Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 45305

Inequality and absolute value questions from my collection [#permalink]
Show Tags
16 Nov 2009, 11:33
176
This post received KUDOS
Expert's post
514
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: http://gmatclub.com/forum/inequalityan ... ml#p6536902. If y is an integer and \(y = x + x\), is \(y = 0\)? (1) \(x < 0\) (2) \(y < 1\) Solution: http://gmatclub.com/forum/inequalityan ... ml#p6536953. Is \(x^2 + y^2 > 4a\)?(1) \((x + y)^2 = 9a\) (2) \((x – y)^2 = a\) Solution: http://gmatclub.com/forum/inequalityan ... ml#p6536974. Are x and y both positive?(1) \(2x2y=1\) (2) \(\frac{x}{y}>1\) Solution: http://gmatclub.com/forum/inequalityan ... ml#p653709 Graphic approach: https://gmatclub.com/forum/inequalitya ... l#p12698025. What is the value of y?(1) \(3x^2 4 = y  2\) (2) \(3  y = 11\) Solution: http://gmatclub.com/forum/inequalityan ... ml#p6537316. If x and y are integer, is y > 0? (1) \(x +1 > 0\) (2) \(xy > 0\) Solution: http://gmatclub.com/forum/inequalityan ... ml#p6537407. \(x+2=y+2\) what is the value of x+y?(1) \(xy<0\) (2) \(x>2\), \(y<2\) Solution: http://gmatclub.com/forum/inequalityan ... ml#p653783 AND https://gmatclub.com/forum/inequalitya ... l#p11117478. \(a*b \neq 0\). Is \(\frac{a}{b}=\frac{a}{b}\)?(1) \(a*b=a*b\) (2) \(\frac{a}{b}=\frac{a}{b}\) Solution: http://gmatclub.com/forum/inequalityan ... ml#p6537899. Is n<0?(1) \(n=n\) (2) \(n^2=16\) Solution: http://gmatclub.com/forum/inequalityan ... ml#p65379210. If n is not equal to 0, is n < 4 ?(1) \(n^2 > 16\) (2) \(\frac{1}{n} > n\) Solution: http://gmatclub.com/forum/inequalityan ... ml#p65379611. Is \(x+y>xy\)?(1) \(x > y\) (2) \(xy < x\) Solution: http://gmatclub.com/forum/inequalityan ... ml#p65385312. Is r=s?(1) \(s \leq r \leq s\) (2) \(r \geq s\) Solution: http://gmatclub.com/forum/inequalityan ... ml#p65387013. Is \(x1 < 1\)?(1) \((x1)^2 \leq 1\) (2) \(x^2  1 > 0\) Solution: http://gmatclub.com/forum/inequalityan ... ml#p653886Official answers (OA's) and detailed solutions are in my posts on pages 2 and 3.PLEASE READ THE WHOLE DISCUSSION BEFORE POSTING A QUESTION.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 08 Nov 2009
Posts: 46

Re: Inequality and absolute value questions from my collection [#permalink]
Show Tags
Updated on: 17 Nov 2009, 10:57
ichha148 wrote: 12. Is r=s?
(1) s<=r<=s
(2) r>=s
E – for this  both can be true or false when 0< r < 1 For example , take r as 0.8 S = 0.86 i.e. 0.86 < = 0.8 < = 0.86 0.8>= 0.86 i.e. 1 >= 0.86 Combining , any values can be taken , on values > =1 , both r and s will be same Taking the modulus does not mean rounding up to the nearest integer; it means removing the negative sign if present. 0.8<0.86 ichha148 wrote: 3. Is x^2 + y^2 > 4a?
(1) (x + y)^2 = 9a
(2) (x – y)^2 = a C is the answer
Combined both and the equation will give x^2 + y^2 = 5a Nowhere it is said that x and y are nonzero. If x and y are zero, 5a=0, therefore a=0, and the stem is false (x^2+y^2=0)
Originally posted by Marco83 on 17 Nov 2009, 10:54.
Last edited by Marco83 on 17 Nov 2009, 10:57, edited 1 time in total.



Manager
Joined: 29 Oct 2009
Posts: 197

Re: Inequality and absolute value questions from my collection [#permalink]
Show Tags
17 Nov 2009, 13:41
Quote: 1. If 6*x*y = x^2*y + 9*y, what is the value of xy? (1) y – x = 3 (2) x^3< 0 \(6*x*y = x^2*y + 9*y\) \(6*x = x^2 + 9 = 0\) \(x^2  6*x + 9 = 0\) \((x3)^2 = 0\) \(x = 3\) St. (1) : y  x = 3
y = 6 Sufficient. St. (2) : x^3 < 0
Invalid statement. Does not give us value of y. Insufficient. Answer : A
_________________
Click below to check out some great tips and tricks to help you deal with problems on Remainders! http://gmatclub.com/forum/compilationoftipsandtrickstodealwithremainders86714.html#p651942
Word Problems Made Easy! 1) Translating the English to Math : http://gmatclub.com/forum/wordproblemsmadeeasy87346.html 2) 'Work' Problems Made Easy : http://gmatclub.com/forum/workwordproblemsmadeeasy87357.html 3) 'Distance/Speed/Time' Word Problems Made Easy : http://gmatclub.com/forum/distancespeedtimewordproblemsmadeeasy87481.html



Manager
Joined: 29 Oct 2009
Posts: 197

Re: Inequality and absolute value questions from my collection [#permalink]
Show Tags
17 Nov 2009, 13:47
1
This post received KUDOS
Quote: 2. If y is an integer and y = x + x, is y = 0? (1) x < 0 (2) y < 1 Question Stem gives us :
(a) If x > 0 ; y = 2x (b) If x < 0 ; y = 0 St. (1) : x < 0
Sufficient. St. (2) : y < 1
Since y is an integer and y cannot be less than 0 (question stem part b) therefore y must be 0. Sufficient. Answer : D
_________________
Click below to check out some great tips and tricks to help you deal with problems on Remainders! http://gmatclub.com/forum/compilationoftipsandtrickstodealwithremainders86714.html#p651942
Word Problems Made Easy! 1) Translating the English to Math : http://gmatclub.com/forum/wordproblemsmadeeasy87346.html 2) 'Work' Problems Made Easy : http://gmatclub.com/forum/workwordproblemsmadeeasy87357.html 3) 'Distance/Speed/Time' Word Problems Made Easy : http://gmatclub.com/forum/distancespeedtimewordproblemsmadeeasy87481.html



Manager
Joined: 29 Oct 2009
Posts: 197

Re: Inequality and absolute value questions from my collection [#permalink]
Show Tags
17 Nov 2009, 13:54
1
This post received KUDOS
Quote: 3. Is x^2 + y^2 > 4a? (1) (x + y)^2 = 9a (2) (x – y)^2 = a St. (1) : (x + y)^2 = 9a
x^2 + y^2 + 2xy = 9a Insufficient. St. (2) : (x  y)^2 = a
x^2 + y^2  2xy = a Insufficient. St. (1) and (2) together : x^2 + y^2 = 5a
When either x or y is not 0, question stem holds true. When x and y are both 0, question stem is false. Hence insufficient. Answer : E
_________________
Click below to check out some great tips and tricks to help you deal with problems on Remainders! http://gmatclub.com/forum/compilationoftipsandtrickstodealwithremainders86714.html#p651942
Word Problems Made Easy! 1) Translating the English to Math : http://gmatclub.com/forum/wordproblemsmadeeasy87346.html 2) 'Work' Problems Made Easy : http://gmatclub.com/forum/workwordproblemsmadeeasy87357.html 3) 'Distance/Speed/Time' Word Problems Made Easy : http://gmatclub.com/forum/distancespeedtimewordproblemsmadeeasy87481.html



Manager
Joined: 29 Oct 2009
Posts: 197

Re: Inequality and absolute value questions from my collection [#permalink]
Show Tags
17 Nov 2009, 14:01
Quote: 4. Are x and y both positive? (1) 2x2y=1 (2) x/y>1 Question Stem : x > 0 ; y > 0 ? St. (1) : 2x 2y = 1
x = y + 0.5 Equation can be satisfied for both positive and negative values of x and y. Hence Insufficient. St. (2) : x/y > 1
Equation can be satisfied when both x and y are either positive or negative. Hence Insufficient. St. (1) and (2) together : (y + 0.5)/y > 1
1 + 0.5/y > 1 0.5/y > 1 For this to be true, y must be positive. If y is positive then x will also be positive. Hence Sufficient. Answer : C
_________________
Click below to check out some great tips and tricks to help you deal with problems on Remainders! http://gmatclub.com/forum/compilationoftipsandtrickstodealwithremainders86714.html#p651942
Word Problems Made Easy! 1) Translating the English to Math : http://gmatclub.com/forum/wordproblemsmadeeasy87346.html 2) 'Work' Problems Made Easy : http://gmatclub.com/forum/workwordproblemsmadeeasy87357.html 3) 'Distance/Speed/Time' Word Problems Made Easy : http://gmatclub.com/forum/distancespeedtimewordproblemsmadeeasy87481.html



Manager
Joined: 29 Oct 2009
Posts: 197

Re: Inequality and absolute value questions from my collection [#permalink]
Show Tags
17 Nov 2009, 14:10
Quote: 5. What is the value of y? (1) 3x^2 4 = y  2 (2) 3  y = 11 Question stem : What is the exact value of y? St. (1) : 3*x^2 4 = y  2
y = 3*x^2 4 + 2 From this we can infer that y will be a positive value. That is, y > 0. However, we want to know the exact value of y. Therefore, Insufficient. St. (2) : 3  y = 11
(a) When (3  y) > 0 ; 3  y = 11 ; y = 8. (b) When (3  y) < 0 ;  (3  y) = 11 ; y = 14. Thus we can see that there are two possible values for y. Hence Insufficient. St. (1) and (2) together : y > 0 ; y = 14 or 8.
Obviously since y has to be greater than 0, it cannot be 8. Therefore value of y = 14. Hence Sufficient. Answer : C
_________________
Click below to check out some great tips and tricks to help you deal with problems on Remainders! http://gmatclub.com/forum/compilationoftipsandtrickstodealwithremainders86714.html#p651942
Word Problems Made Easy! 1) Translating the English to Math : http://gmatclub.com/forum/wordproblemsmadeeasy87346.html 2) 'Work' Problems Made Easy : http://gmatclub.com/forum/workwordproblemsmadeeasy87357.html 3) 'Distance/Speed/Time' Word Problems Made Easy : http://gmatclub.com/forum/distancespeedtimewordproblemsmadeeasy87481.html



Manager
Joined: 29 Oct 2009
Posts: 197

Re: Inequality and absolute value questions from my collection [#permalink]
Show Tags
17 Nov 2009, 14:16
1
This post received KUDOS
Quote: 6. If x and y are integer, is y > 0? (1) x +1 > 0 (2) xy > 0 St. (1) : x + 1 > 0
Tells us nothing about y. Insufficient. St. (2) : xy > 0
Both x and y can either be positive or negative. Neither x nor y can be 0. Insufficient. St. (1) and (2) together :
Since x is an integer and cannot hold the value 0, it has to be greater than 1 in order to satisfy St. (1). Since we know that x will be positive, y will also have to be a positive integer in order to satisfy St. (2). Hence Sufficient. Answer : C
_________________
Click below to check out some great tips and tricks to help you deal with problems on Remainders! http://gmatclub.com/forum/compilationoftipsandtrickstodealwithremainders86714.html#p651942
Word Problems Made Easy! 1) Translating the English to Math : http://gmatclub.com/forum/wordproblemsmadeeasy87346.html 2) 'Work' Problems Made Easy : http://gmatclub.com/forum/workwordproblemsmadeeasy87357.html 3) 'Distance/Speed/Time' Word Problems Made Easy : http://gmatclub.com/forum/distancespeedtimewordproblemsmadeeasy87481.html



Manager
Joined: 29 Oct 2009
Posts: 197

Re: Inequality and absolute value questions from my collection [#permalink]
Show Tags
17 Nov 2009, 14:43
1
This post received KUDOS
3
This post was BOOKMARKED
Quote: 7. x+2=y+2 what is the value of x+y? (1) xy<0 (2) x>2 y<2 Question stem :
Note: Since the equations is symmetrical, there will only be two distinct cases. However, for the sake of explanation, I have illustrated all 4. (a) When both x and y are greater than  2 ; x + 2 = y + 2 ; x = y (b) When both x and y are less than  2 ;  x  2 =  y  2 ; x = y (c) When x is less than 2 and y is greater than 2 ;  x  2 = y + 2 ; x + y =  4 (d) When x is greater than 2 and y is less than 2 ; x + 2 =  y  2 ; x + y =  4 St. (1) : xy < 0
This implies that one is negative and the other is positive. Therefore, in order for xy to be less than 0, x cannot be equal to y. Thus in order to satisfy the question stem, it can only be cases (c) and (d). Thus Sufficient. St. (2) : x > 2 ; y < 2
Again, this implies that x and y cannot be equal. Thus, in order to satisfy the question stem it can only be cases (c) and (d). Thus Sufficient. Answer : D
_________________
Click below to check out some great tips and tricks to help you deal with problems on Remainders! http://gmatclub.com/forum/compilationoftipsandtrickstodealwithremainders86714.html#p651942
Word Problems Made Easy! 1) Translating the English to Math : http://gmatclub.com/forum/wordproblemsmadeeasy87346.html 2) 'Work' Problems Made Easy : http://gmatclub.com/forum/workwordproblemsmadeeasy87357.html 3) 'Distance/Speed/Time' Word Problems Made Easy : http://gmatclub.com/forum/distancespeedtimewordproblemsmadeeasy87481.html



Manager
Joined: 29 Oct 2009
Posts: 197

Re: Inequality and absolute value questions from my collection [#permalink]
Show Tags
17 Nov 2009, 14:48
Quote: 8. a*b#0. Is a/b=a/b? (1) a*b=a*b (2) a/b=a/b Question stem : Neither a nor b can hold the value 0 ; a/b=a/b
For condition to be true, both a and b must hold the same sign. St. (1) : a*b = a*b
This condition will be satisfied only when both a and b are either both positive or both negative. Hence Sufficient. St. (2) : a/b = a/b
This condition can be satisfied when a and b are same sign as well as opposite sign. Hence Insufficient. Answer : A
_________________
Click below to check out some great tips and tricks to help you deal with problems on Remainders! http://gmatclub.com/forum/compilationoftipsandtrickstodealwithremainders86714.html#p651942
Word Problems Made Easy! 1) Translating the English to Math : http://gmatclub.com/forum/wordproblemsmadeeasy87346.html 2) 'Work' Problems Made Easy : http://gmatclub.com/forum/workwordproblemsmadeeasy87357.html 3) 'Distance/Speed/Time' Word Problems Made Easy : http://gmatclub.com/forum/distancespeedtimewordproblemsmadeeasy87481.html



Manager
Joined: 29 Oct 2009
Posts: 197

Re: Inequality and absolute value questions from my collection [#permalink]
Show Tags
Updated on: 18 Nov 2009, 01:07
1
This post was BOOKMARKED
Quote: 9. Is n<0? (1) n=n (2) n^2=16 Question Stem : Is n negative? St. (1) : n = n
Let n = A ; therefore the statement becomes : A = A. This can only be valid when A is positive (or equal to 0). This in turn means that n must be negative (or equal to 0). n=n also for n=0, hence not sufficient. St. (2) : n^2 = 16
n = ±4. Thus Insufficient. Answer : C
_________________
Click below to check out some great tips and tricks to help you deal with problems on Remainders! http://gmatclub.com/forum/compilationoftipsandtrickstodealwithremainders86714.html#p651942
Word Problems Made Easy! 1) Translating the English to Math : http://gmatclub.com/forum/wordproblemsmadeeasy87346.html 2) 'Work' Problems Made Easy : http://gmatclub.com/forum/workwordproblemsmadeeasy87357.html 3) 'Distance/Speed/Time' Word Problems Made Easy : http://gmatclub.com/forum/distancespeedtimewordproblemsmadeeasy87481.html
Originally posted by sriharimurthy on 17 Nov 2009, 14:54.
Last edited by sriharimurthy on 18 Nov 2009, 01:07, edited 1 time in total.



Manager
Joined: 29 Oct 2009
Posts: 197

Re: Inequality and absolute value questions from my collection [#permalink]
Show Tags
17 Nov 2009, 15:04
Quote: 10. If n is not equal to 0, is n < 4 ? (1) n^2 > 16 (2) 1/n > n Question Stem : n # 0 ; 4 > n > 4 (excluding 0) St. (1) : n^2 > 16
(n  4)*(n +4) = 0 Therefore boundary conditions are 4 and  4. Thus we can write it as : n < 4 and n > 4. Sufficient. St. (2) : 1/n > n
This condition will be valid for all n < 1 excluding 0. Thus it will be impossible to tell whether n < 4. Hence Insufficient. Answer : A
_________________
Click below to check out some great tips and tricks to help you deal with problems on Remainders! http://gmatclub.com/forum/compilationoftipsandtrickstodealwithremainders86714.html#p651942
Word Problems Made Easy! 1) Translating the English to Math : http://gmatclub.com/forum/wordproblemsmadeeasy87346.html 2) 'Work' Problems Made Easy : http://gmatclub.com/forum/workwordproblemsmadeeasy87357.html 3) 'Distance/Speed/Time' Word Problems Made Easy : http://gmatclub.com/forum/distancespeedtimewordproblemsmadeeasy87481.html



Manager
Joined: 29 Oct 2009
Posts: 197

Re: Inequality and absolute value questions from my collection [#permalink]
Show Tags
17 Nov 2009, 15:29
3
This post was BOOKMARKED
Quote: 11. Is x+y>xy? (1) x > y (2) xy < x Question Stem : Is the distance between X and Y greater than the distance between X and Y?
Note : Using number line approach. St. (1) : x > y
OR, The distance between X and the origin is greater than the distance between Y and the origin. Now we can have two cases : (a) When X is positive : In this case, X > Y for the above condition to be true. _______________________________________________________ _________________Y______Origin______Y........ Region of X......... Thus we can see that the distance between X and  Y will always be greater than the distance between X and Y. Hence question stem is true. (b) When X is negative : In this case, X < Y for the statement to be true. _______________________________________________________ .... Region of X.....Y_____Origin_______Y___________ Thus we can see that the distance between X and Y will always be less than the distance between X and Y. Hence, question stem becomes false. Due to conflicting statements, St (1) becomes Insufficient. St. (2) : xy < x
OR, the distance between X and Y is less than the distance between X and the origin. Now again let us consider the different cases : (a) When X is positive : For the statement to be true and for X to be positive, X must be greater than Y/2. For any value of X less than Y/2 the statement will become false. The statement will be true for any value greater than Y/2. Thus we see that only one case comes into the picture. Now let us see how it relates to the question stem. ______________________;_____________________ ________Y____Origin__y/2...Y...... Region of X.... Thus we can see that the distance between X and  Y will be greater than the distance between X and Y for all values of X > Y/2. Thus question stem is true. St. (2) is sufficient. Answer : B
_________________
Click below to check out some great tips and tricks to help you deal with problems on Remainders! http://gmatclub.com/forum/compilationoftipsandtrickstodealwithremainders86714.html#p651942
Word Problems Made Easy! 1) Translating the English to Math : http://gmatclub.com/forum/wordproblemsmadeeasy87346.html 2) 'Work' Problems Made Easy : http://gmatclub.com/forum/workwordproblemsmadeeasy87357.html 3) 'Distance/Speed/Time' Word Problems Made Easy : http://gmatclub.com/forum/distancespeedtimewordproblemsmadeeasy87481.html



Manager
Joined: 29 Oct 2009
Posts: 197

Re: Inequality and absolute value questions from my collection [#permalink]
Show Tags
17 Nov 2009, 15:36
1
This post was BOOKMARKED
Quote: 12. Is r=s? (1) s<=r<=s (2) r>=s St. (1) : s <= r < = s
Clearly Insufficient. St. (2) : r >= s
When r > 0 ; r >= s. When r < 0 ; r >= s ; r <= s Therefore, this statement can be rewritten as : s >= r >= s Insufficient. St. (1) and (2) : s <= r < = s ; s >= r >= s
For both statements to be simultaneously valid, r must be equal to s. Hence Sufficient. Answer : C
_________________
Click below to check out some great tips and tricks to help you deal with problems on Remainders! http://gmatclub.com/forum/compilationoftipsandtrickstodealwithremainders86714.html#p651942
Word Problems Made Easy! 1) Translating the English to Math : http://gmatclub.com/forum/wordproblemsmadeeasy87346.html 2) 'Work' Problems Made Easy : http://gmatclub.com/forum/workwordproblemsmadeeasy87357.html 3) 'Distance/Speed/Time' Word Problems Made Easy : http://gmatclub.com/forum/distancespeedtimewordproblemsmadeeasy87481.html



Manager
Joined: 29 Oct 2009
Posts: 197

Re: Inequality and absolute value questions from my collection [#permalink]
Show Tags
17 Nov 2009, 15:48
1
This post was BOOKMARKED
Quote: 13. Is x1 < 1? (1) (x1)^2 <= 1 (2) x^2  1 > 0 Question Stem : Is x1 < 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) : (x1)^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
_________________
Click below to check out some great tips and tricks to help you deal with problems on Remainders! http://gmatclub.com/forum/compilationoftipsandtrickstodealwithremainders86714.html#p651942
Word Problems Made Easy! 1) Translating the English to Math : http://gmatclub.com/forum/wordproblemsmadeeasy87346.html 2) 'Work' Problems Made Easy : http://gmatclub.com/forum/workwordproblemsmadeeasy87357.html 3) 'Distance/Speed/Time' Word Problems Made Easy : http://gmatclub.com/forum/distancespeedtimewordproblemsmadeeasy87481.html



Intern
Joined: 08 Nov 2009
Posts: 46

Re: Inequality and absolute value questions from my collection [#permalink]
Show Tags
17 Nov 2009, 18:24
sriharimurthy wrote: Quote: 9. Is n<0? (1) n=n (2) n^2=16 Question Stem : Is n negative? St. (1) : n = n
Let n = A ; therefore the statement becomes : A = A. This can only be valid when A is positive. This in turn means that n must be negative. Thus Sufficient. n=n also for n=0, hence not sufficient. Everything else is as you suggested, therefore C



Manager
Joined: 29 Oct 2009
Posts: 197

Re: Inequality and absolute value questions from my collection [#permalink]
Show Tags
18 Nov 2009, 01:01
Marco83 wrote: sriharimurthy wrote: Quote: 9. Is n<0? (1) n=n (2) n^2=16 Question Stem : Is n negative? St. (1) : n = n
Let n = A ; therefore the statement becomes : A = A. This can only be valid when A is positive. This in turn means that n must be negative. Thus Sufficient. n=n also for n=0, hence not sufficient. Everything else is as you suggested, therefore C Yes, you are right. I overlooked that. Thanks.
_________________
Click below to check out some great tips and tricks to help you deal with problems on Remainders! http://gmatclub.com/forum/compilationoftipsandtrickstodealwithremainders86714.html#p651942
Word Problems Made Easy! 1) Translating the English to Math : http://gmatclub.com/forum/wordproblemsmadeeasy87346.html 2) 'Work' Problems Made Easy : http://gmatclub.com/forum/workwordproblemsmadeeasy87357.html 3) 'Distance/Speed/Time' Word Problems Made Easy : http://gmatclub.com/forum/distancespeedtimewordproblemsmadeeasy87481.html



Math Expert
Joined: 02 Sep 2009
Posts: 45305

Re: Inequality and absolute value questions from my collection [#permalink]
Show Tags
18 Nov 2009, 08:39
74
This post received KUDOS
Expert's post
88
This post was BOOKMARKED
SOLUTIONS: 1. If 6*x*y = x^2*y + 9*y, what is the value of xy? (1) y – x = 3 (2) x^3< 0 First let's simplify given expression \(6*x*y = x^2*y + 9*y\): \(y*(x^26x+9)=0\) > \(y*(x3)^2=0\). Note here that we CAN NOT reduce this expression by \(y\), as some of you did. Remember we are asked to determine the value of \(xy\), and when reducing by \(y\) you are assuming that \(y\) doesn't equal to \(0\). We don't know that. Next: we can conclude that either \(x=3\) or/and \(y=0\). Which means that \(xy\) equals to 0, when y=0 and x any value (including 3), OR \(xy=3*y\) when y is not equal to zero, and x=3. (1) \(yx=3\). If y is not 0, x must be 3 and yx to be 3, y must be 6. In this case \(xy=18\). But if y=0 then x=3 and \(xy=0\). Two possible scenarios. Not sufficient. OR: \(yx=3\) > \(x=y3\) > \(y*(x3)^2=y*(y33)^2=y(y6)^2=0\) > either \(y=0\) or \(y=6\) > if \(y=0\), then \(x=3\) and \(xy=0\) \(or\) if \(y=6\), then \(x=3\) and \(xy=18\). Two different answers. Not sufficient. (2) \(x^3<0\). x is negative, hence x is not equals to 3, hence y must be 0. So, xy=0. Sufficient. Answer: B.This one was quite tricky and was solved incorrectly by all of you. Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We can not divide by zero.
Never multiply (or reduce) inequality by variable (or expression with variable) if you don't know the sign of it or are not certain that variable (or expression with variable) doesn't equal to zero.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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? Extrahard Quant Tests with Brilliant Analytics



Math Expert
Joined: 02 Sep 2009
Posts: 45305

Re: Inequality and absolute value questions from my collection [#permalink]
Show Tags
18 Nov 2009, 08:47
27
This post received KUDOS
Expert's post
34
This post was BOOKMARKED



Math Expert
Joined: 02 Sep 2009
Posts: 45305

Re: Inequality and absolute value questions from my collection [#permalink]
Show Tags
18 Nov 2009, 08:55
30
This post received KUDOS
Expert's post
68
This post was BOOKMARKED



Math Expert
Joined: 02 Sep 2009
Posts: 45305

Re: Inequality and absolute value questions from my collection [#permalink]
Show Tags
18 Nov 2009, 09:17
15
This post received KUDOS
Expert's post
40
This post was BOOKMARKED
4. Are x and y both positive? (1) 2x2y=1 (2) x/y>1 (1) 2x2y=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. 2x2y=1 > y=x1/2, 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 timeconsuming and comfortable for you personally. One of the approaches: \(2x2y=1\) > \(x=y+\frac{1}{2}\) \(\frac{x}{y}>1\) > \(\frac{xy}{y}>0\) > substitute x > \(\frac{1}{y}>0\) > \(y\) is positive, and as \(x=y+\frac{1}{2}\), \(x\) is positive too. Sufficient. Answer: C.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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? Extrahard Quant Tests with Brilliant Analytics




Re: Inequality and absolute value questions from my collection
[#permalink]
18 Nov 2009, 09:17



Go to page
Previous
1 2 3 4 5 6 7 8 9 10 11
Next
[ 204 posts ]



