Absolute Value sum

[akshaykerur]

What is the value of y?

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

(2) |3 - y| = 11

Can you tell me the correct ans?

Source: MGMAT CAT

[user123321]

What is the value of y?

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

(2) |3 - y| = 11

Can you tell me the correct ans?

Source: MGMAT CAT

IMO C

1) we dont know anything about x. so insuff.
2) y can be -8 or 14. so insuff.

using both,
if we see the option 1) LHS is mod i.e some +ve, so RHS should be +ve as well.
so y will be 14. hence sufficient.

user123321

[fcabanski]

1 - shows that y is positive, but not sufficient to determine a unique value for y.
3*|x^2-4|= y -2
3* |x^2-4| + 2 = y
positive * positive + positive = positive so y is positive.

2 - shows two values for y so not sufficient.
|3-y|=11

3-y = 11
-y=8
y=-8

-(3-y)=11
-3+y=11
y=14

2) shows y = -8 or 14. Throw out -8 because 1) shows that y is positive. The answer is 14. That's a unique value for y. 1 and 2 together are sufficient.

[akshaykerur]

But,

Why is |x2-4| positive and |3-y| negative ?

THanks.

[fcabanski]

|3-y| is not negative. An absolute value is always positive. Absolute value is the distance from zero. |3| = |-3|. 3 and -3 have the same absolute value. Their distance from zero is the same (3 units). |3-y| is positive. But y can be negative.

y can be -8 (negative)
|3-(-8)| = |11| = 11

y can be 14 (positive)
|3-14| = |-11| = 11

In both cases |3-y| is positive.

Whenever there is an absolute value in an equation, set it equal to what's on the other side, and set its opposite equal to what's on the other side. |x|=3 means x=3 and -x = 3 so x=-3.

[akshaykerur]

Sorry maybe I wasn't clear.

Why is |x2-4| positive only and not negative also?

Why don't we take this as a possible equation from data 1?
3 * -(x2-4) = y-2 ?

[chieftang]

Sorry maybe I wasn't clear.

Why is |x2-4| positive only and not negative also?

Absolute values are positive. I think you're confusing the solution for X with the concept of absolute value.

[fcabanski]

As chieftang pointed out, in the first equation the left is 3*|x^2 - 4|. Examine each term:

3 is positive.
|x^2 - 4| is positive. An absolute value is always positive.
The left is therefore positive because + * + = +. What's on the right must be positive. y-2 must be positive, which means y must be positive.

In the second equation y can be positive or negative. Whether y is -8 or +14: |3-y| = 11.

y is either positive or negative, but |3-y| is positive. Any absolute value is positive. In this case it's +11.