Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Jun 0808:00 PM EDT
-10:00 PM EDT
Master the GMAT with expert live instruction, a personalized study plan, and real-time support. Includes 40 hours of online classes plus 6 months of access to the TTP GMAT OnDemand video course. Mon/Wed June 8, 2026 →August 12, 2026 8:00pm-10:00pm EST
Jun 1006:00 AM PDT
-06:15 PM PDT
Register for the GMAT Club Virtual MBA Spotlight Fair – the world’s premier event for serious MBA candidates. This is your chance to hear directly from Admissions Directors at nearly every Top 30 MBA program..- Jun 10
10:00 AM PDT
-11:00 AM PDT
Scoring 715 on the GMAT Focus Edition requires more than just learning formulas, memorizing concepts, or solving hundreds of questions. In this episode, Nishant shares how he improved his GMAT preparation by focusing on application of concepts, and more. 
Jun 1111:00 AM EDT
-01:00 PM EDT
TTP GMAT OnDemand gives serious students 400+ hours of expert video instruction, the full TTP course, AI support, weekly office hours, and a 715+ score guarantee—all built for elite GMAT score improvement.
08 Sep 2022, 04:55
Kudos
Bookmarks
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
52% (03:11) correct
48%
(03:30)
wrong
based on 413
sessions
History
Date
Time
Result
Not Attempted Yet
{x, y, z} is an increasing sequence of numbers such that the ratio between the consecutive terms is constant.
{x + 2y, 2x + y + z, x + 3y + z} is an increasing sequence of numbers such that the difference between the consecutive terms is constant.
What is the value of x/z ?
A. 1/4
B. 1/2
C. 1
D. 2
E. 4
{x + 2y, 2x + y + z, x + 3y + z} is an increasing sequence of numbers such that the difference between the consecutive terms is constant.
What is the value of x/z ?
A. 1/4
B. 1/2
C. 1
D. 2
E. 4
Experience GMAT Club Test Questions
Yes, you've landed on a GMAT Club Tests question
Craving more? Unlock our full suite of GMAT Club Tests here
Want to experience more? Get a taste of our tests with our free trial today
Rise to the challenge with GMAT Club Tests. Happy practicing!
30 Aug 2024, 09:50
Kudos
Bookmarks
Official Solution:
\(\{x, \ y, \ z\}\) is an increasing sequence of numbers such that the ratio between the consecutive terms is constant.
\(\{x + 2y, \ 2x + y + z, \ x + 3y + z\}\) is an increasing sequence of numbers such that the difference between the consecutive terms is constant.
What is the value of \(\frac{x}{z}\) ?
A. \(\frac{1}{4}\)
B. \(\frac{1}{2}\)
C. \(1\)
D. \(2\)
E. \(4\)
The first statement implies that \(\frac{x}{y}=\frac{y}{z}\), which yields \(y^2 = xz\).
The second statement implies that \((2x + y + z) - (x + 2y) = (x + 3y + z) - (2x + y + z)\), which yields \(3y = z + 2x\).
Squaring \(3y = z + 2x\) yields \(9y^2= (z + 2x)^2\). Substituting \(y^2 = xz\) gives us \(9xz = (z + 2x)^2\).
\(9xz= z^2 + 4xz + 4x^2\)
\(4x^2 - 5xz + z^2 = 0\)
\(4x^2 - 4xz - xz + z^2 = 0\)
\(4x(x - z) - z(x - z) = 0\)
\((4x - z)(x - z)= 0\)
\(4x - z = 0\) or \(x - z = 0\), which is not possible since it would give \(x = z\), and this is not possible given that \(\{x, y, z\}\) is an increasing sequence.
Therefore, \(4x = z\), and thus \(\frac{x}{z}=\frac{1}{4}\).
Answer: A
\(\{x, \ y, \ z\}\) is an increasing sequence of numbers such that the ratio between the consecutive terms is constant.
\(\{x + 2y, \ 2x + y + z, \ x + 3y + z\}\) is an increasing sequence of numbers such that the difference between the consecutive terms is constant.
What is the value of \(\frac{x}{z}\) ?
A. \(\frac{1}{4}\)
B. \(\frac{1}{2}\)
C. \(1\)
D. \(2\)
E. \(4\)
The first statement implies that \(\frac{x}{y}=\frac{y}{z}\), which yields \(y^2 = xz\).
The second statement implies that \((2x + y + z) - (x + 2y) = (x + 3y + z) - (2x + y + z)\), which yields \(3y = z + 2x\).
Squaring \(3y = z + 2x\) yields \(9y^2= (z + 2x)^2\). Substituting \(y^2 = xz\) gives us \(9xz = (z + 2x)^2\).
\(9xz= z^2 + 4xz + 4x^2\)
\(4x^2 - 5xz + z^2 = 0\)
\(4x^2 - 4xz - xz + z^2 = 0\)
\(4x(x - z) - z(x - z) = 0\)
\((4x - z)(x - z)= 0\)
Therefore, \(4x = z\), and thus \(\frac{x}{z}=\frac{1}{4}\).
Answer: A
General Discussion
08 Sep 2022, 06:20
Kudos
Bookmarks
Bunuel
{x, y, z} is an increasing sequence of numbers such that the ratio between the consecutive terms is constant.
So, \(\frac{y}{x}=\frac{z}{y}.............xz=y^2...............\frac{xz}{z^2}=\frac{y^2}{z^2}............\frac{x}{z}=(\frac{y}{z})^2\)
{x + 2y, 2x + y + z, x + 3y + z} is an increasing sequence of numbers such that the difference between the consecutive terms is constant.
So, \(2x + y + z-(x + 2y)=x + 3y + z-(2x + y + z)..............x+z-y=2y-x............2x+z=3y\)
Divide by z
\(2(\frac{x}{z})+1=3(\frac{y}{z})\)
Substitute \(\frac{x}{z}=(\frac{y}{z})^2\)
\(2(\frac{y}{z})^2+1=3\frac{y}{z}\)
Let \(\frac{y}{z}=a\), then \(\frac{x}{z}=a^2\) and \(2a^2+1=3a.......2a^2-3a+1=0............(2a-1)(a-1)=0\)
So, \(a=\frac{1}{2}\) or a=1, but \(y\neq z\), so \(a^2=\frac{1}{4}\)
A
