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

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Joined: 02 Aug 2009
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If x^2-xy<0, what is the number of possible integer values of x?  [#permalink]

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14 Aug 2018, 05:12
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Difficulty:

55% (hard)

Question Stats:

49% (01:48) correct 51% (01:44) wrong based on 41 sessions

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

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

Chetan's questions

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

New question!!!..
Kudos for correct solution

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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