Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 07 Dec 2015
Posts: 7

If x and y are positive, is x < y? [#permalink]
Show Tags
25 Mar 2016, 01:43
6
This post received KUDOS
28
This post was BOOKMARKED
Question Stats:
64% (00:43) correct 36% (00:52) wrong based on 681 sessions
HideShow timer Statistics
If x and y are positive, is x < y? (1) \(\sqrt{x} < \sqrt{y}\) (2) \((x3)^2 < (y3)^2\)
Official Answer and Stats are available only to registered users. Register/ Login.



Math Expert
Joined: 02 Sep 2009
Posts: 44668

If x and y are positive, is x < y? [#permalink]
Show Tags
25 Mar 2016, 02:13
27
This post received KUDOS
Expert's post
17
This post was BOOKMARKED
If x and y are positive, is x < y?(1) \(\sqrt{x} < \sqrt{y}\). Since both sides of the inequality are positive (the square root from a positive number is positive), then we can safely square: x < y. Directly answers the question. Sufficient. (2) \((x3)^2 < (y3)^2\). If \(x=3\) and \(y\neq 3\), the inequality will hold true: the left hand side will be 0, while the right hand side will be more than 0. Thus, if \(x=3\), y can be less than 3, giving a NO answer to the question, as well as more than 3, giving an YES answer to the question. Not sufficient. Answer: A. Hope it's clear.
_________________
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 Aug 2009
Posts: 5777

Re: if x and y are positive, is x<y? [#permalink]
Show Tags
25 Mar 2016, 02:13
5
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
Gurshaans wrote: if x and y are positive, is x<y?
(1) \(\sqrt{x} < \sqrt{y}\) (2) \((x3)^2 < (y3)^2\) Hi, we know that x and y are positive.. is x<y? lets see the statements (1) \(\sqrt{x} < \sqrt{y}\)we can say that ans is YES, but lets solve it algebrically too..is x<y can be written as xy<0.. \(\sqrt{x}^2\sqrt{y}^2\)<0.. \((\sqrt{x}\sqrt{y})(\sqrt{x}+\sqrt{y}) <0\).. \((\sqrt{x}+\sqrt{y}) >0\), as x and y are +ive, so we have to find if \((\sqrt{x}\sqrt{y})<0\) or \(\sqrt{x}<\sqrt{y}\).. statement 1 tells us exactly this.. SUFF (2) \((x3)^2 < (y3)^2\)It will hold in many cases : two case a) if x = 1 and y= 7.. y>x b) if x= 4 and y=1.. y<x. two different answers Insuff A
_________________
Absolute modulus :http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
GMAT online Tutor



Intern
Joined: 07 Dec 2015
Posts: 7

Re: If x and y are positive, is x < y? [#permalink]
Show Tags
25 Mar 2016, 02:49
Hi guys, thank you for your explanations Bunuel chetan2u . I have a question, I wanted to understand why we cant use an algebraic approach on the second statement? Since we have squares on either side, can't we take take the square root on either side, which would give us x  3 < y  3, then by adding 3 on either side we get x < y .. ? This is exactly what I did and marked D as the answer when I saw this question for the first time. From both the posts, my understanding is that we cant do what i mentioned earlier because we wouldn't know after taking the root whether x3 and y3 are positive or negative... Is this right? or am I mistaken? I'm asking this because I do not want to be confused in the exam under time pressure.. for example what would have happened had the question not specified that x and y are positive... and the first statement was x^2<y^2... ? would the answer in that case be E... Sorry about the long post, I just wanted clarity on this.. I do NOT want to get a 600700 level question wrong in the exam.



Math Expert
Joined: 02 Sep 2009
Posts: 44668

If x and y are positive, is x < y? [#permalink]
Show Tags
25 Mar 2016, 03:08
3
This post received KUDOS
Expert's post
11
This post was BOOKMARKED
Gurshaans wrote: Hi guys, thank you for your explanations Bunuel chetan2u . I have a question, I wanted to understand why we cant use an algebraic approach on the second statement? Since we have squares on either side, can't we take take the square root on either side, which would give us x  3 < y  3, then by adding 3 on either side we get x < y .. ? This is exactly what I did and marked D as the answer when I saw this question for the first time. From both the posts, my understanding is that we cant do what i mentioned earlier because we wouldn't know after taking the root whether x3 and y3 are positive or negative... Is this right? or am I mistaken? I'm asking this because I do not want to be confused in the exam under time pressure.. for example what would have happened had the question not specified that x and y are positive... and the first statement was x^2<y^2... ? would the answer in that case be E... Sorry about the long post, I just wanted clarity on this.. I do NOT want to get a 600700 level question wrong in the exam. MUST KNOW: \(\sqrt{x^2}=x\):The point here is that since square root function cannot give negative result then \(\sqrt{some \ expression}\geq{0}\). So \(\sqrt{x^2}\geq{0}\). But what does \(\sqrt{x^2}\) equal to? Let's consider following examples: If \(x=5\) > \(\sqrt{x^2}=\sqrt{25}=5=x=positive\); If \(x=5\) > \(\sqrt{x^2}=\sqrt{25}=5=x=positive\). So we got that: \(\sqrt{x^2}=x\), if \(x\geq{0}\); \(\sqrt{x^2}=x\), if \(x<0\). What function does exactly the same thing? The absolute value function: \(x=x\), if \(x\geq{0}\) and \(x=x\), if \(x<0\). That is why \(\sqrt{x^2}=x\). BACK TO THE QUESTION: According to the above if you take the square root from \((x3)^2 < (y3)^2\) you'll get x  3 < y  3, which means that the distance between x and 3 is less than the distance between y and 3, which is not sufficient to say whether x < y. Hope it helps.
_________________
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



Manager
Joined: 09 Oct 2015
Posts: 95

Re: If x and y are positive, is x < y? [#permalink]
Show Tags
25 Mar 2016, 03:59
Hi bunuel, Does this mean given 16<25, can we assume that square root of these will have the same sign? BunuelDoes x^2 Posted from my mobile device



Math Expert
Joined: 02 Sep 2009
Posts: 44668

Re: If x and y are positive, is x < y? [#permalink]
Show Tags
25 Mar 2016, 04:04



Manager
Joined: 09 Oct 2015
Posts: 95

Re: If x and y are positive, is x < y? [#permalink]
Show Tags
25 Mar 2016, 04:06
Bunuel, but it can also be that square root of 16 can be 4 and square root of 25 be  5, in which case 4>5 BunuelPosted from my mobile device



Math Expert
Joined: 02 Aug 2009
Posts: 5777

Re: If x and y are positive, is x < y? [#permalink]
Show Tags
25 Mar 2016, 04:09
rahulkashyap wrote: Bunuel, but it can also be that square root of 16 can be 4 and square root of 25 be  5, in which case 4>5 BunuelPosted from my mobile device hi, square root is always positive so \(\sqrt{25}\) will always be 5
_________________
Absolute modulus :http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
GMAT online Tutor



Manager
Joined: 09 Oct 2015
Posts: 95

Re: If x and y are positive, is x < y? [#permalink]
Show Tags
25 Mar 2016, 04:10
Hi, could u pls explain that statement? According to me 5x5 gives 25, so does 5x5
Posted from my mobile device



Math Expert
Joined: 02 Sep 2009
Posts: 44668

Re: If x and y are positive, is x < y? [#permalink]
Show Tags
25 Mar 2016, 04:12
rahulkashyap wrote: Bunuel, but it can also be that square root of 16 can be 4 and square root of 25 be  5, in which case 4>5 BunuelPosted from my mobile device You should go through basics again before attempting the questions. When the GMAT provides the square root sign for an even root, such as \(\sqrt{x}\) or \(\sqrt[4]{x}\), then the only accepted answer is the positive root. That is, \(\sqrt{25}=5\), NOT +5 or 5. In contrast, the equation \(x^2=25\) has TWO solutions, +5 and 5. Even roots have only a positive value on the GMAT.P.S. You might find the following post useful: All You Need for Quant
_________________
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: 26 Oct 2014
Posts: 24

Re: If x and y are positive, is x < y? [#permalink]
Show Tags
19 Jan 2017, 09:48
BACK TO THE QUESTION:
According to the above if you take the square root from \((x3)^2 < (y3)^2\) you'll get x  3 < y  3, which means that the distance between x and 3 is less than the distance between y and 3, which is not sufficient to say whether x < y.
Hope it helps.
Dear Bunuel,
Stem tells x>0 and y>0, so why cannot we take (x3)<(y3) as it is since we know the signs for both x and y.
In that case, I thought x was indeed less than y. Pls let me know why this is wrong?
Thnak you



Math Expert
Joined: 02 Sep 2009
Posts: 44668

Re: If x and y are positive, is x < y? [#permalink]
Show Tags
20 Jan 2017, 07:15
Liza99 wrote: BACK TO THE QUESTION:
According to the above if you take the square root from \((x3)^2 < (y3)^2\) you'll get x  3 < y  3, which means that the distance between x and 3 is less than the distance between y and 3, which is not sufficient to say whether x < y.
Hope it helps.
Dear Bunuel,
Stem tells x>0 and y>0, so why cannot we take (x3)<(y3) as it is since we know the signs for both x and y.
In that case, I thought x was indeed less than y. Pls let me know why this is wrong?
Thnak you We know that x = x, when \(x \geq{0}\) (so something = something, when that something is >=0) and x = x, when \(x \leq{0}\) (so something = something, when that something is =<0). Know for positive x, x3 (expression in modulus) can be positive (when x>3) as well as negative (when x<3), thus x3 = x3, when x>3 and x3 = (x3), when x<3. Thus knowing that x>0 is not enough to say that x3 = x3. Hope it's clear.
_________________
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: 26 Oct 2014
Posts: 24

Re: If x and y are positive, is x < y? [#permalink]
Show Tags
20 Jan 2017, 09:35
THANK YOU BUNUEL !!! QUANT GOD!



Manager
Joined: 13 Dec 2013
Posts: 163
Location: United States (NY)
Concentration: Nonprofit, International Business
GMAT 1: 710 Q46 V41 GMAT 2: 720 Q48 V40
GPA: 4
WE: Consulting (Consulting)

Re: If x and y are positive, is x < y? [#permalink]
Show Tags
09 Apr 2017, 20:44
Bunuel wrote: Gurshaans wrote: Hi guys, thank you for your explanations Bunuel chetan2u . I have a question, I wanted to understand why we cant use an algebraic approach on the second statement? Since we have squares on either side, can't we take take the square root on either side, which would give us x  3 < y  3, then by adding 3 on either side we get x < y .. ? This is exactly what I did and marked D as the answer when I saw this question for the first time. From both the posts, my understanding is that we cant do what i mentioned earlier because we wouldn't know after taking the root whether x3 and y3 are positive or negative... Is this right? or am I mistaken? I'm asking this because I do not want to be confused in the exam under time pressure.. for example what would have happened had the question not specified that x and y are positive... and the first statement was x^2<y^2... ? would the answer in that case be E... Sorry about the long post, I just wanted clarity on this.. I do NOT want to get a 600700 level question wrong in the exam. MUST KNOW: \(\sqrt{x^2}=x\):The point here is that since square root function cannot give negative result then \(\sqrt{some \ expression}\geq{0}\). So \(\sqrt{x^2}\geq{0}\). But what does \(\sqrt{x^2}\) equal to? Let's consider following examples: If \(x=5\) > \(\sqrt{x^2}=\sqrt{25}=5=x=positive\); If \(x=5\) > \(\sqrt{x^2}=\sqrt{25}=5=x=positive\). So we got that: \(\sqrt{x^2}=x\), if \(x\geq{0}\); \(\sqrt{x^2}=x\), if \(x<0\). What function does exactly the same thing? The absolute value function: \(x=x\), if \(x\geq{0}\) and \(x=x\), if \(x<0\). That is why \(\sqrt{x^2}=x\). BACK TO THE QUESTION: According to the above if you take the square root from \((x3)^2 < (y3)^2\) you'll get x  3 < y  3, which means that the distance between x and 3 is less than the distance between y and 3, which is not sufficient to say whether x < y. Hope it helps. Hi Bunuel, I can't get this statement clear, can you help? x  3 < y  3, which means that the distance between x and 3 is less than the distance between y and 3.



Math Expert
Joined: 02 Sep 2009
Posts: 44668

Re: If x and y are positive, is x < y? [#permalink]
Show Tags
09 Apr 2017, 22:08
Cez005 wrote: Bunuel wrote: Gurshaans wrote: Hi guys, thank you for your explanations Bunuel chetan2u . I have a question, I wanted to understand why we cant use an algebraic approach on the second statement? Since we have squares on either side, can't we take take the square root on either side, which would give us x  3 < y  3, then by adding 3 on either side we get x < y .. ? This is exactly what I did and marked D as the answer when I saw this question for the first time. From both the posts, my understanding is that we cant do what i mentioned earlier because we wouldn't know after taking the root whether x3 and y3 are positive or negative... Is this right? or am I mistaken? I'm asking this because I do not want to be confused in the exam under time pressure.. for example what would have happened had the question not specified that x and y are positive... and the first statement was x^2<y^2... ? would the answer in that case be E... Sorry about the long post, I just wanted clarity on this.. I do NOT want to get a 600700 level question wrong in the exam. MUST KNOW: \(\sqrt{x^2}=x\):The point here is that since square root function cannot give negative result then \(\sqrt{some \ expression}\geq{0}\). So \(\sqrt{x^2}\geq{0}\). But what does \(\sqrt{x^2}\) equal to? Let's consider following examples: If \(x=5\) > \(\sqrt{x^2}=\sqrt{25}=5=x=positive\); If \(x=5\) > \(\sqrt{x^2}=\sqrt{25}=5=x=positive\). So we got that: \(\sqrt{x^2}=x\), if \(x\geq{0}\); \(\sqrt{x^2}=x\), if \(x<0\). What function does exactly the same thing? The absolute value function: \(x=x\), if \(x\geq{0}\) and \(x=x\), if \(x<0\). That is why \(\sqrt{x^2}=x\). BACK TO THE QUESTION: According to the above if you take the square root from \((x3)^2 < (y3)^2\) you'll get x  3 < y  3, which means that the distance between x and 3 is less than the distance between y and 3, which is not sufficient to say whether x < y. Hope it helps. Hi Bunuel, I can't get this statement clear, can you help? x  3 < y  3, which means that the distance between x and 3 is less than the distance between y and 3. Absolute value a number is the distance between this number and 0. For example, x is the distance from 0 to x. Similarly x  3 is the distance between x3 and 0 or between x and 3.
_________________
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



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11515
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: If x and y are positive, is x < y? [#permalink]
Show Tags
19 Dec 2017, 14:44
Hi All, This prompt is based on a couple of Number Property rules  and you can TEST VALUES to solve it. We're told that X and Y are POSITIVE. We're asked if X is less than Y. This is a YES/NO question. 1) √X < √Y Since we know that X and Y are both POSITIVE, squaring or squarerooting those values will NOT change the "order" of them. Even if you're dealing with positive fractions, the 'order' will not change. For example: √X = 1/4 and √Y = 1/2 X = 1/2 and Y = about .71 Thus, the answer to the question is ALWAYS YES. Fact 1 is SUFFICIENT 2) (X3)^2 < (Y3)^2 While X and Y are both POSITIVE, we could end up with an (X3) or (Y3) that is negative though... and that will impact the answer to the question. IF... X = 2, Y = 10.... then (1)^2 is less than (7)^2 and the answer to the question is YES IF... X = 2, Y = 1.... then (1)^2 is less than (2)^2 and the answer to the question is NO Fact 2 is INSUFFICIENT Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



SVP
Joined: 26 Mar 2013
Posts: 1616

Re: If x and y are positive, is x < y? [#permalink]
Show Tags
20 Dec 2017, 16:54
If x and y are positive, is x < y?
(1) \(\sqrt{x} < \sqrt{y}\)
As both sides positive.........> We cab square both sides of inequality safely
x < y
Sufficient
(2) \((x3)^2 < (y3)^2\)
Let x = 0 & y = 100...........(3)^2 < (103)^2..Answer is No
Let x = 0 & y = 100...........(3)^2 < (97)^2..Answer is Yes
Insufficient
Answer: A



Manager
Joined: 11 Sep 2013
Posts: 151
Concentration: Finance, Finance

If x and y are positive, is x < y? [#permalink]
Show Tags
03 Jan 2018, 20:34
St 1 is definitely sufficient. If you square both sides, you will get the answer.
St 2== (x3)^2 < (Y3)^2
Try to get two different answers for y. Take y =5, x = 4 sufficient Take y =5, x = 4 NS
Ans A




If x and y are positive, is x < y?
[#permalink]
03 Jan 2018, 20:34






