Find all School-related info fast with the new School-Specific MBA Forum

It is currently 23 Jul 2014, 02:44

Close

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

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Inequality and absolute value questions from my collection

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Expert Post
67 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18693
Followers: 3233

Kudos [?]: 22239 [67] , given: 2602

Inequality and absolute value questions from my collection [#permalink] New post 16 Nov 2009, 10:33
67
This post received
KUDOS
Expert's post
94
This post was
BOOKMARKED
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: inequality-and-absolute-value-questions-from-my-collection-86939-20.html#p653690

2. If y is an integer and y = |x| + x, is y = 0?
(1) x < 0
(2) y < 1

Solution: inequality-and-absolute-value-questions-from-my-collection-86939-20.html#p653695

3. Is x^2 + y^2 > 4a?
(1) (x + y)^2 = 9a
(2) (x – y)^2 = a

Solution: inequality-and-absolute-value-questions-from-my-collection-86939-40.html#p653697

4. Are x and y both positive?
(1) 2x-2y=1
(2) x/y>1

Solution: inequality-and-absolute-value-questions-from-my-collection-86939-40.html#p653709

5. What is the value of y?
(1) 3|x^2 -4| = y - 2
(2) |3 - y| = 11

Solution: inequality-and-absolute-value-questions-from-my-collection-86939-40.html#p653731

6. If x and y are integer, is y > 0?
(1) x +1 > 0
(2) xy > 0

Solution: inequality-and-absolute-value-questions-from-my-collection-86939-40.html#p653740

7. |x+2|=|y+2| what is the value of x+y?
(1) xy<0
(2) x>2 y<2

Solution: inequality-and-absolute-value-questions-from-my-collection-86939-40.html#p653783 AND inequality-and-absolute-value-questions-from-my-collection-86939-160.html#p1111747

8. a*b#0. Is |a|/|b|=a/b?
(1) |a*b|=a*b
(2) |a|/|b|=|a/b|

Solution: inequality-and-absolute-value-questions-from-my-collection-86939-40.html#p653789

9. Is n<0?
(1) -n=|-n|
(2) n^2=16

Solution: inequality-and-absolute-value-questions-from-my-collection-86939-40.html#p653792

10. If n is not equal to 0, is |n| < 4 ?
(1) n^2 > 16
(2) 1/|n| > n

Solution: inequality-and-absolute-value-questions-from-my-collection-86939-40.html#p653796

11. Is |x+y|>|x-y|?
(1) |x| > |y|
(2) |x-y| < |x|

Solution: inequality-and-absolute-value-questions-from-my-collection-86939-40.html#p653853

12. Is r=s?
(1) -s<=r<=s
(2) |r|>=s

Solution: inequality-and-absolute-value-questions-from-my-collection-86939-40.html#p653870

13. Is |x-1| < 1?
(1) (x-1)^2 <= 1
(2) x^2 - 1 > 0

Solution: inequality-and-absolute-value-questions-from-my-collection-86939-40.html#p653886

Official answers (OA's) and detailed solutions are in my posts on pages 2 and 3.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Kaplan Promo CodeKnewton GMAT Discount CodesGMAT Pill GMAT Discount Codes
Manager
Manager
avatar
Joined: 13 Dec 2009
Posts: 131
Followers: 5

Kudos [?]: 192 [0], given: 10

GMAT Tests User
Re: Inequality and absolute value questions from my collection [#permalink] New post 15 Feb 2010, 01:23
logan wrote:
xyztroy wrote:
Bunuel wrote:
3. Is x^2 + y^2 > 4a?
(1) (x + y)^2 = 9a
(2) (x – y)^2 = a

(1) (x + y)^2 = 9a --> x^2+2xy+y^2=9a. Clearly insufficient.

(2) (x – y)^2 = a --> x^2-2xy+y^2=a. Clearly insufficient.

(1)+(2) Add them up 2(x^2+y^2)=10a --> x^2+y^2=5a. Also insufficient as x,y, and a could be 0 and x^2 + y^2 > 4a won't be true, as LHS and RHS would be in that case equal to zero. Not sufficient.

Answer: E.


Hi Bunuel,

I kind of disagree with your conclusion when you combined both the stmts. If x,y, and a all are 0 then the actual question (x^2+y^2 > 4a) itself will become whether 0 > 0 ?....so I would say that the answer should be C.


hi xyztroy,

i think i can answer ur question.

in question, no limits for x and y are given, like x&y are integers or x&y are real numbers. so x and y can assume any values, including 0. but we have to conclusively show that (x^2+y^2 > 4a).
as you see, 1&2 are individually insufficient.
combining 1&2 we have (x^2+y^2 = 5a), which is definitely greater than 4a. when you substitute values for x,y and a, all values of x,y and a which satisfy (x^2+y^2 = 5a) also satisfies (x^2+y^2 > 4a), except the values x=y=a=0. so two cases arise.
hence insufficient.

answer:E

I think, when statements are given we have to answer whether based on statements given question can be answered, we should not question the validity of statements or a statements derived form the statements.
after deriving from statement 1 and 2 we deduce that x^2+y^2 =5a, this is enough to show that the question asked x^2+y^2>4a is satisfied. we are not supposed to validate whether statement x^2+y^2 =5a holds.
if u try to put x,y as 0 then just ask your self what question is trying to ask?
is 0>0.
so answer has to be C
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18693
Followers: 3233

Kudos [?]: 22239 [0], given: 2602

Re: Inequality and absolute value questions from my collection [#permalink] New post 15 Feb 2010, 05:15
Expert's post
sandeep25398 wrote:
logan wrote:
xyztroy wrote:

Hi Bunuel,

I kind of disagree with your conclusion when you combined both the stmts. If x,y, and a all are 0 then the actual question (x^2+y^2 > 4a) itself will become whether 0 > 0 ?....so I would say that the answer should be C.


hi xyztroy,

i think i can answer ur question.

in question, no limits for x and y are given, like x&y are integers or x&y are real numbers. so x and y can assume any values, including 0. but we have to conclusively show that (x^2+y^2 > 4a).
as you see, 1&2 are individually insufficient.
combining 1&2 we have (x^2+y^2 = 5a), which is definitely greater than 4a. when you substitute values for x,y and a, all values of x,y and a which satisfy (x^2+y^2 = 5a) also satisfies (x^2+y^2 > 4a), except the values x=y=a=0. so two cases arise.
hence insufficient.

answer:E

I think, when statements are given we have to answer whether based on statements given question can be answered, we should not question the validity of statements or a statements derived form the statements.
after deriving from statement 1 and 2 we deduce that x^2+y^2 =5a, this is enough to show that the question asked x^2+y^2>4a is satisfied. we are not supposed to validate whether statement x^2+y^2 =5a holds.
if u try to put x,y as 0 then just ask your self what question is trying to ask?
is 0>0.
so answer has to be C


Is x^2 + y^2 > 4a?
(1) (x+y)^2 = 9a
(2) (x-y)^2 = a

Consider two cases:

1. x=2, y=1 and a=1. These values satisfy both statements and the answer to the question "is x^2+y^2>4a true" is YES, as 5>4 is true. (Note here that these values naturally satisfy x^2+y^2=5a too)

2. x=0, y=0 and a=0. These values ALSO satisfy both statements and the answer to the question "is x^2+y^2>4a true" is NO, as LHS is 0, RHS is also 0 and 0>0 is NOT TRUE. (Note here that these values naturally satisfy x^2+y^2=5a too)

Two different answers. Not sufficient.

Answer: E.

So question is not asking whether 0>0. Question is asking whether "x^2+y^2>4a true". We got that for smoe values YES and for some values NO.

Hope it's clear.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 13 Dec 2009
Posts: 131
Followers: 5

Kudos [?]: 192 [0], given: 10

GMAT Tests User
Re: Inequality and absolute value questions from my collection [#permalink] New post 16 Feb 2010, 05:37
answer:E[/quote]
I think, when statements are given we have to answer whether based on statements given question can be answered, we should not question the validity of statements or a statements derived form the statements.
after deriving from statement 1 and 2 we deduce that x^2+y^2 =5a, this is enough to show that the question asked x^2+y^2>4a is satisfied. we are not supposed to validate whether statement x^2+y^2 =5a holds.
if u try to put x,y as 0 then just ask your self what question is trying to ask?
is 0>0.
so answer has to be C[/quote]

Is x^2 + y^2 > 4a?
(1) (x+y)^2 = 9a
(2) (x-y)^2 = a

Consider two cases:

1. x=2, y=1 and a=1. These values satisfy both statements and the answer to the question "is x^2+y^2>4a true" is YES, as 5>4 is true. (Note here that these values naturally satisfy x^2+y^2=5a too)

2. x=0, y=0 and a=0. These values ALSO satisfy both statements and the answer to the question "is x^2+y^2>4a true" is NO, as LHS is 0, RHS is also 0 and 0>0 is NOT TRUE. (Note here that these values naturally satisfy x^2+y^2=5a too)

Two different answers. Not sufficient.

Answer: E.

So question is not asking whether 0>0. Question is asking whether "x^2+y^2>4a true". We got that for smoe values YES and for some values NO.

Hope it's clear.[/quote]
yes Bunuel, it helped.. thank you for such amazing collections..and explanations
Intern
Intern
avatar
Joined: 01 Feb 2010
Posts: 34
Followers: 1

Kudos [?]: 17 [0], given: 12

Re: Inequality and absolute value questions from my collection [#permalink] New post 17 Feb 2010, 22:19
Bunuel wrote:
GMATMadeeasy wrote:
How do you conclude A here can't make out or I am tired.; anyways, it is mental marathon :) .. wonderful questions Bunuel. Any more link for inequality as I need some more practise .


We have -s<=r<=s --> -s<=s. Now if s in negative, let's say -2, then we would have -(-2)<=-2 --> 2<=-2, which is not right. Hence s can not be negative. But s can be zero --> 0<=0, true.

You can't write it this way. -s<=r<=s means that either r lies between s & -s or r is equal to -s or r can be equal to s. But this certainly doesn't mean that you can equate -s<=s.

If I say that -4<=x<=4. This doesn't mean that I can write -4<=4.

But in any case the answer you've arrived at is correct. We can't derive anything out of the first statement as it says that -s<=r<=s. r can be anything -s or s or between -s & s.

Second says that lrl>=s ---> r>=s or r<=-s. This again is not giving any specific value.

If we combine the two we get that either r=s or r=-s. This is closer but still ambiguous. So we don't know whether r=s. Therefore, answer is E.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18693
Followers: 3233

Kudos [?]: 22239 [0], given: 2602

Re: Inequality and absolute value questions from my collection [#permalink] New post 18 Feb 2010, 07:22
Expert's post
honeyrai wrote:
Bunuel wrote:
GMATMadeeasy wrote:
How do you conclude A here can't make out or I am tired.; anyways, it is mental marathon :) .. wonderful questions Bunuel. Any more link for inequality as I need some more practise .


We have -s<=r<=s --> -s<=s. Now if s in negative, let's say -2, then we would have -(-2)<=-2 --> 2<=-2, which is not right. Hence s can not be negative. But s can be zero --> 0<=0, true.


You can't write it this way. -s<=r<=s means that either r lies between s & -s or r is equal to -s or r can be equal to s. But this certainly doesn't mean that you can equate -s<=s.

If I say that -4<=x<=4. This doesn't mean that I can write -4<=4.

But in any case the answer you've arrived at is correct. We can't derive anything out of the first statement as it says that -s<=r<=s. r can be anything -s or s or between -s & s.


First of all: you are excluding the possibility when -s=r=s=0.

-s<=r<=s, so -s can be equal to s, when s=0. In all other cases -s will be less than s, so there is nothing wrong in writing this as -s<=s.

Second of all: we CAN conclude one more thing from this statement: s is either positive or zero.

Here is what I wrote in my solution from page 3:

(1) -s<=r<=s, we can conclude two things from this statement:
A. s is either positive or zero, as -s<=s;
B. r is in the range (-s,s) inclusive, meaning that r can be -s as well as s.
But we don't know whether r=s or not. Not sufficient.

(2) |r|>=s, clearly insufficient.

(1)+(2) -s<=r<=s, s is not negative, |r|>=s --> r>=s or r<=-s. This doesn't imply that r=s, from this r can be -s as well.
Consider: s=5, r=5 --> -5<=5<=5 |5|>=5
s=5, r=-5 --> -5<=-5<=5 |-5|>=5
Both statements are true with these values. Hence insufficient.

Answer: E.

Hope it's clear.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 01 Feb 2010
Posts: 34
Followers: 1

Kudos [?]: 17 [0], given: 12

Re: Inequality and absolute value questions from my collection [#permalink] New post 18 Feb 2010, 21:02
Yes, you are right. Good explanation.
Senior Manager
Senior Manager
User avatar
Joined: 22 Dec 2009
Posts: 365
Followers: 10

Kudos [?]: 196 [0], given: 47

GMAT ToolKit User GMAT Tests User
Re: Inequality and absolute value questions from my collection [#permalink] New post 20 Feb 2010, 07:10
sriharimurthy wrote:
Quote:
13. Is |x-1| < 1?
(1) (x-1)^2 <= 1
(2) x^2 - 1 > 0


Question Stem : Is |x-1| < 1 ?
When x > 1 ; x - 1 < 1 ; x < 2.
When x < 1 ; -x + 1 < 1 ; x > 0.
Thus it can be written as : 0 < x < 2.

St. (1) : (x-1)^2 <= 1
x^2 + 1 - 2x <= 1
x^2 - 2x <= 0
x(x - 2) <= 0 ; Thus boundary values are 0 and 2.
Therefore statement can be written as : 0 <= x <= 2.
Since the values are inclusive of 0 and 2, it cannot give us the answer.
Insufficient.

St. (2) : x^2 - 1 > 0
(x + 1)*(x - 1) > 0
Statement can be written as x > 1 and x < -1.
Thus it is possible for x to hold values which make the question stem true as well as false.
Insufficient.

St. (1) and (2) : 0 <= x <= 2 ; x > 1 and x < -1
Thus combined, the statements become : 1 < x <= 2.
Since it is inclusive of 2, it will give us conflicting solutions for the question stem.
Hence Insufficient.

Answer : E


How do u get these boundary values. Looking at the equation, I solved it as x(x-2)<=0.... which gives x<=0 or x<=2... I know this isnt correct but can u let me know how u got... x>=0 & x <=2... Thanks :oops:

_________________

Cheers!
JT...........
If u like my post..... payback in Kudos!! :beer

|Do not post questions with OA|Please underline your SC questions while posting|Try posting the explanation along with your answer choice|
|For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|


~~Better Burn Out... Than Fade Away~~

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18693
Followers: 3233

Kudos [?]: 22239 [0], given: 2602

Re: Inequality and absolute value questions from my collection [#permalink] New post 20 Feb 2010, 09:47
Expert's post
jeeteshsingh wrote:
sriharimurthy wrote:
Quote:
13. Is |x-1| < 1?
(1) (x-1)^2 <= 1
(2) x^2 - 1 > 0


Question Stem : Is |x-1| < 1 ?
When x > 1 ; x - 1 < 1 ; x < 2.
When x < 1 ; -x + 1 < 1 ; x > 0.
Thus it can be written as : 0 < x < 2.

St. (1) : (x-1)^2 <= 1
x^2 + 1 - 2x <= 1
x^2 - 2x <= 0
x(x - 2) <= 0 ; Thus boundary values are 0 and 2.
Therefore statement can be written as : 0 <= x <= 2.
Since the values are inclusive of 0 and 2, it cannot give us the answer.
Insufficient.

St. (2) : x^2 - 1 > 0
(x + 1)*(x - 1) > 0
Statement can be written as x > 1 and x < -1.
Thus it is possible for x to hold values which make the question stem true as well as false.
Insufficient.

St. (1) and (2) : 0 <= x <= 2 ; x > 1 and x < -1
Thus combined, the statements become : 1 < x <= 2.
Since it is inclusive of 2, it will give us conflicting solutions for the question stem.
Hence Insufficient.

Answer : E


How do u get these boundary values. Looking at the equation, I solved it as x(x-2)<=0.... which gives x<=0 or x<=2... I know this isnt correct but can u let me know how u got... x>=0 & x <=2... Thanks :oops:


"Boundary values" are the roots of the equation x(x-2)=0 --> x=0 and x=2.

I use "parabola approach" for this kind of quadratic inequalities. Basically as x(x-2)=0 is an equation of upward parabola, x(x-2)\leq{0} (x^2-2x\leq{0}) is the part of the parabola, which does not lie above the X-axis. Parabola x(x-2)\leq{0} does not lie above the X-axis for the values of x in the range 0\leq{x}\leq{2}. If you plug the values from this range you'll see that inequality, x(x-2)\leq{0}, holds true for them.

Consider inequality (x-3)(x-7)>{0} (or x^2-10x+21>0). This is also upward parabola (as the coefficient of x^2 is positive), with boundary values x=3 and x=7. We want to determine for which value of x, this parabola is above (as we have > sign) the X-axis. The answer would be x<3 and x>7.

OR:

(7+x)(3-x)>0 (or -x^2-4x+21>0), this would be downward parabola, with boundary values x=-7 and x=3. This parabola lies above the X-axis for -7<x<3. We can also write this as x^2+4x-21<0 (or (7+x)(x-3)<0), this would be upward parabola, with the same boundary values: x=-7 and x=3. This parabola lies below the X-axis for -7<x<3, the same range as it should be.

Hope it helps.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 20 Jan 2010
Posts: 7
Followers: 0

Kudos [?]: 0 [0], given: 1

Re: Inequality and absolute value questions from my collection [#permalink] New post 22 Feb 2010, 22:25
Hi

Could someone let me know what are the final answers. I am confused since there are many posts and corrections to them too.

Thanks
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18693
Followers: 3233

Kudos [?]: 22239 [0], given: 2602

Re: Inequality and absolute value questions from my collection [#permalink] New post 23 Feb 2010, 07:33
Expert's post
guytree wrote:
Hi

Could someone let me know what are the final answers. I am confused since there are many posts and corrections to them too.

Thanks


OA-s and solutions are given in my posts on pages 2 and 3.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 04 May 2009
Posts: 132
Location: London
Schools: Haas (WL), Kellogg (matricultating), Stanford (R2, ding), Columbia (ding)
WE 1: 3 years hotel industry sales and marketing France
WE 2: 3 years financial industry marketing UK
Followers: 2

Kudos [?]: 18 [0], given: 10

Re: Inequality and absolute value questions from my collection [#permalink] New post 04 May 2010, 11:44
Bunuel wrote:
5. What is the value of y?
(1) 3|x^2 -4| = y - 2
(2) |3 - y| = 11

(1) As we are asked to find the value of y, from this statement we can conclude only that y>=2, as LHS is absolute value which is never negative, hence RHS als can not be negative. Not sufficient.

(2) |3 - y| = 11:

y<3 --> 3-y=11 --> y=-8
y>=3 --> -3+y=11 --> y=14

Two values for y. Not sufficient.

(1)+(2) y>=2, hence y=14. Sufficient.

Answer: C.



Bunuel,

Thanks so much for all these questions and explanations!

I'm having troubles to understand the quoted question. I don't understand your explanation for statement 1, it seems like a great way to solve this problem quickly but I really just don't understand how you get there.

From this 3|x^2 -4| = y - 2 how can you conclude that y must be >=2 ?

Thx for the help!

_________________

Yes I can!

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18693
Followers: 3233

Kudos [?]: 22239 [0], given: 2602

Re: Inequality and absolute value questions from my collection [#permalink] New post 04 May 2010, 12:30
Expert's post
nifoui wrote:
Bunuel wrote:
5. What is the value of y?
(1) 3|x^2 -4| = y - 2
(2) |3 - y| = 11

(1) As we are asked to find the value of y, from this statement we can conclude only that y>=2, as LHS is absolute value which is never negative, hence RHS als can not be negative. Not sufficient.

(2) |3 - y| = 11:

y<3 --> 3-y=11 --> y=-8
y>=3 --> -3+y=11 --> y=14

Two values for y. Not sufficient.

(1)+(2) y>=2, hence y=14. Sufficient.

Answer: C.



Bunuel,

Thanks so much for all these questions and explanations!

I'm having troubles to understand the quoted question. I don't understand your explanation for statement 1, it seems like a great way to solve this problem quickly but I really just don't understand how you get there.

From this 3|x^2 -4| = y - 2 how can you conclude that y must be >=2 ?

Thx for the help!


3|x^2 -4| = y - 2 --> Left hand side (LHS) is an expression with absolute value, absolute value is never negative (|expression|\geq{0}) --> 3|x^2-4|\geq{0}. So as LHS\geq{0}, then RHS also must be more than zero (RHS\geq{0}) --> y-2\geq{0} --> y\geq{2}.

Hope it's clear.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 04 May 2009
Posts: 132
Location: London
Schools: Haas (WL), Kellogg (matricultating), Stanford (R2, ding), Columbia (ding)
WE 1: 3 years hotel industry sales and marketing France
WE 2: 3 years financial industry marketing UK
Followers: 2

Kudos [?]: 18 [0], given: 10

Re: Inequality and absolute value questions from my collection [#permalink] New post 04 May 2010, 12:39
Great!! Thanks Bunuel for the very clear explanation!

_________________

Yes I can!

Intern
Intern
avatar
Joined: 11 Oct 2009
Posts: 26
Followers: 0

Kudos [?]: 2 [0], given: 6

Re: Inequality and absolute value questions from my collection [#permalink] New post 12 May 2010, 08:47
awesome questions .. thought I've improved a lot in DS .. however these questions broke my misconception .. need to work hard ..

lemme know guys, how many of ur answers were correct ? I scored only 4 correct out of 13...
Manager
Manager
avatar
Joined: 16 Feb 2010
Posts: 175
Followers: 2

Kudos [?]: 10 [0], given: 10

GMAT Tests User
Re: Inequality and absolute value questions from my collection [#permalink] New post 15 May 2010, 11:09
great collection !!1 thanks bunuel !!
Intern
Intern
avatar
Joined: 12 Mar 2010
Posts: 25
Followers: 0

Kudos [?]: 5 [0], given: 4

Re: Inequality and absolute value questions from my collection [#permalink] New post 21 May 2010, 01:37
Bunuel wrote:
4. Are x and y both positive?
(1) 2x-2y=1
(2) x/y>1

(1) 2x-2y=1. Well this one is clearly insufficient. You can do it with number plugging OR consider the following: x and y both positive means that point (x,y) is in the I quadrant. 2x-2y=1 --> y=x-1/2, we know it's an equation of a line and basically question asks whether this line (all (x,y) points of this line) is only in I quadrant. It's just not possible. Not sufficient.

(2) x/y>1 --> x and y have the same sign. But we don't know whether they are both positive or both negative. Not sufficient.

(1)+(2) Again it can be done with different approaches. You should just find the one which is the less time-consuming and comfortable for you personally.

One of the approaches:
2x-2y=1 --> x=y+\frac{1}{2}
\frac{x}{y}>1 --> \frac{x-y}{y}>0 --> substitute x --> \frac{1}{y}>0 --> y is positive, and as x=y+\frac{1}{2}, x is positive too. Sufficient.

Answer: C.


I am a little confused on this one . Can the answer be E??

From A:
2x-2y=1
=> x-y= 0.5 INSF

From B
x/y > 1
=> x > y INSF

From A & B
x-y =0.5 and x > y

If x = -0.5 and y = -1 then
x > y
and x - y = (-0.5) - (-1) = -0.5 + 1 = 0.5
Hence both x and y can be negative

If x= 1 and y = 0.5 then
x > y
and x- y = 1 -0.5 = 0.5
Hence both x and y can be positive

Ans = E ??
Intern
Intern
avatar
Joined: 12 Mar 2010
Posts: 25
Followers: 0

Kudos [?]: 5 [0], given: 4

Re: Inequality and absolute value questions from my collection [#permalink] New post 21 May 2010, 02:21
Bunuel wrote:
ManishS wrote:
I am a little confused on this one . Can the answer be E??

From A:
2x-2y=1
=> x-y= 0.5 INSF

From B
x/y > 1
=> x > y INSF

From A & B
x-y =0.5 and x > y

If x = -0.5 and y = -1 then
x > y
and x - y = (-0.5) - (-1) = -0.5 + 1 = 0.5
Hence both x and y can be negative

If x= 1 and y = 0.5 then
x > y
and x- y = 1 -0.5 = 0.5
Hence both x and y can be positive

Ans = E ??


Problem with your solution is that the red part is not correct.

\frac{x}{y}>1 does not mean that x>y. If both x and y are positive, then x>y, BUT if both are negative, then x<y.

From (2) \frac{x}{y}>1, we can only deduce that x and y have the same sigh (either both positive or both negative).

When we consider two statement together:

From (1): 2x-2y=1 --> x=y+\frac{1}{2}

From (2): \frac{x}{y}>1 --> \frac{x}{y}-1>0 --> \frac{x-y}{y}>0 --> substitute x from (1) --> \frac{y+\frac{1}{2}-y}{y}>0--> \frac{1}{2y}>0 (we can drop 2 as it won't affect anything here and write as I wrote \frac{1}{y}>0, but basically it's the same) --> \frac{1}{2y}>0 means y is positive, and from (2) we know that if y is positive x must also be positive.

OR: as y is positive and as from (1) x=y+\frac{1}{2}, x=positive+\frac{1}{2}=positive, hence x is positive too.

Answer: C.

Hope it's clear.

:o :oops:
Thank you so much. This really was helpful. :-)
Manager
Manager
avatar
Joined: 04 Dec 2009
Posts: 72
Location: INDIA
Followers: 2

Kudos [?]: 9 [0], given: 4

Re: Inequality and absolute value questions from my collection [#permalink] New post 14 Jun 2010, 21:47
h2polo wrote:
Bunuel wrote:
2. If y is an integer and y = |x| + x, is y = 0?
(1) x < 0
(2) y < 1


Another way of looking at the problem is to ask, is x<0? Because if it is, then we know that y is zero. The only case in which y will not be zero is if x is positive.

Statement 1:

x<0... answers my question above.

SUFFICIENT

Statement 2:

y<1

Because y is an integer, it must be one of the following values: 0, -1, -2, -3...

BUT |x| + x can never be a negative value. The lowest value that it can be is 0.

Hence, y can never be negative and the only possible value it can be then is 0.

SUFFICIENT

ANSWER: D.

----------------------------
hear it is not give that X is also a integer,

S1: if X=1/2 or -1/2 then also Y is integer ,

in this case Ans: B

Is i am missing somthing?

_________________

MBA (Mind , Body and Attitude )

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18693
Followers: 3233

Kudos [?]: 22239 [0], given: 2602

Re: Inequality and absolute value questions from my collection [#permalink] New post 15 Jun 2010, 12:54
Expert's post
varun2410 wrote:
----------------------------
hear it is not give that X is also a integer,

S1: if X=1/2 or -1/2 then also Y is integer ,

in this case Ans: B

Is i am missing somthing?


OA' s and solutions for all the problems are given in my posts on pages 2 and 3.

OA for this question is D. Below is solution for it.

2. If y is an integer and y = |x| + x, is y = 0?
(1) x < 0
(2) y < 1

Note: y=|x|+x, this expression is never negative. For x>{0} then y=x+x=2x and for x\leq{0} then (when x is negative or zero) then y=-x+x=0.

(1) x<0 --> y=|x|+x=-x+x=0. Sufficient.

(2) y<1, as we concluded y is never negative, and we are given that y is an integer, hence y=0. Sufficient.

Answer: D.

Hope it's clear.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Affiliations: CFA
Joined: 09 Dec 2009
Posts: 37
Schools: Columbia Business School '13
Followers: 0

Kudos [?]: 2 [0], given: 1

Re: Inequality and absolute value questions from my collection [#permalink] New post 16 Jun 2010, 14:07
3. is X^2+Y^2 > 4a?

1) (X+Y)^2= 9a

x^2+2xy+Y^2=9a

Insufficient

2) (X-y)^2= a

x^2-2XY+Y^2 = a

Insufficient

Combining 1 & 2, 2(X^2+Y^2)=10a X^2+Y^2 = 5a, thus C
Re: Inequality and absolute value questions from my collection   [#permalink] 16 Jun 2010, 14:07
    Similar topics Author Replies Last post
Similar
Topics:
2 Inequalities and Absolute value Question Bank gmatsheeba 0 18 Sep 2013, 05:59
1 Experts publish their posts in the topic Good Inequality with absolute value question u0422811 3 22 May 2011, 19:32
1 Inequality involving absolute values english_august 5 08 Nov 2007, 16:14
Inequality and absolute values Futuristic 4 25 Jun 2006, 16:08
Another DS from GMATPrep -- Absolute Value Inequalities lackeym77 7 10 May 2006, 14:31
Display posts from previous: Sort by

Inequality and absolute value questions from my collection

  Question banks Downloads My Bookmarks Reviews Important topics  

Go to page   Previous    1  ...  3   4   5   6   7   8   9   10   11  ...  16    Next  [ 312 posts ] 



GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.