Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 06 Sep 2012
Posts: 39
Concentration: Social Entrepreneurship

Is (y  10)^2 > (x + 10)^2?
[#permalink]
Show Tags
Updated on: 05 Apr 2018, 13:53
Question Stats:
38% (01:55) correct 62% (02:24) wrong based on 331 sessions
HideShow timer Statistics
Is \((y10)^2 > (x+10)^2\)? (1) \(y > x + 5\) (2) \(x > y\)
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Life begins at the edge of your comfort zone.
Appreciate the +1!
Originally posted by JJ2014 on 15 Dec 2012, 11:31.
Last edited by Bunuel on 05 Apr 2018, 13:53, edited 1 time in total.
Edited the question.




Math Expert
Joined: 02 Sep 2009
Posts: 49271

Re: Is (y  10)^2 > (x + 10)^2
[#permalink]
Show Tags
19 Nov 2013, 01:39
Is \((y  10)^2 > (x + 10)^2\)Is \((y  10)^2 > (x + 10)^2\)? > is \((y  10)^2  (x + 10)^2>0\)? > is \((y10x10)(y10+x+10)>0\)? > is \((yx20)(y+x)>0\)? This to hold true (yx20) and (y+x) must have the same sign. (1) \(y > x + 5\) > \(x+y<5\). The second multiple, (x+y), is negative but the first multiple, (yx20), can be negative as well as positive. Not sufficient. (2) \(x > y\) > \(yx<0\). The first multiple, (yx20), is negative but the first multiple, (x+y), can be negative as well as positive. Not sufficient. (1)+(2) Both (x+y) and (yx20) are negative, thus their product is positive. 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




Director
Joined: 25 Apr 2012
Posts: 700
Location: India
GPA: 3.21
WE: Business Development (Other)

Re: Is (y  10)^2 > (x + 10)^2?
[#permalink]
Show Tags
Updated on: 02 Jan 2014, 01:19
JJ2014 wrote: Is (y10)^2 > (x+10)^2?
(1) y > x+5 (2) x > y Hi JJ2014, 1. From St 1 , we get x+y<5 X=10 Y= 4 Then St under consideration is not true i.e (y10)^2> (x+10)^2 X=11 y= 5 Then st under consideration is true So A and D ruled out. St 2 alone is not sufficient. Ex X=3, y=2, St not true X=2, y=3, St is true So B ruled out. Combining both the statements we get x+y<5 and x>y We see that y<0 as otherwise if y>0 then the eqn X>y is not true. Hence ans C
_________________
“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”
Originally posted by WoundedTiger on 17 Dec 2012, 00:34.
Last edited by WoundedTiger on 02 Jan 2014, 01:19, edited 1 time in total.



Intern
Joined: 16 Nov 2013
Posts: 28
Location: United States
Concentration: Entrepreneurship, General Management
GPA: 3.49

Re: Is (y  10)^2 > (x + 10)^2
[#permalink]
Show Tags
19 Nov 2013, 02:15
Bunuel wrote: Is \((y  10)^2 > (x + 10)^2\)
Is \((y  10)^2 > (x + 10)^2\)? > is \((y  10)^2  (x + 10)^2>0\)? > is \((y10x10)(y10+x+10)>0\)? > is \((yx20)(y+x)>0\)? This to hold true (yx20) and (y+x) must have the same sign.
(1) \(y > x + 5\) > \(x+y<5\). The second multiple, (x+y), is negative but the first multiple, (yx20), can be negative as well as positive. Not sufficient.
(2) \(x > y\) > \(yx<0\). The first multiple, (yx20), is negative but the first multiple, (x+y), can be negative as well as positive. Not sufficient.
(1)+(2) Both (x+y) and (yx20) are negative, thus their product is positive. Sufficient.
Answer: C. Great explanation once again. Thank you



Manager
Status: Student
Joined: 26 Aug 2013
Posts: 210
Location: France
Concentration: Finance, General Management
GPA: 3.44

Re: Is (y  10)^2 > (x + 10)^2?
[#permalink]
Show Tags
01 Jan 2014, 11:35
JJ2014 wrote: Is (y10)^2 > (x+10)^2?
(1) y > x+5 (2) x > y Hi, I answered using the following process: If (y10)^2 > (x+10)^2 is true, then the difference between the two Y and X needs to be over 10 (Example: Y=6 and X=5) With 1) We have the beginning of the information If y > x+5 then it will be true for some numbers BUT, if Y=5 and X=100) Then you will have (15)^2 > (90)^2 which is impossible. You need X>YWith 2) Used alone, the statement is not correct. If Y=10 and X=10255 than the equation (y10)^2 > (x+10)^2 is false. if you select other numbers than the equation will be right. Then you comfirm the statement one with statement two. Answer CHope it helps!
_________________
Think outside the box



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8281
Location: Pune, India

Is (y  10)^2 > (x + 10)^2
[#permalink]
Show Tags
03 Jan 2014, 04:46
JJ2014 wrote: Is (y10)^2 > (x+10)^2?
(1) y > x+5 (2) x > y Responding to a pm: The algebraic solution to this has been provided by Bunuel here: https://gmatclub.com/forum/isy102x ... l#p1294316You can use the concept of mods and visualize it on the number line too. Is (y10)^2 > (x+10)^2? Is y10 > x+10? Is distance of y from 10 greater than distance of x from 10? (1) y > x+5 x+y < 5 ________10________x____y__________0__________________10 Yes, distance of y from 10 is greater than distance of x from 10. __x_________________________10______________________0____________y______10 No, distance of y from 10 is not greater than distance of x from 10. Not Sufficient. (2) x > y y is to the left of x on the number line. ________10________y____x_______0___________________10 Yes, distance of y from 10 is greater than distance of x from 10. ________10____________________0_________y___x______10 No, distance of y from 10 is not greater than distance of x from 10. Not Sufficient. Using Both, y will be to the left of x and y+x < 5 ________10________y____x_______0___________________10 Yes, distance of y from 10 is greater than distance of x from 10. __y________10___________________0_______x_____________10 Yes, distance of y from 10 is greater than distance of x from 10. So in any case, distance of y from 10 will be greater than distance of x from 10. Sufficient Answer (C)
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Director
Joined: 10 Mar 2013
Posts: 550
Location: Germany
Concentration: Finance, Entrepreneurship
GPA: 3.88
WE: Information Technology (Consulting)

Re: Is (y  10)^2 > (x + 10)^2
[#permalink]
Show Tags
02 Jan 2016, 09:50
registerincog wrote: Is \((y  10)^2 > (x + 10)^2\)
(1) \(y > x + 5\) (2) \(x > y\) Question: \(y^220y+10 > x^2+20x+100\)> \((yx)(y+x) > 20(y+x)\)? (1) \(x+y < 5\) means we can divide the expression above while changing the sign > \(yx < 20\), we cannot go any further here. Not sufficient (2) We have too many combinations considering this information. Just insert some values in the first expression \((y  10)^2 > (x + 10)^2\) \(x=1, y=90\): \((100)^2 > (1+10)^2?\) YES \(x=1, y=2\): \((210)^2 > (1+10)^2\)? No, hence not sufficient (1) + (2) From (1) \(yx < 20\) and from (2) \(yx < 0\)the answer is YES as, if \(yx\) is negative, then it diffenetelly will be less than 20. Answer C
_________________
When you’re up, your friends know who you are. When you’re down, you know who your friends are.
Share some Kudos, if my posts help you. Thank you !
800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50 GMAT PREP 670 MGMAT CAT 630 KAPLAN CAT 660



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6219
GPA: 3.82

Re: Is (y  10)^2 > (x + 10)^2
[#permalink]
Show Tags
02 Jan 2016, 23:19
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution Is (y−10)^2>(x+10)^2 (1) −y>x+5 (2) x>y If we modify the original condition and the question, the question, (y10)^2>(x+10)^2?, can be changed to (y10)^2(x+10)^2>0?. Then, if we further modify, (y10x10)(y10+x+10)>0? Thus, the question is essentially asking if (yx20)(y+x)>0? There are 2 variables (x and y) in the original condition. In order to match the number of variables and the number of equations, we need 2 equations. Using both the condition 1) and 2), we get yx<0. Then, yx20<0 and x+y<5<0. So, we get (yx20)(y+x)>0 and the answer is always ‘yes’. The condition, thus, is sufficient, and the correct answer is C. For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $99 for 3 month Online Course" "Free Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"



NonHuman User
Joined: 09 Sep 2013
Posts: 8105

Re: Is (y  10)^2 > (x + 10)^2?
[#permalink]
Show Tags
05 Apr 2018, 13:51
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: Is (y  10)^2 > (x + 10)^2? &nbs
[#permalink]
05 Apr 2018, 13:51






