Is 5 x 0 ?

Question

Is 5 > x > 0 ?

(1) x is an integer greater than 4
(2) 5x^2 - 25x > 0

gmat1220 · Answer

1) is Sufficient. Easy 2) rephrased as x(x-5) > 0 hence x < 0 or x > 5. Sufficient. Even if you draw the number line the region 0 < x < 5 is excluded. Hence the answer is NO. D it is.

beyondgmatscore · Answer

GMATD11 - your workings are correct but conclusion is not. For statement B, you have proven that x is either less than 0 or more than 5, so we can certainly say that x does not lie between 0 and 5 and this is sufficient to answer the question is 5>x>0, hence sufficient and answer is D.

Please remember, a definite No answer is also sufficient.

Please remember, a definite No answer is also sufficient.

Bunuel · Answer

Is 5 > x > 0 ?

(1) x is an integer greater than 4

x must be 5 or greater. Sufficient.

(2) 5x^2 - 25x > 0

5x(x-5) > 0
x(x-5) > 0
The only way x(x-5) is positive is if both x and (x-5) are positive or negative.

We can conclude that x < 0 or x > 5. Sufficient.

Answer is D.

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m990540 · Answer

Bunuel, out of curiosity how would you graph (x^2) - 5x? I understand how you did it here (x2-4x-94661.html#p731476), but graphing it doesn't really seem to be working for this equation.

Bunuel · Answer

x^2-5x=0: MSP216419ef1hab97a0ab1200005h6b9b331di3gh21.gif As you can see x^2-5x>0 for x<0 and x>5.

m990540 · Answer

Thank you! That makes it much easier to see the answer.

beyondgmatscore · Answer

You don't really need the ability to draw the actual graph - You just need to know that an equation of this form with likely multiple roots would change signs at those roots.

Lets look at x^2-5x

This can be rewritten as  x*(x-5) , so points of interest are  x = 0  and  x=5  (where this function equals to zero). So, it can be deduced that this function will change a sign at  x=0  and then again at x=5 .

Whats the sign when x<0 . Lets put x=-1  and see, it is +ve , so between 0 and 5, function will be negative and again for  x > 5 , it will be positive.

So, without drawing exact graph, you can estimate that for x<0, the curve would be in 2nd quadrant (x is -ve and y is positive), between 0 and 5 it will be 4th quadrant (x is positive and y is negative) and again after x=5, it will be 1st quadrant (both x and y are positive)

Bunuel · Answer

All that is explained here: x2-4x-94661.html#p731476

stonecold · Answer

We need to check the range here 
Statement 1 is sufficient to say that x will never be in the range (0,5)
and Statement 2 too .
hence D

Basshead · Answer

Is 5 > x > 0 ?

(1) x is an integer greater than 4

x must be 5 or greater. Sufficient.

(2) 5x^2 - 25x > 0

5x(x-5) > 0
x(x-5) > 0
The only way x(x-5) is positive is if both x and (x-5) are positive or negative.

We can conclude that x < 0 or x > 5. Sufficient.

Answer is D.

Is 5 > x > 0 ?

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