Given that x, y, z are non zero integers. Is (x^3)(y^5)(z^4)

Question

Given that x, y, z are non zero integers. Is (x^3)(y^5)(z^4)>0?

(1) xy > z^4
(2) x > z

Bunuel · Answer

Given that X, Y, Z are non zero integers. Is (X^3)(Y^5)(Z^4)>0?

Notice that since z is a non-zero integer, then z^4>0, so we can reduce the given inequality by it and the question becomes: is x^3*y^5>0? or: is xy>0?

(1) XY > Z^4 --> since z^4>0, then we have that xy>z^4>0. Sufficient.
(2) X > Z. Not sufficient as we don't know anything about y.

Answer: A,

EvaJager · Answer

The sign of the given expression depends on the sign of the product  XY  because  X^3Y^5Z^4=XY*X^2Y^4Z^4  and  X^2Y^4Z^4  is always non-negative. The given product can be 0 as well, if at least one of the variables is 0.

(1) Not sufficient, because Z can be 0.
(2) Not sufficient, because Z can be 0.

(1) and (2): Although from (1) we can deduce that  XY>0,  (because  Z^4\geq0 ) again not sufficient, the same fast reasoning, Z can still be 0.

Bunuel · Answer

Eva, notice that we are told that X, Y, Z are  non zero  integers.

EvaJager · Answer

Oooooops! Thanks.

So, forget about any of the variables being 0. We need to check whether  XY>0. 
Then the above solution changes:

(1) Sufficient, since  XY>0,  (because  Z^4>0 ).
(2) Not sufficient, as we don't know anything about Y.

Answer A

thevenus · Answer

Given that X, Y, Z are non zero integers. Is (X^3)(Y^5)(Z^4)>0?

(1) XY > Z^4
(2) X > Z

My approach :-

(i) XY>Z^4
RHS is always +ve , so XY both can either be +ve or -ve
a)if XY both +ve then (X^3)(Y^5)(Z^4)>0 (because Z^4 is +ve
b)if XY both -ve then (X^3)(Y^5)(Z^4)>0 (because - - + is +ve

Suffficient

(ii) no clue about Y -insufficient

(A) wins

alchemist009 · Answer

it is given that x, y and z are no zero integer, if so z^4 is always positive what ever the z is.

to be positive the given expression we have to determine whether x and y have the same sign or not, keeping in mind that x and y have odd power.

statement 1

xy > z^4 
XY > positive that means X and Y have the same sign

so the given expression must be positive

statement 1 is sufficient

statement 2 does not tell anything about y so insufficient

please correct me if i am wrong

Chethan92 · Answer

Question, whether  X^3Y^5Z^4 > 0

From statement 1:

XY > Z^4 
Since Z^4 is always positive.
Either X and Y are both negative or X and Y are both positive.
Hence,  X^3Y^5Z^4  will always be greater than 0.
Sufficient.

From statement 2:

X > Z 
If X = -2 and Z = -3.
-2 > -3
But,  X^3Y^5Z^4 < 0 
If x = 2 and Z = 1.
Then  X^3Y^5Z^4 > 0 
Hence, Insufficient.

A is the answer.

tapasgupta · Answer

We need to see whether both x and y are positive or not for the inequality to be true.

1. product of xy is greater than z^4. We already know that z^4 will be positive so xy is positive. Hence Sufficient

2. we cannot conclude the value of y (+ve or -ve). Insufficient.

Hence A is the answer

abannore · Answer

To prove: X^3*Y^5*Z^4>0
For this statement to be true, following cases must be satisfied:
Case 1: All terms: x^(3), y^(5) and z^(4) are positive
 so possible values :X,Y should be positive, Z can be positive or negative
Case 2: z^(4) is positive, y^(5)*x^(3) is negative
 Possible values:Z is positive/negative, y is positive, x is negative...xy is negative
 Z is positive/negative, x is positive, y is negative.....xy is negative

Statement 1: XY>Z^4
z^(4) is always positive. so XY is also positive. so from above, case 1 is satisfied. Statement is sufficient

Statement 2: X>Z
Insufficient

Answer A

ocelot22 · Answer

(1) XY> Z^4. Since X>4 must >0, this means XY>0. This is good because we can factor out XY without changing the sign of our expression

XY(x^2Y^4Z^4) >0 Now, since xy>0, x^2,y^2, z^4 must >0 then the entire expression must >0 Suff

(2) X> Z Suppose x=-2 z=-1 y=1 our expression becomes (-2)^3(1)^5(1)^4<0 giving us a NO. Now suppose x=1, y=1 Z=1, our expression becomes 1>0 giving us a yes. Since we get a Yes and a No by testing different appropriate values (2) is NS

Answer is A

bumpbot · Answer

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Given that x, y, z are non zero integers. Is (x^3)(y^5)(z^4)

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Given that x, y, z are non zero integers. Is (x^3)(y^5)(z^4)

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