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If x^2-xy<0, what is the number of possible integer values of x?

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If x^2-xy<0, what is the number of possible integer values of x?  [#permalink]

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New post 14 Aug 2018, 05:12
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If \(x^2-xy<0\), what is the number of possible integer values of x?

(1) \(|y|=5\)
(2) \(y^3=125\)


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Re: If x^2-xy<0, what is the number of possible integer values of x?  [#permalink]

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New post 14 Aug 2018, 05:36
1
Lets check question statement itself
\(x^{2}\)−xy<0
x(x-y) < 0

that means either x or x-y one of them is negative . (both cannot be negative or positive)

lets check statement 1 : |y| = 5
this tells us that y = 5 or -5

case 1: so if y is positive , x (x-5) < 0
so x can take values between 0 to 5 , integer values = 1,2,3,4

Case 2: so if y is negative , x (x+5) < 0
so x can take any values between -5 to 0 , integer values = -1,-2,-3,-4

so in either case possible integer values for x are 4.

Statement 2 : \(y^{3}\) = 125
so value of y can only be y = 5 , which we have already solved and gives count of integer values = 4

So both statements are sufficient
Ans should be D
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Re: If x^2-xy<0, what is the number of possible integer values of x?  [#permalink]

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New post 14 Aug 2018, 05:38
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chetan2u wrote:
If \(x^2-xy<0\), what is the number of possible integer values of x?
(1)\(|y|=5\)
(2)\(y^3=125\)


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Question stem:- what is the number of possible integer values of x?

St1:- \(|y|=5\)
Or, y=5, -5
Given, \(x^2-xy<0\)
a) when y=5, we have \(x^2-5x<0\)
Or, x(x-5)<0
Or, 0<x<5
Possible integer values:- 4 (1,2,3,4)
b) when y= -5, we have \(x^2+5x<0\)
Or, x(x+5)<0
Or, -5<x<0
Possible integer values:- 4 (-4,-3,-2,-1)
Sufficient.
St2:- \(y^3=125\)
Or, y=5
a) when y=5, we have \(x^2-5x<0\)
Or, x(x-5)<0
Or, 0<x<5
Possible integer values:- 4 (1,2,3,4)
Sufficient.

Ans. (D)
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Re: If x^2-xy<0, what is the number of possible integer values of x?   [#permalink] 14 Aug 2018, 05:38
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