Data Sufficiency

What is the value of y?

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

(2) |3 - y| = 11


OA: C

Why is the answer not B

If you solve this equation you get 2 values for y, y=-8 and y=14

However, if you put y=14 back to the original stem (3-14)=11 -> -11 = 11 and this is not true.

Can somebody please help me out here?








OA from MGMAT:

(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.

(2) is Insufficient because the question wants to know what does Y = ?

If we plug in -8 into the formula:

|3-y|=11 = |3--8|=11 = |3+8|=11 = |11|=11 = 11=11;

So why can equal -8 here, but if we plug in 14 we can also get the answer of 11.

|3-y|=11 = |3-14|=11 = |-11|=11 = 11=11

I think here you might be forgetting to take the absolute value of the -11, which is 11.

Goldfinger2001 wrote:
Why is the answer not B

If you solve this equation you get 2 values for y, y=-8 and y=14

However, if you put y=14 back to the original stem (3-14)=11 -> -11 = 11 and this is not true.

Can somebody please help me out here?

|3-y|=11; when y>3, |3-y|=-(3-y)=11, -3+y=11, y=14;
when y<3, |3-y|=(3-y)=11, y=-8..!!
as here two different values are possible therefore B can't be the answer,

please remember that |x|= x, when x>0, and -x when x<0,

Thanks guys, my bad.... indeed I forgot to take the absolute value...

I was thinking about a different scenario... |-11| = -11 wouldn't work out....I was confused