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.
Nov 1912:30 PM EST
-01:30 PM EST
Learn how Keshav, a Chartered Accountant, scored an impressive 705 on GMAT in just 30 days with GMATWhiz's expert guidance. In this video, he shares preparation tips and strategies that worked for him, including the mock, time management, and more
Nov 2001:30 PM EST
-02:30 PM IST
Learn how Kamakshi achieved a GMAT 675 with an impressive 96th %ile in Data Insights. Discover the unique methods and exam strategies that helped her excel in DI along with other sections for a balanced and high score.
Nov 2211:00 AM IST
-01:00 PM IST
Do RC/MSR passages scare you? e-GMAT is conducting a masterclass to help you learn – Learn effective reading strategies Tackle difficult RC & MSR with confidence Excel in timed test environment- Nov 23
11:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease. 
Nov 2407:00 PM PST
-08:00 PM PST
Full-length FE mock with insightful analytics, weakness diagnosis, and video explanations!
Nov 2510:00 AM EST
-11:00 AM EST
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors.
20 Feb 2014, 01:15
Kudos
Bookmarks
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
59% (02:13) correct
41%
(02:33)
wrong
based on 4647
sessions
History
Date
Time
Result
Not Attempted Yet
If x is a positive number less than 10, is z greater than the average (arithmetic mean) of x and 10?
(1) On the number line, z is closer to 10 than it is to x.
(2) z = 5x
(1) On the number line, z is closer to 10 than it is to x.
(2) z = 5x
20 Feb 2014, 01:16
Kudos
Bookmarks
If x is a positive number less than 10, is z greater than the average (arithmetic mean) of x and 10?
(1) On the number line, z is closer to 10 than it is to x:
This means that \(|10-z|<|z-x|\). Since z is closer to 10 than it (z) is to x (and from the stem we know that x < 10), then \(z > x\), thus \(|z-x|=z-x\). We can have the following two cases for 10-z:
OR another approach:
Given:
Now, as z is closer to 10 than it (z) is to x, then z is either in the blue area, so more than average OR in the green area, so also more than average. Answer to the question YES.
Sufficient.
(2) z = 5x
(IF \(x>\frac{10}{9}\), then the answer to the question is YES, but IF \(0<x\leq{\frac{10}{9}}\), then the answer to the question is NO.)
Answer: A.
Similar questions to practice:
- Given: \(0<x<10\).
Question: is z greater than the average of x and 10?
- Is \(z>\frac{10+x}{2}\)?
Is \(2z>10+x\)?
(1) On the number line, z is closer to 10 than it is to x:
This means that \(|10-z|<|z-x|\). Since z is closer to 10 than it (z) is to x (and from the stem we know that x < 10), then \(z > x\), thus \(|z-x|=z-x\). We can have the following two cases for 10-z:
- A. \(z\leq{10}\);
If \(z\leq{10}\), then \(|10-z|=10-z\);
Therefore, \(|10-z|<|z-x|\) becomes: \(10-z<z-x\);
\(2z>10+x\).
Answer to the question YES.
B. \(z>{10}\);
In this case \(2z>20\) and since \(x<10\), then \(x+10<20\), hence \(2z>10+x\).
Answer to the question YES.
OR another approach:
Given:
- x-----average-----10----- (average of x and 10 halfway between x and 10).
Now, as z is closer to 10 than it (z) is to x, then z is either in the blue area, so more than average OR in the green area, so also more than average. Answer to the question YES.
Sufficient.
(2) z = 5x
- The question (is \(2z>10+x\)?) becomes:
Is \(10x>10+x\)?
Is \(x>\frac{10}{9}\).
We don't now that. Not sufficient.
(IF \(x>\frac{10}{9}\), then the answer to the question is YES, but IF \(0<x\leq{\frac{10}{9}}\), then the answer to the question is NO.)
Answer: A.
Similar questions to practice:
- https://gmatclub.com/forum/if-x-is-a-positive-integer-less-than-10-is-z-greater-than-128086.html
https://gmatclub.com/forum/if-y-is-a-ne ... 95138.html
https://gmatclub.com/forum/if-x-is-a-po ... 31322.html
https://gmatclub.com/forum/if-a-is-a-po ... 05650.html
https://gmatclub.com/forum/if-x-and-z-a ... 55651.html
20 Feb 2014, 03:18
Kudos
Bookmarks
If x is a positive number less than 10, is z greater than the average (arithmetic mean) of x and 10?
(1) On the number line, z is closer to 10 than it is to x.
(2) z = 5x
On st1 i'll draw a number line. 0----------------------x-----------------z---10
We can see that z will always be greater than the average. Sufficient
St2 say that z=5x. we'll choose 2 cases:
Case 1: x=2, so z=10. avarge is 6 and z is greater than the avarage.
Case 2: x=1, so z=5 avarge is 5.5 and z is smaller than the avarage. Insufficient
So ans is A.
(1) On the number line, z is closer to 10 than it is to x.
(2) z = 5x
On st1 i'll draw a number line. 0----------------------x-----------------z---10
We can see that z will always be greater than the average. Sufficient
St2 say that z=5x. we'll choose 2 cases:
Case 1: x=2, so z=10. avarge is 6 and z is greater than the avarage.
Case 2: x=1, so z=5 avarge is 5.5 and z is smaller than the avarage. Insufficient
So ans is A.
