Is x^2yz negative? (1) x

Question

Is  x^2yz  negative?

(1) x < 0
(2) y < 0

joohwangie · Answer

Is x^2yz negative?

(1) x < 0
insufficient we know only x is negative we don't know the other 2 variables.
(2) y < 0
insufficient we know only y is negative we don't know the other 2 variables.

together we still don't know z
therefore, E

rsrighosh · Answer

the question states x^2yz <0 ? This means whether the expression is less than 0 or greater than 0 or 0 will depend on y and z mainly. x should not be equal to 0. x<0 or x>0 does not matter as x is squared. 1st Statement x<0 Doesn't matter whether x <0 because the expression has x^2 which is positive. No idea on y and z 2nd statement y<0 Does not give idea on the value of x and z Together statement 1&2 No idea on value of z. If z=0 then entire expression becomes 0 If z<0, then entire expression becomes greater than 0 If z>0, then entire expression becomes less than 0 Hence E.

Kinshook · Answer

Asked: Is x^2yz negative? x^2yz is negative when yz is negative since x^2 is non-negative. (1) x < 0 NOT SUFFICIENT (2) y < 0 If z>0; x^2yz is 0 or negative. But if z<0; x^2yz is 0 or positive. NOT SUFFICIENT (1) + (2) If z>0; x^2yz is 0 or negative. But if z<0; x^2yz is 0 or positive. NOT SUFFICIENT IMO E

AndrewN · Answer

This is a case in which a little visualizing ahead of time can ensure that you arrive at an accurate answer efficiently. If any of the variables equal 0, then it is game over: the product will be 0.  Apart from that scenario , we know the following:

1)  x^2  will be positive (so, provided x ≠ 0, we only need to look at y and z);

2) The combinations of negatives and positives are as follows, but  they are each dependent on knowing the values of y and z, relative to 0 :

y    z    Product     +  +  +    +  -  -    -  +  -    -  -  +

Statement (1) tells us about x. Since it is not 0, we know squaring it will yield a positive value. But we know nothing of y or z.  Not sufficient.

Statement (2) tells us about y: it is negative. But we know nothing of z, and we can see from our table above that the product could go either way.  Not sufficient.

Putting the two statements together still leaves us wondering about z. Hence,   the answer must be (E)  .

Happy studies.

- Andrew

Crytiocanalyst · Answer

(1) x < 0 if y>0 , z>0 then the equation is positive y<0, z>0 , the equation is negative Clearly insufficient (2) y < 0 for z>0 the eqn is negative for z<0 it's positive Clearly insufficient When 1 and 2 is combined we get We still can get 2 possibilities Clearly insufficient Therefore IMO E

Archit3110 · Answer

#1
x<0
Sign of x would have no effect on x^2yz being + or -ve as either of y or z has to be -ve
Insufficient
#2
Y<0
Value of z if <0 will make target + and if z>0 then -ve
Insufficient
From. 1&2
We cannot determine conclusively as z sign is not known
Insufficient
Option E

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Is x^2yz negative? (1) x < 0 (2) y < 0

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