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 2010:00 AM PDT
-11:00 AM PDT
Class is officially in session! Join Charles Bibilos from GMAT Ninja and GMAC’s own Jaime Malatesta, Senior Psychometrician, as they simplify some of the complexities of GMAT scoring.
Jun 2106:30 AM PDT
-08:30 AM PDT
Not only the typical inference questions but also all other CR questions on the GMAT require the ability to deduce from the given information. Come master how to draw inferences accurately and efficiently with Verbal Expert-Sunita Singhvi. Limited Seats!
Jun 2111:00 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
Jun 2211:30 AM EDT
-12:30 PM EDT
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.
Jun 2308:00 PM PDT
-09:00 PM PDT
Full-length FE mock with insightful analytics, weakness diagnosis, and video explanations!- Jun 30
08:00 AM PDT
-11:59 PM PDT
Join us June 30th for 2 weeks of GMAT questions (just 8 per day) to help with your prep and to compete with your fellow GMAT Clubbers for a chance to win a prize fund of $30,000 for you and your team-mates!
16 Nov 2009, 11:33
Kudos
Bookmarks
Guys I didn't forget your request, just was collecting good questions to post.
So here are some inequality and absolute value questions from my collection. Not every problem below is hard, but there are a few, which are quite tricky. Please provide your explanations along with the answers.
1. If \(6*x*y = x^2*y + 9*y\), what is the value of xy?
(1) \(y – x = 3\)
(2) \(x^3< 0\)
Solution: https://gmatclub.com/forum/inequality-a ... ml#p653690
2. If y is an integer and \(y = |x| + x\), is \(y = 0\)?
(1) \(x < 0\)
(2) \(y < 1\)
Solution: https://gmatclub.com/forum/inequality-a ... ml#p653695
3. Is \(x^2 + y^2 > 4a\)?
(1) \((x + y)^2 = 9a\)
(2) \((x – y)^2 = a\)
Solution: https://gmatclub.com/forum/inequality-a ... ml#p653697
4. Are x and y both positive?
(1) \(2x-2y=1\)
(2) \(\frac{x}{y}>1\)
Solution: https://gmatclub.com/forum/inequality-a ... ml#p653709
Graphic approach: https://gmatclub.com/forum/inequality-a ... l#p1269802
5. What is the value of y?
(1) \(3|x^2 -4| = y - 2\)
(2) \(|3 - y| = 11\)
Solution: https://gmatclub.com/forum/inequality-a ... ml#p653731
6. If x and y are integer, is y > 0?
(1) \(x +1 > 0\)
(2) \(xy > 0\)
Solution: https://gmatclub.com/forum/inequality-a ... ml#p653740
7. \(|x+2|=|y+2|\) what is the value of x+y?
(1) \(xy<0\)
(2) \(x>2\), \(y<2\)
Solution: https://gmatclub.com/forum/inequality-a ... ml#p653783 AND https://gmatclub.com/forum/inequality-a ... l#p1111747
8. \(a*b \neq 0\). Is \(\frac{|a|}{|b|}=\frac{a}{b}\)?
(1) \(|a*b|=a*b\)
(2) \(\frac{|a|}{|b|}=|\frac{a}{b}|\)
Solution: https://gmatclub.com/forum/inequality-a ... ml#p653789
9. Is n<0?
(1) \(-n=|-n|\)
(2) \(n^2=16\)
Solution: https://gmatclub.com/forum/inequality-a ... ml#p653792
10. If n is not equal to 0, is |n| < 4 ?
(1) \(n^2 > 16\)
(2) \(\frac{1}{|n|} > n\)
Solution: https://gmatclub.com/forum/inequality-a ... ml#p653796
11. Is \(|x+y|>|x-y|\)?
(1) \(|x| > |y|\)
(2) \(|x-y| < |x|\)
Solution: https://gmatclub.com/forum/inequality-a ... ml#p653853
12. Is r=s?
(1) \(-s \leq r \leq s\)
(2) \(|r| \geq s\)
Solution: https://gmatclub.com/forum/inequality-a ... ml#p653870
13. Is \(|x-1| < 1\)?
(1) \((x-1)^2 \leq 1\)
(2) \(x^2 - 1 > 0\)
Solution: https://gmatclub.com/forum/inequality-a ... ml#p653886
Official answers (OA's) and detailed solutions are in my posts on pages 2 and 3.
PLEASE READ THE WHOLE DISCUSSION BEFORE POSTING A QUESTION.
So here are some inequality and absolute value questions from my collection. Not every problem below is hard, but there are a few, which are quite tricky. Please provide your explanations along with the answers.
1. If \(6*x*y = x^2*y + 9*y\), what is the value of xy?
(1) \(y – x = 3\)
(2) \(x^3< 0\)
Solution: https://gmatclub.com/forum/inequality-a ... ml#p653690
2. If y is an integer and \(y = |x| + x\), is \(y = 0\)?
(1) \(x < 0\)
(2) \(y < 1\)
Solution: https://gmatclub.com/forum/inequality-a ... ml#p653695
3. Is \(x^2 + y^2 > 4a\)?
(1) \((x + y)^2 = 9a\)
(2) \((x – y)^2 = a\)
Solution: https://gmatclub.com/forum/inequality-a ... ml#p653697
4. Are x and y both positive?
(1) \(2x-2y=1\)
(2) \(\frac{x}{y}>1\)
Solution: https://gmatclub.com/forum/inequality-a ... ml#p653709
Graphic approach: https://gmatclub.com/forum/inequality-a ... l#p1269802
5. What is the value of y?
(1) \(3|x^2 -4| = y - 2\)
(2) \(|3 - y| = 11\)
Solution: https://gmatclub.com/forum/inequality-a ... ml#p653731
6. If x and y are integer, is y > 0?
(1) \(x +1 > 0\)
(2) \(xy > 0\)
Solution: https://gmatclub.com/forum/inequality-a ... ml#p653740
7. \(|x+2|=|y+2|\) what is the value of x+y?
(1) \(xy<0\)
(2) \(x>2\), \(y<2\)
Solution: https://gmatclub.com/forum/inequality-a ... ml#p653783 AND https://gmatclub.com/forum/inequality-a ... l#p1111747
8. \(a*b \neq 0\). Is \(\frac{|a|}{|b|}=\frac{a}{b}\)?
(1) \(|a*b|=a*b\)
(2) \(\frac{|a|}{|b|}=|\frac{a}{b}|\)
Solution: https://gmatclub.com/forum/inequality-a ... ml#p653789
9. Is n<0?
(1) \(-n=|-n|\)
(2) \(n^2=16\)
Solution: https://gmatclub.com/forum/inequality-a ... ml#p653792
10. If n is not equal to 0, is |n| < 4 ?
(1) \(n^2 > 16\)
(2) \(\frac{1}{|n|} > n\)
Solution: https://gmatclub.com/forum/inequality-a ... ml#p653796
11. Is \(|x+y|>|x-y|\)?
(1) \(|x| > |y|\)
(2) \(|x-y| < |x|\)
Solution: https://gmatclub.com/forum/inequality-a ... ml#p653853
12. Is r=s?
(1) \(-s \leq r \leq s\)
(2) \(|r| \geq s\)
Solution: https://gmatclub.com/forum/inequality-a ... ml#p653870
13. Is \(|x-1| < 1\)?
(1) \((x-1)^2 \leq 1\)
(2) \(x^2 - 1 > 0\)
Solution: https://gmatclub.com/forum/inequality-a ... ml#p653886
Official answers (OA's) and detailed solutions are in my posts on pages 2 and 3.
PLEASE READ THE WHOLE DISCUSSION BEFORE POSTING A QUESTION.
Pure algebraic questions are no longer a part of the DS syllabus of the GMAT.
DS questions in GMAT Focus encompass various types of word problems, such as:
While these questions may involve or necessitate knowledge of algebra, arithmetic, inequalities, etc., they will always be presented in the form of word problems. You won’t encounter pure "algebra" questions like, "Is x > y?" or "A positive integer n has two prime factors..."
Check GMAT Syllabus for Focus Edition
You can also visit the Data Sufficiency forum and filter questions by OG 2024-2025, GMAT Prep (Focus), and Data Insights Review 2024-2025 sources to see the types of questions currently tested on the GMAT.
So, you can ignore these question.
DS questions in GMAT Focus encompass various types of word problems, such as:
- Word Problems
- Work Problems
- Distance Problems
- Mixture Problems
- Percent and Interest Problems
- Overlapping Sets Problems
- Statistics Problems
- Combination and Probability Problems
While these questions may involve or necessitate knowledge of algebra, arithmetic, inequalities, etc., they will always be presented in the form of word problems. You won’t encounter pure "algebra" questions like, "Is x > y?" or "A positive integer n has two prime factors..."
Check GMAT Syllabus for Focus Edition
You can also visit the Data Sufficiency forum and filter questions by OG 2024-2025, GMAT Prep (Focus), and Data Insights Review 2024-2025 sources to see the types of questions currently tested on the GMAT.
So, you can ignore these question.
22 Nov 2019, 11:23
Kudos
Bookmarks
ssshyam1995
Bunuel
13. Is |x-1| < 1?
(1) (x-1)^2 <= 1
(2) x^2 - 1 > 0
Last one.
Is |x-1| < 1? Basically the question asks is 0<x<2 true?
(1) (x-1)^2 <= 1 --> x^2-2x<=0 --> x(x-2)<=0 --> 0<=x<=2. x is in the range (0,2) inclusive. This is the trick here. x can be 0 or 2! Else it would be sufficient. So not sufficient.
(2) x^2 - 1 > 0 --> x<-1 or x>1. Not sufficient.
(1)+(2) Intersection of the ranges from 1 and 2 is 1<x<=2. Again 2 is included in the range, thus as x can be 2, we cannot say for sure that 0<x<2 is true. Not sufficient.
Answer: E.
If the combination range was 1<x<2, then will correct answer be option C??(1) (x-1)^2 <= 1
(2) x^2 - 1 > 0
Last one.
Is |x-1| < 1? Basically the question asks is 0<x<2 true?
(1) (x-1)^2 <= 1 --> x^2-2x<=0 --> x(x-2)<=0 --> 0<=x<=2. x is in the range (0,2) inclusive. This is the trick here. x can be 0 or 2! Else it would be sufficient. So not sufficient.
(2) x^2 - 1 > 0 --> x<-1 or x>1. Not sufficient.
(1)+(2) Intersection of the ranges from 1 and 2 is 1<x<=2. Again 2 is included in the range, thus as x can be 2, we cannot say for sure that 0<x<2 is true. Not sufficient.
Answer: E.
Posted from my mobile device
Absolutely. In that case we'd have an YES answer to the question.
24 Nov 2019, 07:37
Kudos
Bookmarks
Bunuel
2. If y is an integer and y = |x| + x, is y = 0?
Notice that from \(y=|x|+x\) it follows that y cannot be negative:
If \(x>0\), then \(y=x+x=2x=2*positive=positive\);
If \(x\leq{0}\) (when x is negative or zero) then \(y=-x+x=0\).
(1) \(x<0\) --> \(y=|x|+x=-x+x=0\). Sufficient.
(2) \(y<1\). We found out above that y cannot be negative and we are given that y is an integer, hence \(y=0\). Sufficient.
Answer: D.
Why is it x<=0 and not x>=0??Notice that from \(y=|x|+x\) it follows that y cannot be negative:
If \(x>0\), then \(y=x+x=2x=2*positive=positive\);
If \(x\leq{0}\) (when x is negative or zero) then \(y=-x+x=0\).
(1) \(x<0\) --> \(y=|x|+x=-x+x=0\). Sufficient.
(2) \(y<1\). We found out above that y cannot be negative and we are given that y is an integer, hence \(y=0\). Sufficient.
Answer: D.
Posted from my mobile device
