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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.
03 Oct 2012, 07:13
Kudos
Bookmarks
liarish
Hi Bunuel,
I have read all the responses to Q4. But I am still confused why C is the answer. Here is how I solved it.
4. Are x and y both positive?
(1) 2x-2y=1
(2) x/y>1
1) Insufficient . First reduced equation to x-y=0.5 . Plugged in 2 positive and 2 negative values. I chose x=3, y=2.5 => 3-2.5=0.5 works.. then chose x= -1, y=-1.5 => -1 - (-1.5)= 0.5. works again. So x and y can be both +ve and -ve. So 1) is Insufficient.
2) x/y>1. Just tells us that both x and y have same sign. both are -ve or both are +ve. So Insufficient.
Now Combining,
Picking the same values used in 1) x=3, y=2.5. both signs positive and x-y=0.5. works
then chose x= -1, y=-1.5 => -1 - (-1.5)= 0.5 both signes negative. works as well. So we still don't know if both signs are +ve or -ve. So my answer is E.
Could you please take a look at my solution and tell me where I am going wrong? That would be a big help. Thanks a ton!
I have read all the responses to Q4. But I am still confused why C is the answer. Here is how I solved it.
4. Are x and y both positive?
(1) 2x-2y=1
(2) x/y>1
1) Insufficient . First reduced equation to x-y=0.5 . Plugged in 2 positive and 2 negative values. I chose x=3, y=2.5 => 3-2.5=0.5 works.. then chose x= -1, y=-1.5 => -1 - (-1.5)= 0.5. works again. So x and y can be both +ve and -ve. So 1) is Insufficient.
2) x/y>1. Just tells us that both x and y have same sign. both are -ve or both are +ve. So Insufficient.
Now Combining,
Picking the same values used in 1) x=3, y=2.5. both signs positive and x-y=0.5. works
then chose x= -1, y=-1.5 => -1 - (-1.5)= 0.5 both signes negative. works as well. So we still don't know if both signs are +ve or -ve. So my answer is E.
Could you please take a look at my solution and tell me where I am going wrong? That would be a big help. Thanks a ton!
If x= -1 and y=-1.5, then x/y=2/3<1, so these values don't satisfy the second statement.
This question is also discussed here: are-x-and-y-both-positive-1-2x-2y-1-2-x-y-93964.html
Hope it helps.
03 Oct 2012, 12:26
Kudos
Bookmarks
Quote:
liarish wrote:
Hi Bunuel,
I have read all the responses to Q4. But I am still confused why C is the answer. Here is how I solved it.
4. Are x and y both positive?
(1) 2x-2y=1
(2) x/y>1
1) Insufficient . First reduced equation to x-y=0.5 . Plugged in 2 positive and 2 negative values. I chose x=3, y=2.5 => 3-2.5=0.5 works.. then chose x= -1, y=-1.5 => -1 - (-1.5)= 0.5. works again. So x and y can be both +ve and -ve. So 1) is Insufficient.
2) x/y>1. Just tells us that both x and y have same sign. both are -ve or both are +ve. So Insufficient.
Now Combining,
Picking the same values used in 1) x=3, y=2.5. both signs positive and x-y=0.5. works
then chose x= -1, y=-1.5 => -1 - (-1.5)= 0.5 both signes negative. works as well. So we still don't know if both signs are +ve or -ve. So my answer is E.
Could you please take a look at my solution and tell me where I am going wrong? That would be a big help. Thanks a ton!
If x= -1 and y=-1.5, then x/y=2/3<1, so these values don't satisfy the second statement.
This question is also discussed here: are-x-and-y-both-positive-1-2x-2y-1-2-x-y-93964.html
Hope it helps.
Hi Bunuel,
I have read all the responses to Q4. But I am still confused why C is the answer. Here is how I solved it.
4. Are x and y both positive?
(1) 2x-2y=1
(2) x/y>1
1) Insufficient . First reduced equation to x-y=0.5 . Plugged in 2 positive and 2 negative values. I chose x=3, y=2.5 => 3-2.5=0.5 works.. then chose x= -1, y=-1.5 => -1 - (-1.5)= 0.5. works again. So x and y can be both +ve and -ve. So 1) is Insufficient.
2) x/y>1. Just tells us that both x and y have same sign. both are -ve or both are +ve. So Insufficient.
Now Combining,
Picking the same values used in 1) x=3, y=2.5. both signs positive and x-y=0.5. works
then chose x= -1, y=-1.5 => -1 - (-1.5)= 0.5 both signes negative. works as well. So we still don't know if both signs are +ve or -ve. So my answer is E.
Could you please take a look at my solution and tell me where I am going wrong? That would be a big help. Thanks a ton!
If x= -1 and y=-1.5, then x/y=2/3<1, so these values don't satisfy the second statement.
This question is also discussed here: are-x-and-y-both-positive-1-2x-2y-1-2-x-y-93964.html
Hope it helps.
Great.. I get it now.. Thanks Bunuel.
I am also stuck at Q10 :
10. If n is not equal to 0, is |n| < 4 ?
(1) n^2 > 16
(2) 1/|n| > n
We need to see if |n|<4 (this means -4<n<4)
1) n^2>16 => n<-4 and n>4
So from n<-4, |n|<|-4| = |n|<4 (works)
But n>4 does not work.
Doesn't that make 1) Insufficient?
Could you please tell me what I am doing wrong here ??
