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Math Revolution and GMAT Club Contest! x + y = ?

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Re: Math Revolution and GMAT Club Contest! x + y = ?  [#permalink]

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New post 17 Dec 2015, 20:58
x + y = ?
(1) y=2x−1
(2) y^2=−|1−2x|

As this is a two variable equation with two unknowns there should be two equations to solve it.
From eq1 alone we cant find x+y so using eq2 we should see wether x+y can be found or not
From eq2 for x<1/2 |1-2x| is positive so y^2=2x-1 this happens only when y=y^2 so Y=1 => X=1
for x>1/2 Y^2=1-2X and Y=2x-1 this happens when Y=-1 => X=0
for x=1/2 Y=0 so, by using the above two conditions we can determine x+y
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Re: Math Revolution and GMAT Club Contest! x + y = ?  [#permalink]

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New post 19 Dec 2015, 01:57
1
x+y = ?

1) y = 2x -1 clearly INSUFFICIENT. two unknown one equation.
for x = 0, y = -1
for x = 1/2, y = 0
for x = 1, y = 1

2) y^2 = - |1-2x|
y^2 + |1-2x| = 0, As we know that square of a number is always +ve and absolute value is always positive too. sum of two +ve entities can be zero only when their individual value is zero

Hence, y = 0 and |1-2x| will only be zero when x = 1/2

x+y = 1/2+0 = 1/2 --- definite, SUFFICIENT.

Option B is the correct answer.

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Re: Math Revolution and GMAT Club Contest! x + y = ?  [#permalink]

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New post 19 Dec 2015, 03:30
x + y = ?

Taking choice 1
(1) y=2x−1
x, y can be anything. When x =0, y=-1 or when x=1,y=1.
Therefore this choice is not sufficient.

(2) y2=−|1−2x|

x, y can be anything. When x =-1, y=- (3^0.5) or when x=1/2,y=0.
Therefore this choice is not sufficient.

Combining choice 1 and choice 2.
y=2x−1 , y2=−|1−2x|
Squaring choice 1. y^2 = (2x-1)^2 and substituting in choice 2 in place of y^2.
(2x-1)^2 = - |1-2x|

|1-2x| can also be written as (1-2x)^2 which can also be written as ((-1)(2x-1))^2 which is (2x-1)^2.
Therefore (2x-1)^2 = - (2x-1)^2
(2x-1)^2 + (2x-1)^2 =0
2((2x-1)^2)=0
x=1/2.
Substituting x value in choice 1 y=2x-1 gives y=0.
Therefore x+y= 1/2.
So, both statements (1) and (2) TOGETHER are sufficient to answer the question and answer choice C.
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Re: Math Revolution and GMAT Club Contest! x + y = ?  [#permalink]

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New post 19 Dec 2015, 04:49
x+y =?

1) y=2x-1
so x+y
x+2x-1
3x-1 (ns)

2) y^2=-|1-2x|

as LHS will be positive always..

so RHS has to be positive

so, y^2 = -(1-2x)
y^2 = 2x-1
(NS)

1+2

Y=2X-1
Y^2= 2X-1
(2x-1)^2 = (2x-1)
x=1/2, 1
y=0,1

so ans, E
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Re: Math Revolution and GMAT Club Contest! x + y = ?  [#permalink]

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New post 20 Dec 2015, 09:40
Bunuel wrote:

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 Contest

The 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 6-months 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!



MATH REVOLUTION OFFICIAL SOLUTION:

Since we have 2 variables in the original condition, we also need 2 equations. Since we need both 1) and 2), the correct answer is likely C. Using con 1) & 2) together, we get x=1/2, y=0. This is unique and sufficient. Therefore, the correct answer is C. However, since this is an “absolute value” problem, which is one of the key questions, we should apply Common Mistake Type 4(A).

In case of con 1), the values of x, y are not unique. Therefore, it is not sufficient.
In case of con 2), the only values that satisfy y^2+|1-2x|=0 are x=1/2, y=0. Therefore, it is unique and sufficient. The correct answer is B.

If C and B are both correct answers, B is would be the final correct answer.

Note 1 : a=b=0 is required to satisfy |a|+|b|=0 or a2+b2=0. Also, solving this type of question usually takes over 5 minutes during the actual exam. However, if you understand the relationship between Variable Approach Method and Common Mistake Types, you will be able to solve this type of question in just about 2 minutes.

Note 2 : 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.
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Re: Math Revolution and GMAT Club Contest! x + y = ?  [#permalink]

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New post 25 Dec 2015, 06:46
x + y = ?

(1) y=2x−1
(2) y2=−|1−2x|

I have a doubt. Here no information about x and y are given as they are integers. Is it correct to assume that
y2=−|1−2x| , here y^2 cannot be a negative number and therefore y^2= 0 and mark B as sufficient. Can't y be a complex number as no information is given that y is integer?

y2 = - negative number I assumed that y = complex number and marked choice B as insufficient since y can be any complex number based on x, in my
above answer.

MathExperts! Can you please help clear my doubt. Is it wrong to assume in GMAT , that a number can be complex number if no information is given about it.
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Re: Math Revolution and GMAT Club Contest! x + y = ?  [#permalink]

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New post 27 Dec 2015, 03:52
sri1sastra wrote:
x + y = ?

(1) y=2x−1
(2) y2=−|1−2x|

I have a doubt. Here no information about x and y are given as they are integers. Is it correct to assume that
y2=−|1−2x| , here y^2 cannot be a negative number and therefore y^2= 0 and mark B as sufficient. Can't y be a complex number as no information is given that y is integer?

y2 = - negative number I assumed that y = complex number and marked choice B as insufficient since y can be any complex number based on x, in my
above answer.

MathExperts! Can you please help clear my doubt. Is it wrong to assume in GMAT , that a number can be complex number if no information is given about it.


All numbers on the GMAT are by default real numbers. So, we do not consider complex/imaginary numbers on the GMAT.
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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.


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Re: Math Revolution and GMAT Club Contest! x + y = ?  [#permalink]

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Re: Math Revolution and GMAT Club Contest! x + y = ? &nbs [#permalink] 19 Jul 2018, 15:26

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