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16 Nov 2009, 11:33
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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
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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
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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
