 Jul 2009, 10:50
i simplified to 10(y+2)/x+y= ?

then plugged in the first answer choice

10(y+2)/x+y=10 y's cancel and x=2, so y's can be any value. I picked A as the answer.
Manager
Joined: 27 Jun 2008
Posts: 157

### Show Tags

22 Jul 2009, 16:43
Can you pls provide the steps
Manager
Joined: 24 Apr 2009
Posts: 93

### Show Tags

23 Jul 2009, 05:58
bigtreezl wrote:
i simplified to 10(y+2)/x+y= ?

then plugged in the first answer choice

10(y+2)/x+y=10 y's cancel and x=2, so y's can be any value. I picked A as the answer.

please elaborate some more on ur solution..
Manager
Joined: 24 Apr 2009
Posts: 93

### Show Tags

25 Jul 2009, 12:49
guys, i confirmed this question with the experts and the answer to this question is definitely C.. oa is incorrect..
Manager
Joined: 22 Mar 2008
Posts: 53

### Show Tags

29 Jul 2009, 22:36
1
KUDOS
Another way of solving this problem

let's say c = [10x/(x+y)] +[20y/(x+y)] = (10x+20y)/(x+y) = 10 + {10y/(x+y)} = 10 + [10/((x/y)+1)]
so ans should be > 10
now, x<y
hence, x/Y <1
hence, (x/Y) + 1 <2
so, 10/ [(x/y)+ 1] >5
so, c> 15
now, since both x and y are positive and (1+(x/y)) > 1
therefore, 10 /(1+(x/y) must be <10

so, c < 10 + 10
c<20
so, 15<c<20
and only 16 satisfy this condition. hence ans is C.
Intern
Joined: 13 Jul 2009
Posts: 20

### Show Tags

30 Jul 2009, 13:57
@sudiptak
(10x+20y)/(x+y)
= 10 + {10y/(x+y)}

How did you get this (10 + {10y/(x+y)})? Please explain

regards,
hhk
Manager
Joined: 21 Jul 2009
Posts: 249
Location: New York, NY

### Show Tags

31 Jul 2009, 09:33
C. 16

As follows:

(x/x+y)*10+(y/x+y)*20

=10*(x/(y+x))+10*(y/(y+x))+10*(y/(y+x))

=10*(x/(y+x)+y/(y+x)+y/(y+x))

=10*((x+y+y)/(x+y))

=10+10*(y/(y+x))

only possibility is 16.
Intern
Joined: 13 Jul 2009
Posts: 20

### Show Tags

31 Jul 2009, 17:06
10+10*(y/(y+x))
From qn,
x/y<1

A.Not possible
B.
Substitute 10(y/y+x) =4
X/y>1 Hence, it is false.
C.x/y=2/3 Hence, it is correct
D& E. As per the qn, x and y are positive integers.

regards,
hhk
Senior Manager
Joined: 26 Jul 2009
Posts: 347

### Show Tags

31 Jul 2009, 18:02
nice work sudiptak.
Manager
Joined: 22 Mar 2008
Posts: 53

### Show Tags

01 Aug 2009, 08:20
1
KUDOS
@sudiptak
(10x+20y)/(x+y)
= 10 + {10y/(x+y)}

How did you get this (10 + {10y/(x+y)})? Please explain

regards,
hhk

hi HHk,
(10x+20y)/(x+y)
=(10x+10y +10y)/(x+y)
=[(10x+10y)/(x+y)] + [10y/(x+y)]
=[10(x+y)/(x+y)] + [10y/(x+y)]
=10 + {10y/(x+y)}

Hope this helps.
Manager
Joined: 20 May 2008
Posts: 56

### Show Tags

01 Aug 2009, 17:24
guys u can also try dis way..its quite simple and short:

firstly let the ans be 'k'

therefore,

10x + 20y / x + y = k

10x + 20y = kx + ky

kx - 10x = 20y - ky

x(k - 10) = y(20 - k)

now since x<y...

therefore (k - 10) will have to be greater than (20 - k)

just plug in the options and the only one ur left wit is 16.

hence the ans must be C.

hope dis helps....
Re: positive integer   [#permalink] 01 Aug 2009, 17:24
Display posts from previous: Sort by