Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49303

Math Revolution and GMAT Club Contest! x + y = ?
[#permalink]
Show Tags
12 Dec 2015, 08:51
Question Stats:
45% (01:12) correct 55% (01:48) wrong based on 297 sessions
HideShow timer Statistics
Math Revolution and GMAT Club Contest Starts! QUESTION #9:x + y = ? (1) \(y = 2x  1\) (2) \(y^2 = 1  2x\) Check conditions below: Math Revolution and GMAT Club ContestThe Contest Starts November 28th in Quant Forum We are happy to announce a Math Revolution and GMAT Club Contest For the following four (!) weekends we'll be publishing 4 FRESH math questions per weekend (2 on Saturday and 2 on Sunday). To participate, you will have to reply with your best answer/solution to the new questions that will be posted on Saturday and Sunday at 9 AM Pacific. Then a week later, the forum moderator will be selecting 2 winners who provided most correct answers to the questions, along with best solutions. Those winners will get 6months access to GMAT Club Tests. PLUS! Based on the answers and solutions for all the questions published during the project ONE user will be awarded with ONE Grand prize: PS + DS course with 502 videos that is worth $299! All announcements and winnings are final and no whining GMAT Club reserves the rights to modify the terms of this offer at any time. NOTE: Test Prep Experts and Tutors are asked not to participate. We would like to have the members maximize their learning and problem solving process.
Thank you!
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
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






Current Student
Joined: 25 Feb 2014
Posts: 225

Re: Math Revolution and GMAT Club Contest! x + y = ?
[#permalink]
Show Tags
12 Dec 2015, 09:23
x + y = ? (1) y=2x−1. Clearly insufficient. (2) y^2=−1−2x. y^2 cannot be negative but it can be zero. So y^2 = 0 or y = 0. So 1−2x is 0. or x = 1/2. So x+y = 1/2. Sufficient. Ans. B
_________________
Consider KUDOS if my post helped
I got the eye of the tiger, a fighter, dancing through the fire 'Cause I am a champion and you're gonna hear me roar




Intern
Joined: 21 Jan 2013
Posts: 41
Concentration: General Management, Leadership
GPA: 3.82
WE: Engineering (Computer Software)

Re: Math Revolution and GMAT Club Contest! x + y = ?
[#permalink]
Show Tags
12 Dec 2015, 10:19
QUESTION #9: x + y = ? (1) y=2x−1 (2) y2=−1−2x (1) : y = 2x  1 : no additional information to identify the combination of x+y or to solve individually for x or y. clearly insufficient. (2) y^2 = 12x y^2 is clearly always >=0 ; since all absolutes are always >=0 ; it follows that 12x >=0 and therefore 12x is less than equal to zero Given the constraints on both left hand side and right hand side of the equation  y^2 >=0 and 12x <=0 .. it follows that only one value is possible for both the sides , that is both are equal to 0. so y^2 = 0 and y = 0; similarily 12x = 0 => 12x = 0 => x = 1/2 so x+y = 1/2 (unique answer)  hence sufficient. Correct answer : B
_________________

Consider +1 Kudos if you find my post useful



Intern
Joined: 03 Dec 2015
Posts: 7

Re: Math Revolution and GMAT Club Contest! x + y = ?
[#permalink]
Show Tags
12 Dec 2015, 10:30
Guys,
The first statement doesnt give us any value for x+y and the 2nd statement is against the math basics being that the absolute value of (12x) is always positive for all x and y^2 cannot be a negative number so answer is E right?



Board of Directors
Joined: 17 Jul 2014
Posts: 2683
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Re: Math Revolution and GMAT Club Contest! x + y = ?
[#permalink]
Show Tags
12 Dec 2015, 11:20
I picked E, although i have my doubts.
x + y = ?
(1) y=2x−1 knowing this, we have x+2x1 = 3x1, not sufficient.
(2) y^2=−1−2x ok, how the hell can a squared number be negative? impossible. let's multiply everything by 1. y^2 = 12x ok, now: y^2 = 12x or y^2 = 2x1
doesn't tell us much:
combine 1+2.
y=2x1 y^2 = either 12x or 2x1.
square first equation to get 4x^2  4x + 1
now, negative of this, will equal either 12x or 2x1, let's test both cases: (4x^2  4x + 1) = 12x 4x^2 +4x  1 = 12x 4x^2 +6x 2 = 0  divide everything by 2 2x^2 +3x  2 = 0 2 = 2x^2  3x 2 = x(2x3) doesn't tell much. so this should raise red flags that C is not sufficient.
4x^2 +4x1 = 2x1 4x^2 2x=0 4x^2 = 2x  divide by 2x 2x = 1 x = 1/2 ok, now if x=1/2, then y should be 0.
nevertheless, since 2 outcomes are possible. C is insufficient, and the answer is E.



Intern
Joined: 29 Sep 2014
Posts: 16

Re: Math Revolution and GMAT Club Contest! x + y = ?
[#permalink]
Show Tags
12 Dec 2015, 15:29
We're asked whether, given the information in the two statements we can calculate the one value of x+y. Statement 1) is obviously not sufficient to tie down \(x+y\) as \(y\) increases with \(x\) and therefore \(x+y\) can take an infinite number of values. For example if \(x=1\), \(y=1\), and \(x+y=2\); and if \(x=2\), \(y=3\), and \(x+y=5\). We have two different answers and therefore 1) is not sufficient. Statement 2) is a little more complicated. We know that in GMAT no imaginary numbers are allowed, therefore a square number must not be \(<0\), and the left hand side of the equation is \(>=0\). The right hand side of the equation is a negative sign next to a modulus, and since a modulus is \(>=0\), the negative of a modulus is \(<=0\). The only value which each side of the equation can take is \(0\), and this gives us \(y=0\) and \((12x)=0\) which gives us \(x=1/2\). Therefore statement 2) is sufficient and the answer is B.
_________________
Target GMAT 650. Please help by giving Kudos, it's free!



Manager
Joined: 09 Jul 2015
Posts: 57

Re: Math Revolution and GMAT Club Contest! x + y = ?
[#permalink]
Show Tags
12 Dec 2015, 18:39
Find x+y 1) y = 2x  1 > no way to find what x+y is. Insufficient 2) y^2 = 12x > this can be written as follows. y^2 = 2x1 (x can be any positive integer greater than 0) y^2 = 12x (x can be any negative integer <= 0) In either case, we cannot find x+y. 1&2 together  when y^2 = 2x1 & y = 2x1 > (x, y) = (1/2, 0) or (1, 1) when Y^2 = 12x & y=2x1 > (x, y) = (1/2, 0) or (0, 1) here (1/2, 0) satisfies both forms of y^2 = 12x. Hence x+y  1/2. or Answer is C
_________________
Please kudos if you find this post helpful. I am trying to unlock the tests



Intern
Joined: 21 Nov 2014
Posts: 31
Location: Viet Nam

Re: Math Revolution and GMAT Club Contest! x + y = ?
[#permalink]
Show Tags
12 Dec 2015, 20:33
(1) Insufficient. (2) \(y^2 = 12x => y = 0 & x = 1/2 => x+y = 1/2\) Sufficient Answer B
_________________
GMAT Group for Vietnamese:
https://www.facebook.com/groups/644070009087525/



SC Moderator
Joined: 13 Apr 2015
Posts: 1703
Location: India
Concentration: Strategy, General Management
GPA: 4
WE: Analyst (Retail)

Re: Math Revolution and GMAT Club Contest! x + y = ?
[#permalink]
Show Tags
13 Dec 2015, 02:50
x + y =?
St1: y = 2x−1 x = 1 > y = 1 > x + y = 2 x = 2 > y = 3 > x + y = 5 St1 does not result in a unique solution. So St1 is not sufficient.
St2: y^2 = 1  2x x = 1 > y^2 = 1 > y^2 can never be negative. So this answer is not possible. x = 1 > y^2 = 3 > Again it is not possible x = 1/2 > y^2 = 0 > y = 0 > Possible
Thus x = 1/2 and y = 0 > x + y = 1/2 St2 is sufficient
Answer: B



Intern
Joined: 06 Jul 2014
Posts: 20
WE: Supply Chain Management (Manufacturing)

Re: Math Revolution and GMAT Club Contest! x + y = ?
[#permalink]
Show Tags
13 Dec 2015, 05:40
x + y = ?
(1) y=2x−1 (2) y 2 =−1−2x Solution 1)y+x=3x1 ,hence not sufficient. 2)y 2 =−1−2x >y2=0 (since y2 can't be negative)>12x=0>x=1/2>x+y=1/2 Hence sufficient.
Correct ChoiceB



Intern
Joined: 17 Aug 2014
Posts: 10

Re: Math Revolution and GMAT Club Contest! x + y = ?
[#permalink]
Show Tags
13 Dec 2015, 08:03
Statement 1: x+y=x+2x1=3x1, not suficient Statement 2:Y^2=mod(12x) the only possibility is 12x should be 0 because square of a number cannot be negative =>x=1/2, y=0, x+y=1/2, sufficient Answer=B



Intern
Joined: 01 Nov 2015
Posts: 36
Location: India
Concentration: Marketing, Entrepreneurship
WE: Engineering (Computer Software)

Re: Math Revolution and GMAT Club Contest! x + y = ?
[#permalink]
Show Tags
13 Dec 2015, 10:08
With Just I, we have 1 equation and 2 variables. Hence Not Sufficient
with II, we can construct 2 equations for 2 variables \(y^2 = 1  2x\) and \(y^2 = 2x  1\) we can solve for x and y and find the value of x + y
Answer is B



Intern
Joined: 01 Nov 2015
Posts: 36
Location: India
Concentration: Marketing, Entrepreneurship
WE: Engineering (Computer Software)

Re: Math Revolution and GMAT Club Contest! x + y = ?
[#permalink]
Show Tags
13 Dec 2015, 10:09
With Just I, we have 1 equation and 2 variables. Hence Not Sufficient
with II, we can construct 2 equations for 2 variables \(y^2 = 1  2x\) and \(y^2 = 2x  1\) we can solve for x and y and find the value of x + y
Answer is B



Intern
Joined: 10 Sep 2015
Posts: 32

Re: Math Revolution and GMAT Club Contest! x + y = ?
[#permalink]
Show Tags
13 Dec 2015, 22:27
1) y=2x1
2) y^2= 12x
now x+y=?
1) insufficient
2) as LHS will always be positive, we can say 12x will be positive , so its equal to (12x)
thus, y^2 = ( 12x) y^2 = 2x1
again In sufficient
1+2.. gives (1/2,0) and (1,1).. but not unique soln
Thus ans E



Intern
Joined: 29 Aug 2013
Posts: 40
Location: Bangladesh
GPA: 3.76
WE: Supply Chain Management (Transportation)

Re: Math Revolution and GMAT Club Contest! x + y = ?
[#permalink]
Show Tags
14 Dec 2015, 02:16
QUESTION #9: x + y = ? (1) y=2x−1 (2) y2=−1−2x Solution: Statement: (A): not sufficient (B): Not Sufficient H'ever, taking both the statements together we got: y^2=−1−2x or, y^2=(12x) or, (2x1)^2=1+2x or, (2x1)(2x1)=2x1 or, (2x1)(2x1)(2x1)=0 or, (2x1)((2x11)=0 so, 2x1=0; 2x11=0 so, x=1/2; x1 so, x=1/2, 1 when x=1, y=(2x2)1=3 when x=1/2, y=(2.1/2)1=0 Answer: "C"
_________________
Appreciate Kudos if the post seems worthwhile!



Intern
Joined: 22 Dec 2014
Posts: 38

Re: Math Revolution and GMAT Club Contest! x + y = ?
[#permalink]
Show Tags
14 Dec 2015, 19:44
QUESTION #9:
x + y = ?
(1) \(y=2x−1\) (2) \(y^2=−1−2x\)
Answer:
(1) \(x+y=x+2x1=3x1\)  unknown x > insufficient (2) \(y^2=−1−2x\): can find x as function of \(y^2\) and plug in \(x+y\) but still y is unknown > insufficient
(1) + (2): \(y=2x1\) > \(x=\frac{y+1}{2}\) > \(x+y= \frac{3y+1}{2}\) (*) \(y^2=−1−2x\) When \(x =<1/2\) > \(y^2=2x−1\) > \(x = \frac{y^2+1}{2}\) > \(x+y=\frac{y^2+2y+1}{2}\) (**) from (*) and (**) > \(\frac{3y+1}{2}=\frac{y^2+2y+1}{2}\) > \(y=0\) or \(y=1\) > \(x+y\) has 2 solution > insufficient
Answer E



Manager
Status: single
Joined: 19 Jan 2015
Posts: 90
Location: India
GPA: 3.2
WE: Sales (Pharmaceuticals and Biotech)

Re: Math Revolution and GMAT Club Contest! x + y = ?
[#permalink]
Show Tags
14 Dec 2015, 23:32
from statement 1 y=2x1. we cant find the values of x and y
from statement 2
y^2=mod12x
square of any number is always>=0. of non negative.
mod always non negative. but statment mentions Y^2=mod. only Y=0 satisfy the equaiton so mod also 0.
so 12x=0, imply x=1/2.now we both values of x and y. so option B is correct.



Retired Moderator
Joined: 23 Sep 2015
Posts: 385
Location: France
GMAT 1: 690 Q47 V38 GMAT 2: 700 Q48 V38
WE: Real Estate (Mutual Funds and Brokerage)

Re: Math Revolution and GMAT Club Contest! x + y = ?
[#permalink]
Show Tags
15 Dec 2015, 02:28
1) \(y=2x−1\) ==> \(y^2 =(2x−1)^2\) insufficient 2)\(y^2=−1−2x ==> y^2 =  1  2x\) or \(y^2 = 1 + 2x\) insufficient The two statments together: Case 1\((2x−1)^2=  1  2x\) \(4x^2  4x+1=12x\) \(4x^22x+2=0\) No solution for x, discriminant (\(b^2 4ac < 0\)) Case 2\((2x−1)^2= 1 + 2x\) \(4x^2  6x=0\) \(x(4x6) =0\) \(x = 0\) or \(x =3/2\) when \(x =0, y = 1 ==> x + y = 1\) When \(x = 3/2, y = 2 ==> x + y = 7/2\) We can't find a single result for the sum of x and y Answer E
_________________
New Application Tracker : update your school profiles instantly!



Current Student
Joined: 10 Aug 2015
Posts: 54
Concentration: General Management, Entrepreneurship

Re: Math Revolution and GMAT Club Contest! x + y = ?
[#permalink]
Show Tags
16 Dec 2015, 12:36
\(x + y =_________ ?\) We are asked to find the value of \(x + y\).
Statement 1 : \(y = 2x − 1\) > \(y  2x =  1\) There is no way this equation can be further modified to obtain the value of \(x + y\).
Not Sufficient.
Statement 2 : \(y^2 = −  1 − 2x \) First, look closely at each part of this equation.
We have \(y^2\) on one side so we know that \(y^2\) on is either equal to a positive number or equal to \(0\).
We have \(−  1 − 2x \) on the other side. \( 1 − 2x \) is either equal to a positive number or to \(0\). Therefore \(−  1 − 2x \) will either be equal to a negative number or to \(0\). So the only way \(y^2\) and \(−  1 − 2x \) can be equal to each other is if they are both equal to 0.
\(y^2 =\)0 so \(y = 0\). So you can solve the equation for x by plugging in the value of y. Once you will have done this, you will have the individual values of \(x\) and \(y\) and a fortiori the value of \(x + y\) . Note that at this stage, you don't need to calculate any further since this is a DS question. Just for the sake of completeness, here is the end of the explanation: \(−  1 − 2x  = 0\) > \(1  2x = 0\) > \(x = \frac{1}{2}\) So \(x + y = \frac{1}{2}\)
Sufficient
Answer: B



Current Student
Joined: 20 Jan 2015
Posts: 51

Re: Math Revolution and GMAT Club Contest! x + y = ?
[#permalink]
Show Tags
17 Dec 2015, 05:27
Statement 2 is sufficient. Statement 1 We are given nothing that will help us get to the values for x and y or rather x+y. Statement 2 we are given that square of y is equal to a negative number. This is only possible if that number is zero. Thus, y=0 and 12x=0 . which implies x=1/2. Thus we can get x+y = 1/2. So, the answer is statement 2 sufficient but statement 1 is not sufficient. => option B.
_________________
Please take a moment to hit Kudos if you like my post




Re: Math Revolution and GMAT Club Contest! x + y = ? &nbs
[#permalink]
17 Dec 2015, 05:27



Go to page
1 2
Next
[ 28 posts ]



