What is the value of x? (1) x(y - z) = 0 (2) yz

Question

What is the value of x?

(1) x(y - z) = 0

(2) yz < 0

Neha2404 · Answer

IMO-C
X=?

Statement-1
X(y-z)=0
According to the equation 
Value of one x =0
Or 
y-z =0
X=0,
Or
X= more than or less than zero
Not sufficient

Statement-2
Yz<0
Using this statement unable to identify the value of x

Not sufficient

Both 
If yz<0
Means y or z both are not equal to zero
It means x is zero

Sufficient

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Russ19 · Answer

BrentGMATPrepNow ,  VeritasKarishma , could you please resolve the problem above?

suchita2409 · Answer

C

Stmt 1 says either x =0 or y= z or both.

Can't say.
 Insufficient.

yz less than 0 says nothing about x.

Combining them we can conclude that y != z.
So we can say that x is 0.

C it is!

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QuantMadeEasy · Answer

Understanding (1) 
From the given equation either x=0 OR y=z.
when y=z, then could take x any value
Insufficient

Understanding (2) 
product of y and z is negative, therefore sign of y and z must be opposite.
x cannot be determined with the information
Insufficient

Combining (1)+(2), 
as y and z have opposite signs, they cannot be equal, hence x =0.
Sufficient

(C) is correct

BrentGMATPrepNow · Answer

Target question :    What is the value of x?

Statement 1 : x(y - z) = 0  
This means EITHER x = 0 OR y - z = 0
 IMPORTANT: If y - z = 0, then y = z

So, it could be the case that x = 0, y = 2 and z = 1, in which case, the answer to the target question is  x = 0 
Or it could be the case that x = 1, y = 2 and z = 2, in which case, the answer to the target question is  x = 1 
Since we can't answer the  target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 : yz < 0  
No information about x. Statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined    
Statement 1 tells us that EITHER x = 0 OR y = z
IMPORTANT: If y - z = 0, then y = z
Statement 2 tells us that yz < 0, which means one value (y or z) is POSITIVE and the other value is NEGATIVE
If one value (y or z) is POSITIVE and the other value is NEGATIVE, then we can be certain that  y does not equal z 
If  y does not equal z , we can be certain that  x = 0  
Since we can answer the  target question  with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

KarishmaB · Answer

(1) x(y - z) = 0

means either x = 0 or (y - z) = 0
So either x = 0 or y = z
We don't know the value of x. It may be 0 or it may be something else (if y = z).

(2) yz < 0
yz < 0 means one and only one of y and z is negative and the other is positive (so their product is negative)
No value known for x.

Using both, we know that one of y and z is positive and the other negative. So CERTAINLY y and z are not equal. This means x must be 0. Sufficient

Answer (C)

ifteec464 · Answer

Statement 1, not sufficient since we can't be sure if X is 0 or (Y - Z). But we know for sure either X is 0 or (Y - Z) is 0. For Y - Z to be zero Y has to be equal to Z.

Statement 2 doesn't tell us anything about X. But since YZ is less than 0 i.e. negative, then Y and Z must have opposite signs, i.e. if Y is positive, Z must be negative or vice versa. Hence Y can't be equal to Z.

Now combining both, we know from statement 2 that (y - z) can't be 0 since they are not equal and have opposite signs. So, X must be 0 based on statement 1.

Ans. C

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What is the value of x? (1) x(y - z) = 0 (2) yz < 0

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What is the value of x? (1) x(y - z) = 0 (2) yz < 0

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