This question is from one of MGMAT CAT exam.
What is the value of y?
(1) 3|x2 - 4| = y - 2 (read as 3|x(sqaure)-4|=y-2
(2) |3 - y| = 11
In the solution, it says |x(sqaure)-4| must be greater than 0. Can someone please explain why |x(sqaure)-4| must be greater than 0?
Thanks.
GMAT Forum
- cooper2248817
x square
statement 2 is easy and yields two answers;
ACE
Statement 2 when simplified will yield:
3x^2+10=y
or
-3x^2+14=y
we can not find the value of Y through these equations so CE
We will also yield multiple answers when combined, so i would have to say the answer to this question is "E"
What say you?
ACE
Statement 2 when simplified will yield:
3x^2+10=y
or
-3x^2+14=y
we can not find the value of Y through these equations so CE
We will also yield multiple answers when combined, so i would have to say the answer to this question is "E"
What say you?
- JK
Bro's
Statement one says that |x2-4| is greater than or equal to zero. There's no question that's true. An absolute value of number is zero or positive. You are assuming this question is saying there are two answers but there's only one since its the whole expression. Get it?
You can't solve this since there are two variables.
So you can deduce from it.
3 times zero or positive = ?? Zero or Positive!
SO!
Y-2 is the answer to 3 times zero or positive. SO! Y-2 is greater than or equal to zero. So Y >= 2, And that is all you know so it isn't sufficient.
BUT! Statement two gives you Y=-8 and 14.
Together, Y>=2 and Y = -8 or 14, you know Y = 14.
WORD
Statement one says that |x2-4| is greater than or equal to zero. There's no question that's true. An absolute value of number is zero or positive. You are assuming this question is saying there are two answers but there's only one since its the whole expression. Get it?
You can't solve this since there are two variables.
So you can deduce from it.
3 times zero or positive = ?? Zero or Positive!
SO!
Y-2 is the answer to 3 times zero or positive. SO! Y-2 is greater than or equal to zero. So Y >= 2, And that is all you know so it isn't sufficient.
BUT! Statement two gives you Y=-8 and 14.
Together, Y>=2 and Y = -8 or 14, you know Y = 14.
WORD
- Guest
JK Wrote:Bro's
Statement one says that |x2-4| is greater than or equal to zero. There's no question that's true. An absolute value of number is zero or positive. You are assuming this question is saying there are two answers but there's only one since its the whole expression. Get it?
You can't solve this since there are two variables.
So you can deduce from it.
3 times zero or positive = ?? Zero or Positive!
SO!
Y-2 is the answer to 3 times zero or positive. SO! Y-2 is greater than or equal to zero. So Y >= 2, And that is all you know so it isn't sufficient.
BUT! Statement two gives you Y=-8 and 14.
Together, Y>=2 and Y = -8 or 14, you know Y = 14.
WORD
*************************
Thanks for the input.
Here is the solution:
(1) INSUFFICIENT: Since this equation contains two variables, we cannot determine the value of y. We can, however, note that the absolute value expression |x2 - 4| must be greater than or equal to 0. Therefore, 3|x2 - 4| must be greater than or equal to 0, which in turn means that y - 2 must be greater than or equal to 0. If y - 2 > 0, then y > 2.
(2) INSUFFICIENT: To solve this equation for y, we must consider both the positive and negative values of the absolute value expression:
If 3 - y > 0, then 3 - y = 11
y = -8
If 3 - y < 0, then 3 - y = -11
y = 14
Since there are two possible values for y, this statement is insufficient.
(1) AND (2) SUFFICIENT: Statement (1) tells us that y is greater than or equal to 2, and statement (2) tells us that y = -8 or 14. Of the two possible values, only 14 is greater than or equal to 2. Therefore, the two statements together tell us that y must equal 14.
The correct answer is C.
______________
JK,
If statement 1 read as |x^2-4| instead of 3|x^2-4| then we will assume that expression has two solution.
Let me know if this is correct or not.
- JK
I actually don't think that's correct since you still have two variables in the first statement. You can't really come to a solid conclusion. You only know that Y>=0 when Y>2
Sorry bro - but if it was |x2-4| = 4 then you got two answers.
Word up man - don't worry so much about this problem. Worry about understanding absolutes.
Sorry bro - but if it was |x2-4| = 4 then you got two answers.
Word up man - don't worry so much about this problem. Worry about understanding absolutes.
- cooper 2248817
abs
now that i look back, why isn't the answer b
y<0 y=4 and y>0 y= 2
obvious y=4 contradicts to y<0; so y must be 2.
So the answer should be B
What say you?
y<0 y=4 and y>0 y= 2
obvious y=4 contradicts to y<0; so y must be 2.
So the answer should be B
What say you?
- guest
x>2
i dont understand.
i can't understand why c is right
i understand why statements 1 and 2 are wrong, but i dont not understand why C is correct. More particularly I dont understand how you deduce y>2?
i can't understand why c is right
i understand why statements 1 and 2 are wrong, but i dont not understand why C is correct. More particularly I dont understand how you deduce y>2?
- cooper2248817
abs
I was wondering if my thought process is correct.
Statement 1:
3x^2-10=y or -3x^2+10=y
bce
statement 2:
y=-8 and y=14
ce
since y is positive in statement 's equation the answer must be 14. Is it safe to assume that since the simplified equations in statement 1 yields positive Ys in both instances, therefore the answer must be 14.
Statement 1:
3x^2-10=y or -3x^2+10=y
bce
statement 2:
y=-8 and y=14
ce
since y is positive in statement 's equation the answer must be 14. Is it safe to assume that since the simplified equations in statement 1 yields positive Ys in both instances, therefore the answer must be 14.
- cooper2248817
abs
I had a tutor look at the original problem and he says the answer is E. It can only be C if the problem specifically says y>2; which it does not.
If it does..... please explain how
If it does..... please explain how
- Guest
JK pretty much laid this out for everyone, but just to reinforce this for myself if nothing else:
The problem DOES say that y >= 2. Where does it say that? Statement 1. If you remember a few things about absolute value and number properties, then you'll come to that conclusion. Statement 1 says:
3 | x^2 - 4 | = y - 2
First, remember that any expression within absolute value signs must equal either zero or a positive number. That means whatever the solutions are for | x^2 - 4 | , they must be either zero or positive.
Now remember your number properties, specifically positives/negatives. The left hand side of this equation is a positive number (3) multiplied by either zero or a positive number. That means the right hand side of the equation (y - 2) is either zero or a positive number. So that means:
y - 2 >= 0
(add 2 to both sides)
y >= 2
So Statement 1 can just be rephrased as "y >= 2" This is of course insufficient on its own to answer the question; however, combined with the solutions for y as per Statement 2, Statement 1 removes -8 as a possible solution (as it is obviously less than 0) to leave us with one definitive answer: 14.
So I agree that the answer is (C).
The problem DOES say that y >= 2. Where does it say that? Statement 1. If you remember a few things about absolute value and number properties, then you'll come to that conclusion. Statement 1 says:
3 | x^2 - 4 | = y - 2
First, remember that any expression within absolute value signs must equal either zero or a positive number. That means whatever the solutions are for | x^2 - 4 | , they must be either zero or positive.
Now remember your number properties, specifically positives/negatives. The left hand side of this equation is a positive number (3) multiplied by either zero or a positive number. That means the right hand side of the equation (y - 2) is either zero or a positive number. So that means:
y - 2 >= 0
(add 2 to both sides)
y >= 2
So Statement 1 can just be rephrased as "y >= 2" This is of course insufficient on its own to answer the question; however, combined with the solutions for y as per Statement 2, Statement 1 removes -8 as a possible solution (as it is obviously less than 0) to leave us with one definitive answer: 14.
So I agree that the answer is (C).
- cooper2248817
abs
Sorry for my ignorance!
I guess I will have my professor look at this.
This is the way i interpret the statement:
3lx^2-4l=y-2
solve for positive
y-2=3x^2-12
y=3x^2-10
now if you plug in values for x=0,1,2,3,4,.... you will get both positive and negative values
solve for negatice
y-2=-3x^2+12
y=-3x^2+14
now if you plug in values for x=0,1,2,3,4,.... you will get both positive and negative values
***********************************************************************************************
Now when you put values of -8 and 14 in any of the equations you will yield different answers for both and for "X" and therefore when you combine both statements -8 and 14; together they are insufficient.
How can C be right and if it is I really questions it. I don't doubt that my method is incorrect but if it is please explain as to why.
I guess I will have my professor look at this.
This is the way i interpret the statement:
3lx^2-4l=y-2
solve for positive
y-2=3x^2-12
y=3x^2-10
now if you plug in values for x=0,1,2,3,4,.... you will get both positive and negative values
solve for negatice
y-2=-3x^2+12
y=-3x^2+14
now if you plug in values for x=0,1,2,3,4,.... you will get both positive and negative values
***********************************************************************************************
Now when you put values of -8 and 14 in any of the equations you will yield different answers for both and for "X" and therefore when you combine both statements -8 and 14; together they are insufficient.
How can C be right and if it is I really questions it. I don't doubt that my method is incorrect but if it is please explain as to why.
- sumit
is answer c or e
i also got thtow eqns fm statemtn 1 i.e. 3x^2-10=y or -3x^2+14 =y
fm 2 i got y=-8 0r y=14
while the argument fm JK is pretty compelling, it kind of does away with the need of an eqn. ...they could have put any variable in any form in the absolute marks and the conclusion according to JK would have been that y is +ve.
Can someone fm MGMAt staff pls confirm the answer??
fm 2 i got y=-8 0r y=14
while the argument fm JK is pretty compelling, it kind of does away with the need of an eqn. ...they could have put any variable in any form in the absolute marks and the conclusion according to JK would have been that y is +ve.
Can someone fm MGMAt staff pls confirm the answer??