M60-13

I agree with you. I believe the answer they provided is wrong. This is not the first time REVOLUTION posted a wrong answer.

Asked:-
XIYI =XZ?

Break Down:- IYI = Z (canceling out x)
i.e. Z must be positive. (as IYI is always positive)
So one need to verify that Z is +ve as well as it is equal to Y in magnitude

1) The statement says that Z is +ve . But doesn't tell about magnitude of Z.
Hence Insufficient.

2)The statement says that Z can be + ve OR -ve . But magnitude of Z will be equal to that of Y.
Hence Insufficient.

Combining 1 & 2 , both conditions are satisfied. (Z is +ve as well as it is equal to Y in magnitude)

answer c

since y2= z2 and if z=negative then it does not satisfy the given equation. Hence we have to ensure if z is positive. Hence the answer is c

Because the reverse is not true. it only says |y|=z, not |z|=y.

Lets take an example. x=1, y=-2, z=2. This satisfies (2). And it also satisfies the stem. LHS = 1.|-2| = 2. RHS = 1.2=2.
Now lets switch things around. x=1, y=2, z=-2. This also satisfies (2). But look at what happens when we plug it in the stem. LHS = 1.|2| = 2. RHS = 1.(-2) = -2. So LHS not equal to RHS.

Question stem simplyfication:

X|Y|=XZ?

Step 1/ Take the right side to left side of the equation by subtraction:

X|Y|-XZ=0 ?

Step 2/ pull out common factors:

X(|Y|-Z)=0 ?

or is X=0? or (|Y|-Z)=0?_____|Y|-Z=0 ______ |Y|=Z_____ Y=Z 0r Y=-Z


The final question becomes: Is X=0? or Y=Z 0r Y=-Z or all of them are=0?



Statement 1/ For X,Y,and Z to be positive means:

1- X#0 but we still donot know if Y and Z have the same value? if Y and Z have the same value, then the answer on the final question is YES but if Y and Z donot have the same value, then the answer is NO! Not sufficient!


Statement 2/ Y^2=Z^2 means that Y^2-Z^2=0 or (Y+Z)(Y-Z)=0

for (Y+Z)(Y-Z)=0,

Case 1/ (Y+Z)=0 which means Y=-Z, which means Y and Z are not equal to each other, meaning the answer would be NO if X#0, but since the value of X is unknown, the question cannot be answerd.

Case 2/ (Y-Z)=0 which means Y=Z or Y and Z are equal to each other, in this case the value of X doesnot matter since Y=Z and Y-Z=0 and Zero multiply by any number the result will alway zero, so the answer on the question will be YES!

Since Statement 2 provides us case 1,inwhich the question cannot be answerd and case 2, inwhich the question will be answerd with a yes, it means we have two possible answers, statement 2 is not sufficient.


Statement 1 and 2 together:

From statement 1 X,Y,and z are all positive, which means X#0 #=not equal

From statement 2 Y=z or Y=-Z

Both statements together provide us that since X,Y,and z are all positive, then X#0 and Y=Z.

Since Y=Z then Y-Z=0 or (|Y|-Z)=0, so substitute 0 for (|Y|-Z), then we get, is X(0)=0 the answer is YES!


Both statements together are sufficient answer C

x|y| = yz ?

I squared both sides to get (xy)^2 = (yz)^2

and ended up with x^2 (y^2 - z^2) = 0 and chose B as the answer.

Is it wrong to square both sides in this case? Why?

I think this is a high-quality question and the explanation isn't clear enough, please elaborate. As y = +/- Z and X|y| than why i need to define whether z is positive or negative

Is \(x|y| = xz\) ?

Is \(x|y| - xz = 0\)?
Is \(x(|y| - z) = 0\) ?
Is \(x = 0\) or \(|y| = z \)?

(1) x, y, and z are positive

Since x and y are positive, then x ≠ 0 and |y| = y. So, the question boils down to is y = z ?. We don't know that. Insufficient.

(2) y^2 = z^2. Clearly insufficient.

(1)+(2) From (1) the question became whether y = z. But (1) also says that y and z are positive, thus y^2 = z^2 (from (2)) means that y = z. Sufficient.

Answer: C.

I think this is a high-quality question and I agree with explanation.