It is currently 11 Dec 2018, 05:59

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

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

Author Message
TAGS:
GRE Instructor
Joined: 10 Apr 2015
Posts: 1232
Followers: 45

Kudos [?]: 1113 [1] , given: 7

If 0 < y < x, then which of the following [#permalink]  31 Jan 2017, 06:43
1
KUDOS
Expert's post
00:00

Question Stats:

10% (01:44) correct 90% (01:37) wrong based on 10 sessions
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
[Reveal] Spoiler: OA

_________________

Brent Hanneson – Creator of greenlighttestprep.com

Intern
Joined: 20 Mar 2017
Posts: 1
Followers: 0

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

Re: If 0 < y < x, then which of the following [#permalink]  11 Apr 2017, 11:02
Does anyone have the solution for this problem.
GRE Instructor
Joined: 10 Apr 2015
Posts: 1232
Followers: 45

Kudos [?]: 1113 [5] , given: 7

Re: If 0 < y < x, then which of the following [#permalink]  11 Apr 2017, 11:14
5
KUDOS
Expert's post
GreenlightTestPrep 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

One approach is to simplify the expression.
(27x + 23y)/(3x + 2y) = (27x + 18y + 5y)/(3x + 2y)
= (27x + 18y)/(3x + 2y) + (5y)/(3x + 2y)
= 9 + (5y)/(3x + 2y)

First recognize that, since x and y are both POSITIVE, the numerator and denominator of (5y)/(3x + 2y) will be POSITIVE, which means (5y)/(3x + 2y) is equal to a POSITIVE value.
This means that 9 + (5y)/(3x + 2y) will evaluate to be a number that's GREATER THAN 9
So, value I (8.7) is not possible

Now let's take a closer look at (5y)/(3x + 2y)
Notice that (5y)/(3y + 2y) = 5y/5y = 1 [since the numerator and denominator are EQUAL]
However, since we're told that y < x, we know that 3y + 2y < 3y + 2x
This means that (5y)/(3x + 2y) < 1, [since the numerator is LESS THAN the denominator]

If (5y)/(3x + 2y) < 1, then we can conclude that 9 + (5y)/(3x + 2y) < 10

So, value III (10.8) is not possible

This leaves us with value II (9.2), which IS possible.

[Reveal] Spoiler:
B

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com

Re: If 0 < y < x, then which of the following   [#permalink] 11 Apr 2017, 11:14
Display posts from previous: Sort by