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Given that x, y, z are non zero integers. Is (x^3)(y^5)(z^4)
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25 Aug 2012, 04:59
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Given that x, y, z are non zero integers. Is (x^3)(y^5)(z^4)>0? (1) xy > z^4 (2) x > z
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Re: Given that X, Y, Z are non zero integers. Is X^3Y^5Z^4>0?
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25 Aug 2012, 05:19
Given that X, Y, Z are non zero integers. Is (X^3)(Y^5)(Z^4)>0?Notice that since z is a nonzero 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,
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Re: Given that X, Y, Z are non zero integers. Is X^3Y^5Z^4>0?
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25 Aug 2012, 05:23
vinay911 wrote: Given that X, Y, Z are non zero integers. Is (X^3)(Y^5)(Z^4)>0?
(1) XY > Z^4 (2) X > Z 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 nonnegative. 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.
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Re: Given that X, Y, Z are non zero integers. Is X^3Y^5Z^4>0?
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25 Aug 2012, 05:34
EvaJager wrote: vinay911 wrote: Given that X, Y, Z are non zero integers. Is (X^3)(Y^5)(Z^4)>0?
(1) XY > Z^4 (2) X > Z 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 nonnegative. 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. Eva, notice that we are told that X, Y, Z are non zero integers.
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Re: Given that X, Y, Z are non zero integers. Is X^3Y^5Z^4>0?
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25 Aug 2012, 05:47
Bunuel wrote: EvaJager wrote: vinay911 wrote: Given that X, Y, Z are non zero integers. Is (X^3)(Y^5)(Z^4)>0?
(1) XY > Z^4 (2) X > Z 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 nonnegative. 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. Eva, notice that we are told that X, Y, Z are non zero integers. 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
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Re: Given that X, Y, Z are non zero integers. Is X^3Y^5Z^4>0?
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26 Aug 2012, 10:34
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
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Re: Given that X, Y, Z are non zero integers. Is X^3Y^5Z^4>0?
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26 Aug 2012, 22:07
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
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Given that X, Y and Z are non zero integers. Is X^3*Y^5*Z^4>0 ?
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21 Dec 2018, 11:12
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.
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Re: Given that X, Y and Z are non zero integers. Is X^3*Y^5*Z^4>0 ?
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08 Jan 2019, 19:33
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
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Re: Given that X, Y and Z are non zero integers. Is X^3*Y^5*Z^4>0 ?
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09 Jan 2019, 07:29
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



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Re: Given that X, Y and Z are non zero integers. Is X^3*Y^5*Z^4>0 ?
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09 Jan 2019, 10:54
chand567 wrote: Given that X, Y and Z are non zero integers. Is X^3*Y^5*Z^4>0 ?
(1) XY>Z^4
(2) X > Z (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




Re: Given that X, Y and Z are non zero integers. Is X^3*Y^5*Z^4>0 ?
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