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(1) \(3|x^2-4|=y-2\). Now, since we are asked to find the value of y, from this statement we can conclude only that \(y\geq{2}\), as LHS is absolute value which is never negative, hence RHS als cannot be negative. Not sufficient.

(1)+(2) Since from (1) \(y\geq{2}\), then from (2) \(y=14\). Sufficient.

Answer: C.

Hope it's clear.

Hi Bunuel,

in the second statement, you solved the inequality and got -8 and 14 which satisfy the inequality if you plug them.

but, what about if you get two answers, and one satisfies the inequality and one doesn't. for example |x+3| = 4x-3, how do you go about that?
_________________

(1) \(3|x^2-4|=y-2\). Now, since we are asked to find the value of y, from this statement we can conclude only that \(y\geq{2}\), as LHS is absolute value which is never negative, hence RHS als cannot be negative. Not sufficient.

(1)+(2) Since from (1) \(y\geq{2}\), then from (2) \(y=14\). Sufficient.

Answer: C.

Hope it's clear.

I have a general question... I went ahead and solved the equation in st. 1 and got that x = sqrt(8)... Now, if we were told that both x and y were integers, than does that mean that both statements were not sufficient? Would have it affected our final result? Because st.1 doesn't really just say that y>= 2 right? It actually gives y a value.....?

(1) \(3|x^2-4|=y-2\). Now, since we are asked to find the value of y, from this statement we can conclude only that \(y\geq{2}\), as LHS is absolute value which is never negative, hence RHS als cannot be negative. Not sufficient.

(1)+(2) Since from (1) \(y\geq{2}\), then from (2) \(y=14\). Sufficient.

Answer: C.

Hope it's clear.

I have a general question... I went ahead and solved the equation in st. 1 and got that x = sqrt(8)... Now, if we were told that both x and y were integers, than does that mean that both statements were not sufficient? Would have it affected our final result? Because st.1 doesn't really just say that y>= 2 right? It actually gives y a value.....?

How did you get from (1) that \(x=\sqrt{8}\)? That's not correct. You cannot solve \(3|x^2-4|=y-2\).

Next, yes y is some number but whatever number it is from \(3|x^2-4|=y-2\) it follows that it's more than or equal to 2.
_________________

Bunuel, I understand from statement 1 we get y>=2 , but when we combine both statements together we get y>=2 and y=14. Now how can we just assume y to be 14, because y can also take the value of 2 right . I chose E on this basis .

Bunuel, I understand from statement 1 we get y>=2 , but when we combine both statements together we get y>=2 and y=14. Now how can we just assume y to be 14, because y can also take the value of 2 right . I chose E on this basis .

tnx dear

From (1): \(y\geq{2}\); From (2): \(y=-8\) or \(y=14\).

1. from one we could conclude either y is greater than or equal to 2 as |x^2 - 4| always greater than -ive values. but we cant determine the values hence Insuff.

2. y could be -8 or 14 , two values .. In sufff.

combining-- from one , y is greater than or equal to 2 & from two y= -8 or 14 .. y should be 14. Hence C

Quick couple of questions around Absolute value and inequalities

1.When 4\(|x + 1/2|\) = 18 can become + (x + 1/2) = 4.5 or –(x + 1/2) = 4.5, why can't 3|\(x^2\) – 4| = y – 2 become (\(x^2\) – 4)= (y – 2)/3 or -(\(x^2\) – 4) = (y – 2)/3 ?

2. What happens to the inequality when you take the square root on both the sides? For e.g. \(x^2\) \(<=\)1. Also, please let me know if there are any specific rules when squaring on both sides?

Quick couple of questions around Absolute value and inequalities

1.When 4\(|x + 1/2|\) = 18 can become + (x + 1/2) = 4.5 or –(x + 1/2) = 4.5, why can't 3|\(x^2\) – 4| = y – 2 become (\(x^2\) – 4)= (y – 2)/3 or -(\(x^2\) – 4) = (y – 2)/3 ?

2. What happens to the inequality when you take the square root on both the sides? For e.g. \(x^2\) \(<=\)1. Also, please let me know if there are any specific rules when squaring on both sides?

Thanks in advance

1. We could, but this is no help in finding the value of y.

1. We could, but this is no help in finding the value of y.

Thank you. For a few hours I was searching all over fanatically to verify if my fundamental understanding of modulus theory is flawed. Now, I know what else I could do when a modulus operator is present. And thanks also for the linky, I will check it out now.

Btw, Why couldn't 'y' take both the values ( -8 & 14) as per statement 2?!

Iam unable to paste links;I could find sites like 'sosmath' where both the values are shown as solutions

y could be either -8 or 14. What is confusing there?

So,if 'y' can take both values, that would mean statement 2 is right kno? Linear absolute value equations can have 2 values as solutions, am i right please?

Btw, Why couldn't 'y' take both the values ( -8 & 14) as per statement 2?!

Iam unable to paste links;I could find sites like 'sosmath' where both the values are shown as solutions

y could be either -8 or 14. What is confusing there?

So,if 'y' can take both values, that would mean statement 2 is right kno? Linear absolute value equations can have 2 values as solutions, am i right please?

No. When a DS question asks about the value of some variable, then the statement(s) is sufficient ONLY if you can get the single numerical value of this variable. So, the second statement is NOT sufficient because we can two possible values of y, not one.

(1) \(3|x^2-4|=y-2\). Now, since we are asked to find the value of y, from this statement we can conclude only that \(y\geq{2}\), as LHS is absolute value which is never negative, hence RHS als cannot be negative. Not sufficient.

(1)+(2) Since from (1) \(y\geq{2}\), then from (2) \(y=14\). Sufficient.

Answer: C.

Hope it's clear.

Hi,

Can I solve statement 1 like this:

3|x^2-4|=y-2

Now since this is an absolute value

I would 1st solve for x

x^2-4=0 x2=4 and x=+/-2 now if I substituent the value of x in the above expression If x= +2 3|x^2-4|=y-2 3|(2)^2-4|=y-2 3|0|=y-2 therefore y=2

now if x=-2 3|x^2-4|=y-2 3|(-2)^2-4|=y-2 3|0|=y-2 and therefore y=2

In both the cases I will get the same value for Y.

Can someone please explain what is wrong with this approach.

We don't know whether x^2-4=0, thus all your further steps are based on that false assumption. If we knew that x^2-4=0, then x^2-4=0=y-2 --> y-2=0 --> y=2.

Also, you can notice that your approach is not correct from the fact that on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other. From (2) we have that y is -8 or 14, and if from (1) you get that y is 2 it would mean that the statements clearly contradict.

x^2-4=0 x2=4 and x=+/-2 now if I substituent the value of x in the above expression If x= +2 3|x^2-4|=y-2 3|(2)^2-4|=y-2 3|0|=y-2 therefore y=2

now if x=-2 3|x^2-4|=y-2 3|(-2)^2-4|=y-2 3|0|=y-2 and therefore y=2

In both the cases I will get the same value for Y.

Can someone please explain what is wrong with this approach.

We don't know whether x^2-4=0, thus all your further steps are based on that false assumption. If we knew that x^2-4=0, then x^2-4=0=y-2 --> y-2=0 --> y=2.

Also, you can notice that your approach is not correct from the fact that on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other. From (2) we have that y is -8 or 14, and if from (1) you get that y is 2 it would mean that the statements clearly contradict.

Does this make sense?

Why cannot we solve the 1st as :

3|x^2-4| =y-2

x^2-4 = (y-2)/3

x^2= (y+10)/3 -----(1)

and considering the negative sign i.e

x^2-4=-(y-2)/3

x^2= (-y+14)/3 -----(2)

and then equating 1 and 2

we will get y = 2

What is wrong with this approach??

Those are 2 separate cases: |x^2 - 4| = x^2 - 4, when x^2 - 4 > 0 and |x^2 - 4| = -(x^2 - 4), when x^2 - 4 < 0.
_________________

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