• 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

Is Z Between X and Y?

This topic has 6 expert replies and 2 member replies

Is Z Between X and Y?

Post
If x, y, and z are positive numbers, is z between x and y?

(1) x < 2z < y
(2) 2x < z < 2y


OA: C

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
bml1105 wrote:
If x, y, and z are positive numbers, is z between x and y?

(1) x < 2z < y
(2) 2x < z < 2y

Target question: Is z between x and y?

Statement 1: x < 2z < y
There are several set values of x, y and z that satisfy this condition. Here are two:
Case a: x = 3, y = 10, and z = 2, in which case z is NOT between x and y
Case b: x = 1, y = 10, and z = 3, in which case z IS between x and y
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 2x < z < 2y
There are several set values of x, y and z that satisfy this condition. Here are two:
Case a: x = 1, y = 2, and z = 3, in which case z is NOT between x and y
Case b: x = 1, y = 10, and z = 3, in which case z IS between x and y
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1: x < 2z < y
Statement 2: 2x < z < 2y
Since the two inequalities are facing the same direction, we can add them to get:
3x < 3z < 3y
Divide all three parts by 3 to get: x < z < y
As we can see, z IS definitely between x and y
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent

_________________
Brent Hanneson – Creator of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Sign up for our free Question of the Day emails
And check out all of our free resources

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

GMAT/MBA Expert

Post
bml1105 wrote:
If x, y, and z are positive numbers, is z between x and y?

(1) x < 2z < y
(2) 2x < z < 2y
Statement 1: x < 2z < y
Let x=2 and y=10.
In this case:
2 < 2z < 10
1 < z < 5.
If z=4, then it is between x=2 and y=10.
If z=1.5, then it is not between x=2 and y=10.
INSUFFICIENT.

Statement 2: 2x < z < 2y
Let x=2 and y=10.
In this case:
2*2 < z < 2*10
4 < z < 20
If z=5, then it is between x=2 and y=10.
If z=19, then it is not between x=2 and y=10.
INSUFFICIENT.

Statements combined:
Inequalities can be ADDED TOGETHER.
Adding together x < 2z < y and 2x < z < 2y, we get:
(x+2x) < (2z+z) < (y+2y)
3x < 3z < 3y
x < z < y.
Thus, z is between x and y.
SUFFICIENT.

The correct answer is C.

_________________
Mitch Hunt
Private Tutor for the GMAT and GRE
GMATGuruNY@gmail.com

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.
Student Review #1
Student Review #2
Student Review #3

  • +1 Upvote Post
  • Quote
  • Flag
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.
Master | Next Rank: 500 Posts Default Avatar
Joined
05 Jun 2015
Posted:
359 messages
Followed by:
2 members
Upvotes:
3
Post
bml1105 wrote:
If x, y, and z are positive numbers, is z between x and y?

(1) x < 2z < y
(2) 2x < z < 2y


OA: C
Hi GMATGuruNY And Brent@GMATPrepNow,

How to quickly choose the numbers to satisfy

(1) x < 2z < y
(2) 2x < z < 2y

I'm Getting Stuck to choose the numbers. Please throw some light

Thanks
Nandish

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
NandishSS wrote:
bml1105 wrote:
If x, y, and z are positive numbers, is z between x and y?

(1) x < 2z < y
(2) 2x < z < 2y


OA: C
Hi GMATGuruNY And Brent@GMATPrepNow,

How to quickly choose the numbers to satisfy

(1) x < 2z < y
(2) 2x < z < 2y

I'm Getting Stuck to choose the numbers. Please throw some light

Thanks
Nandish
The process of choosing numbers isn't always easy. In most cases, we are looking for numbers that meet the given information AND provide conflicting answers to the target question.

So, for example, for statement 1, we have x < 2z < y
Notice that this statement is similar to what the target question is asking, yet instead of z, we have 2z.
So, we might first make x and y spread out apart enough to allow us to play with the z values.
Let's start with x = 3 and y = 10
First value of z is kind of irrelevant (as long as it meets the given information).
Let's say z = 4.
This value of z meets the condition that x < 2z < y. Also, when x = 3, y = 10, and z = 4, the answer to the target question is "YES, z IS between x and y"

At this point, we'll try to find a value of z so that the answer to the target question is "NO, z is NOT between x and y."
This is where we need to play around with some z-values.
Let's see what happens if we keep x = 3 and y = 10, and work with different z-values.
In this case, if we make z small AND close to the x-value, it might be the case that doubling z (aka 2z) will make 2z big enough so that x < 2z < y, HOWEVER z itself will NOT be between x and y.
So, how about z = 2. When we double z, we get 2z = 6, so we meet the condition that x < 2z < y, however z itself (z = 2) leads us to a DIFFERENT answer to our target question: "NO, z is NOT between x and y."

As I said, choosing numbers isn't always easy. It can take a lot of playing around with numbers.

If you're interested, we have a video on choosing numbers to test when answer Data Sufficiency questions: https://www.gmatprepnow.com/module/gmat-data-sufficiency/video/1102

Cheers,
Brent

_________________
Brent Hanneson – Creator of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Sign up for our free Question of the Day emails
And check out all of our free resources

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
Post
NandishSS wrote:
How to quickly choose the numbers to satisfy

(1) x < 2z < y
(2) 2x < z < 2y

I'm Getting Stuck to choose the numbers. Please throw some light

Thanks
Nandish
Here's my general process: go BIG then small!

So for each statement, I think "is there an example in which the numbers are HUGE or FAR APART that keeps the statement true?"
ex: (1) x < 2z < y
x = 0
y = 1,000,000
2z = 100, z = 50
When x and y are far apart, it's easy to think of a number for z where both z and 2z are between x and y.

Next, I think: "is there an example in which the numbers are SMALL or very CLOSE TOGETHER that keeps the statement true?"
ex: (1) x < 2z < y
x = 3
y = 5
2z = 4, z = 2
When x and y are close together, it's possible for 2z to be in between x and y, but for 2z not to be.

Then repeat the same thought process of BIG then small (or FAR then CLOSE) for the 2nd statement.

_________________


Ceilidh Erickson
Manhattan Prep GMAT & GRE instructor
EdM in Mind, Brain, and Education
Harvard Graduate School of Education


Manhattan Prep instructors all have 99th+ percentile scores and expert teaching experience.
Sign up for a FREE TRIAL, and learn why we have the highest ratings in the GMAT industry!

  • +1 Upvote Post
  • Quote
  • Flag
Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week.
Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week.
Master | Next Rank: 500 Posts Default Avatar
Joined
05 Jun 2015
Posted:
359 messages
Followed by:
2 members
Upvotes:
3
Post
ceilidh.erickson wrote:
NandishSS wrote:
How to quickly choose the numbers to satisfy

(1) x < 2z < y
(2) 2x < z < 2y

I'm Getting Stuck to choose the numbers. Please throw some light

Thanks
Nandish
Here's my general process: go BIG then small!

So for each statement, I think "is there an example in which the numbers are HUGE or FAR APART that keeps the statement true?"
ex: (1) x < 2z < y
x = 0
y = 1,000,000
2z = 100, z = 50
When x and y are far apart, it's easy to think of a number for z where both z and 2z are between x and y.

Next, I think: "is there an example in which the numbers are SMALL or very CLOSE TOGETHER that keeps the statement true?"
ex: (1) x < 2z < y
x = 3
y = 5
2z = 4, z = 2
When x and y are close together, it's possible for 2z to be in between x and y, but for 2z not to be.

Then repeat the same thought process of BIG then small (or FAR then CLOSE) for the 2nd statement.
Hi ceilidh,

Thanks A lot:-) You People made my day

Thanks
Nandish

  • +1 Upvote Post
  • Quote
  • Flag
Post
NandishSS wrote:
Hi ceilidh,

Thanks A lot:-) You People made my day

Thanks
Nandish
My pleasure! Very glad to help.

_________________


Ceilidh Erickson
Manhattan Prep GMAT & GRE instructor
EdM in Mind, Brain, and Education
Harvard Graduate School of Education


Manhattan Prep instructors all have 99th+ percentile scores and expert teaching experience.
Sign up for a FREE TRIAL, and learn why we have the highest ratings in the GMAT industry!

  • +1 Upvote Post
  • Quote
  • Flag
Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week.
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh

Top First Responders*

1 fskilnik@GMATH 74 first replies
2 Jay@ManhattanReview 49 first replies
3 Brent@GMATPrepNow 47 first replies
4 GMATGuruNY 43 first replies
5 Rich.C@EMPOWERgma... 36 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description fskilnik@GMATH

GMATH Teacher

195 posts
2 image description Scott@TargetTestPrep

Target Test Prep

183 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

123 posts
4 image description Max@Math Revolution

Math Revolution

89 posts
5 image description GMATGuruNY

The Princeton Review Teacher

87 posts
See More Top Beat The GMAT Experts