ABSOLUTE VALUES (CONFUSION!!)

[mparakala]

What is the value of y?

(1) 3|x^2 - 4| = y - 2

(2) |3 - y| = 11

Answer: C (source: MGMAT)

I learnt somewhere that whenever there is an absolute value question, one obtains two values. The two values must be plugged into the equation normally and checked as one of them will yield a value equivalent to the answer in the eq.
ex: in option (2), y = -8 or y = 14. Now, if I plug these values separately in a normal equation, (3-y) = 11, y = -8 seems to be the only right answer and hence, the only right value of y. Is this procedure correct?
DO WE NEED TO PLUG IN THE TWO VALUES INTO THE ABSOLUTE VALUE EQUATION? ARE THERE ANY EXCEPTIONS?

Kindly resolve this confusion. Thanks a lot!!

[aneesh.kg]

What is the value of y?

(1) 3|x2 - 4| = y - 2

(2) |3 - y| = 11

Answer: C (source: MGMAT)

I learnt somewhere that whenever there is an absolute value question, one obtains two values. The two values must be plugged into the equation normally and checked as one of them will yield a value equivalent to the answer in the eq.
ex: in option (2), y = -8 or y = 14. Now, if I plug these values separately in a normal equation, (3-y) = 11, y = -8 seems to be the only right answer and hence, the only right value of y. Is this procedure correct?
DO WE NEED TO PLUG IN THE TWO VALUES INTO THE ABSOLUTE VALUE EQUATION? ARE THERE ANY EXCEPTIONS?

Kindly resolve this confusion. Thanks a lot!!

Yes, there are exceptions.
Let me clear a few things here.

Misconception: 'whenever there is an absolute value question, one obtains two values'
NO. One normally obtains two values.
You may also obtain ZERO, just ONE, more than two or INFINITELY MANY solutions in an absolute value problem.
Examples:
|x + 2| = - 3.5 has NO SOLUTION because the modulus value can never be positive.
|x^2| = 0 has just ONE solution. I hope you can guess what that solution is.
|x| < 2 has infinitely many values of x satisfying it.
|x| < 2 with x being an integer has three values of x as its solution.

It will help you if you understand the concept of modulus/absolute value in depth rather than just following one rule blindly.

Let me solve this problem:
Statement1:
x is there in this statement to distract you. The bottomline is: The absolute value of any number has to be greater than or equal to zero.
The absolute value of anything has to be greater than/equal 0,
so y - 2 >= 0
y >= 2
INSUFFICIENT

Statement2:
3 - y = 11
OR
y - 3 = 11
So, y = -8 OR 14
INSUFFICIENT

Upon combining, just y = 14 remains.

Hence C is the answer.

[mparakala]

Hi,

Thank you for responding to my question.

Good explanation!

Can you give me an example where one of the two values of y is used to obtain an answer? ( as i mentioned earlier, I read it somewhere).
For example, in the option (2) , y has 2 values. Is there a situation where one of the two values is chosen to solve a problem?

I greatly appreciate your help.

What is the value of y?

(1) 3|x2 - 4| = y - 2

(2) |3 - y| = 11

Answer: C (source: MGMAT)

I learnt somewhere that whenever there is an absolute value question, one obtains two values. The two values must be plugged into the equation normally and checked as one of them will yield a value equivalent to the answer in the eq.
ex: in option (2), y = -8 or y = 14. Now, if I plug these values separately in a normal equation, (3-y) = 11, y = -8 seems to be the only right answer and hence, the only right value of y. Is this procedure correct?
DO WE NEED TO PLUG IN THE TWO VALUES INTO THE ABSOLUTE VALUE EQUATION? ARE THERE ANY EXCEPTIONS?

Kindly resolve this confusion. Thanks a lot!!

Yes, there are exceptions.
Let me clear a few things here.

Misconception: 'whenever there is an absolute value question, one obtains two values'
NO. One normally obtains two values.
You may also obtain ZERO, just ONE, more than two or INFINITELY MANY solutions in an absolute value problem.
Examples:
|x + 2| = - 3.5 has NO SOLUTION because the modulus value can never be positive.
|x^2| = 0 has just ONE solution. I hope you can guess what that solution is.
|x| < 2 has infinitely many values of x satisfying it.
|x| < 2 with x being an integer has three values of x as its solution.

It will help you if you understand the concept of modulus/absolute value in depth rather than just following one rule blindly.

Let me solve this problem:
Statement1:
x is there in this statement to distract you. The bottomline is: The absolute value of any number has to be greater than or equal to zero.
The absolute value of anything has to be greater than/equal 0,
so y - 2 >= 0
y >= 2
INSUFFICIENT

Statement2:
3 - y = 11
OR
y - 3 = 11
So, y = -8 OR 14
INSUFFICIENT

Upon combining, just y = 14 remains.

Hence C is the answer.

[aneesh.kg]

I don't think I understand your query very well.

y has two possible values from the second statement: -8 and 14. When you are combining the two statements you can substitute these two values in statement(1) to see with which one of the values does Statement(1) agree.

Substitute '-8':
3 |x^2 - 4| = -8 - 2
3 |x^2 - 4| = - 10
|x^2 - 4| = - 10/3
which is rejected because it's impossible for the absolute value function to yield a negative value.

Substitute '14':
3 |x^2 - 4| = 14 - 2
3 |x^2 - 4| = 12
|x^2 - 4| = 4
which is the only possibility. y = 14 accepted!

Does that help?

[mparakala]

Hi,

I clarified my misunderstanding by going back to what I read earlier in the MGMAT guide. Now, it is crystal clear!
Thanks for your help

I don't think I understand your query very well.

y has two possible values from the second statement: -8 and 14. When you are combining the two statements you can substitute these two values in statement(1) to see with which one of the values does Statement(1) agree.

Substitute '-8':
3 |x^2 - 4| = -8 - 2
3 |x^2 - 4| = - 10
|x^2 - 4| = - 10/3
which is rejected because it's impossible for the absolute value function to yield a negative value.

Substitute '14':
3 |x^2 - 4| = 14 - 2
3 |x^2 - 4| = 12
|x^2 - 4| = 4
which is the only possibility. y = 14 accepted!

Does that help?