Data Sufficiency

What is the value of y?

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

(2) |3 - y| = 11

Hi,

Statement 1:

If x = 1, y = 11
If x = 2, y = 8

(I am assuming x2 stands for x^2)

We are getting different values of y - depending on the value of x. Hence, insuff

Statement 2:

3 - y = -11 or 11

y = 14 or -8

We are getting different values of y. Hence, insuff.

Combining both 1 & 2:

If y = -8,

3|x2 - 4| = -10

|x2 - 4| = -10/3 -> a negative number which is NOT a possibility

If y = 14,

3|x2 - 4| = 12

|x2 - 4| = 4

x2 - 4 = -4 or +4

x2 = 0 or 8

x = 0, -2root(2) or +2root(2).

There may be three values of x - however, all of them lead to only one value of y; which is 14. Hence, suff. Is it C ???

Thanks. Hope this helps.

What is the value of y?

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

(2) |3 - y| = 11

Statement 1: 3|x² - 4| = y - 2.
If x=0, then y=14.
If x=2, then y=2.
Since y can be different values, insufficient.

Statement 2: |3 - y| = 11.
Solving 3-y = 11 and 3-y = -11, we get:
y = -8 or y=14.
Since both y = -8 and y=14 are possible, insufficient.

Statements 1 and 2 combined:
Statement 2 requires that y = -8 or y=14.
Plugging y = -8 into 3|x² - 4| = y - 2, we get:
3|x² - 4| = -8-2
3|x² - 4| = -10
Not possible, since the left side cannot yield a negative result.
Thus, y=14.
Sufficient.

The correct answer is C.

Hello-

For statement 1 what is the assumption that you had made to take as 0 in the first instance

I could have taken 1 or 10 why 0

that does get you to thr right solution but why 0?

Thanks

GMATGuruNY wrote:

Stendulkar wrote:What is the value of y?

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

(2) |3 - y| = 11

Statement 1: 3|x^2 - 4| = y - 2.
If x=0, y=14.
If x=2, y=2.
Since both y=14 and y=2 are possible, insufficient.

Statement 2: |3 - y| = 11.
Solving 3-y = 11 and 3-y = -11, we get:
y= -8 or y=14.
Since both y= -8 and y=14 are possible, insufficient.

Statements 1 and 2 combined:
Statement 2 requires that y= -8 or y=14.
Plugging y= -8 into 3|x^2 - 4| = y - 2, we get:
3|x^2 - 4| = -8-2
3|x^2 - 4| = -10
Not possible, since the left side cannot yield a negative result.
Thus, y=14.
Sufficient.

The correct answer is C.

venmic wrote:Hello-

For statement 1 what is the assumption that you had made to take as 0 in the first instance

I could have taken 1 or 10 why 0

that does get you to thr right solution but why 0?

Thanks

GMATGuruNY wrote:

Stendulkar wrote:What is the value of y?

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

(2) |3 - y| = 11

Statement 1: 3|x^2 - 4| = y - 2.
If x=0, y=14.
If x=2, y=2.
Since both y=14 and y=2 are possible, insufficient.

Statement 2: |3 - y| = 11.
Solving 3-y = 11 and 3-y = -11, we get:
y= -8 or y=14.
Since both y= -8 and y=14 are possible, insufficient.

Statements 1 and 2 combined:
Statement 2 requires that y= -8 or y=14.
Plugging y= -8 into 3|x^2 - 4| = y - 2, we get:
3|x^2 - 4| = -8-2
3|x^2 - 4| = -10
Not possible, since the left side cannot yield a negative result.
Thus, y=14.
Sufficient.

The correct answer is C.

When we evaluate statement 1, we could plug in any value for x; I just happened to choose x=0 and x=2. The point is that since x can be more than value, y can be more than one value. Thus, statement 1 is insufficient.