GMAT Changed on April 16th - Read about the latest changes here

It is currently 22 May 2018, 14:48

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 0 < y < x, then which of the following is

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

Hide Tags

Expert Post
Top Contributor
1 KUDOS received
SVP
SVP
User avatar
P
Joined: 12 Sep 2015
Posts: 2461
Location: Canada
If 0 < y < x, then which of the following is [#permalink]

Show Tags

New post 31 Jan 2017, 07:38
1
This post received
KUDOS
Expert's post
Top Contributor
17
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

41% (01:53) correct 59% (02:02) wrong based on 152 sessions

HideShow timer Statistics

If 0 < y < x, then which of the following is a possible value of \(\frac{27x + 23y}{3x + 2y}\)?
    I. 8.7
    II. 9.2
    III. 10.8

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

*Kudos for all correct solutions

_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

3 KUDOS received
Senior CR Moderator
User avatar
V
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1379
Location: Viet Nam
GMAT ToolKit User Premium Member
Re: If 0 < y < x, then which of the following is [#permalink]

Show Tags

New post 31 Jan 2017, 08:10
3
This post received
KUDOS
5
This post was
BOOKMARKED
GMATPrepNow wrote:
If 0 < y < x, then which of the following is a possible value of \(\frac{27x + 23y}{3x + 2y}\)?
    I. 8.7
    II. 9.2
    III. 10.8

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

*Kudos for all correct solutions


\(A=\frac{27x + 23y}{3x + 2y}=\frac{9(3x+2y)+5y}{3x+2y}=9+\frac{5y}{3x+2y}\)

Since \(0<y<x\), we have \(A > 9\), so (I) is out.

Also \(\frac{5y}{2x+3y}<\frac{5y}{2y+3y}=1 \implies A < 9+1=10\), so (III) is out.

Hence (II) is left. The answer is B.

To check the answer, we have \(A=9.2 \iff \frac{5y}{3x+2y}=0.2=\frac{1}{5} \iff 25y = 3x+2y \iff 3x=23y \iff x=\frac{23y}{3}\)
This result satisfies the condition \(0<y<x\).
_________________

Actual LSAT CR bank by Broall

How to solve quadratic equations - Factor quadratic equations
Factor table with sign: The useful tool to solve polynomial inequalities
Applying AM-GM inequality into finding extreme/absolute value

New Error Log with Timer

Expert Post
3 KUDOS received
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 5779
Re: If 0 < y < x, then which of the following is [#permalink]

Show Tags

New post 31 Jan 2017, 09:13
3
This post received
KUDOS
Expert's post
4
This post was
BOOKMARKED
GMATPrepNow wrote:
If 0 < y < x, then which of the following is a possible value of \(\frac{27x + 23y}{3x + 2y}\)?
    I. 8.7
    II. 9.2
    III. 10.8

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

*Kudos for all correct solutions


Hi

If you look at a Q like this, where the variable can take any value and you have to find which values can fit in, it will help you if you find the MINIMUM and MAX value..


Let's see now..

\(\frac{27x + 23y}{3x + 2y}=\frac{27x+18y+5y}{3x+2y}=\frac{9(3x+2y)}{3x+2y}+\frac{3y+2y}{3x+2y}\)

1) Min value..
It is 9 + something, so min value is slightly more than 9..
I is out..

2) Max value..
Let's check \(\frac{3y+2y}{3x+2y}\)..
Now x>y so 3x>3y thus 3x+2y>3y+2y....
This means \(\frac{3y+2y}{3x+2y}<1\).
So value will be LESS than 9+1 or <10...
III is also out

ONLY 9.2 is left
B
_________________

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


GMAT online Tutor

Expert Post
Top Contributor
1 KUDOS received
SVP
SVP
User avatar
P
Joined: 12 Sep 2015
Posts: 2461
Location: Canada
Re: If 0 < y < x, then which of the following is [#permalink]

Show Tags

New post 31 Jan 2017, 13:20
1
This post received
KUDOS
Expert's post
Top Contributor
GMATPrepNow wrote:
If 0 < y < x, then which of the following is a possible value of \(\frac{27x + 23y}{3x + 2y}\)?
    I. 8.7
    II. 9.2
    III. 10.8

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

*Kudos for all correct solutions


The two approaches above are great, so I won't duplicate them :)
Instead, I'll show you another approach.

Let's check to see whether (27x + 23y)/(3x + 2y) can equal any of the 3 given values (8.7, 9.2 and 10.8)

Start with I.
Can (27x + 23y)/(3x + 2y) = 8.7?
To make our work easier (without tons of decimals), let's rewrite 8.7 as 87/10
So, we have: (27x + 23y)/(3x + 2y) = 87/10
Cross multiply to get: 10(27x + 23y) = 87(3x + 2y)
Expand: 270x + 230y = 261x + 174y
Rearrange to get: 9x = -56y
Divide both sides by 9 to get: x = (-56/9)y
This is a problem, since x and y are both SUPPOSED to be positive. However, we can see by this equation that, if y is positive then x is NEGATIVE. Likewise, if x is positive then y is NEGATIVE.
This tells us that it's IMPOSSIBLE to find x- and y-values that satisfy the given condition (0 < y < x) so that (27x + 23y)/(3x + 2y) = 8.7
So, statement I is not possible

Now try II.
Can (27x + 23y)/(3x + 2y) = 9.2?
To make our work easier, notice that 9.2 = 92/10 = 46/5
So, we have: (27x + 23y)/(3x + 2y) = 46/5
Cross multiply to get: 5(27x + 23y) = 46(3x + 2y)
Expand: 135x + 115y = 138x + 92y
Rearrange to get: 23y = 3x
Divide both sides by 3 to get: (23/3)y = x
One possible solution to this equation is x = 23 and y = 3
Since these x- and y-values satisfy the given condition (0 < y < x), we can see that it IS POSSIBLE for (27x + 23y)/(3x + 2y) to equal 9.2
So, statement II IS possible


Now try III.
Can (27x + 23y)/(3x + 2y) = 10.8?
To make our work easier, notice that 10.8 = 108/10 = 54/5
So, we have: (27x + 23y)/(3x + 2y) = 54/5
Cross multiply to get: 5(27x + 23y) = 54(3x + 2y)
Expand: 135x + 115y = 162x + 108y
Rearrange to get: 7y = 27x
Divide both sides by 7 to get: y = (27/7)x
This is a problem, since x and y are both SUPPOSED to be such that 0 < y < x.
However, we can see by the equation, y = (27/7)x, that y will always be greater than x.
For example, if x = 7, then y = 27. Likewise, if x = 14, then y = 54, and so on.
This tells us that it's IMPOSSIBLE to find x- and y-values that satisfy the given condition (0 < y < x) so that (27x + 23y)/(3x + 2y) = 10.8
So, statement III is not possible

This is a TIME-CONSUMING approach, but it's better than guessing!

Answer: B
_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 6812
Premium Member
Re: If 0 < y < x, then which of the following is [#permalink]

Show Tags

New post 07 Feb 2018, 11:59
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: If 0 < y < x, then which of the following is   [#permalink] 07 Feb 2018, 11:59
Display posts from previous: Sort by

If 0 < y < x, then which of the following is

  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®.