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GMAT PRP QUESTION

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by lolap4 » Tue Mar 15, 2011 2:38 am
If n is an integer is -3x^n positive ?

(1) x is negative
(2) n is odd

My answer was A bcos it doesnt have parentheses so x would keep the negative sign no matter what n was. Thus -3*-x = would al ways yield > 0 RIGHTT???
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by HSPA » Tue Mar 15, 2011 2:42 am
If the question is (-3x)^n the value of X is sufficient

If the question is -3* (x^n) we need both the values of x and n

So it is C for me
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by lolap4 » Tue Mar 15, 2011 2:47 am
Yes, definitely that's what comes to mind. However I have seen recently this norm:

(-2)^2 = 4
-2^2= -4

This is why I chose A... I saw this rule in a manhattangmat test.. so maybe it does not apply to real GMAT problems ?
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by lolap4 » Tue Mar 15, 2011 2:51 am
btw the question isnt more specific that what I posted, but I suppose is how you stated it the second time: -3(x^n).. but still I am confused with the () rule.. am I missing something=?
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by HSPA » Tue Mar 15, 2011 3:11 am
consider x = -2 and n = 3 then x^n = -8

1) -3* (x^n) = -3*-8 is +ve

2) (-3x)^n = (-3*-2)^n ... irrespective of value of n the value is positive

consider x= -2 and n=2

1) -3*4 = -ve
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by lolap4 » Tue Mar 15, 2011 3:20 am
Thanks for your reply! but look at it this way:

so I get what you are saying but shoudnt you be doing the exponent first ??? By RULE PEMDAS: it should be this order
-3(x)^n so we have to do (x)^n first but we have no parentheses.

Mathematics state that if the X has no parenthesis the sign is not powered so take x= - 2 we would get - (4) and then multiply -3*-4 = always positive..

On the other hand if the Q was written like this -3*(x)^n it would def be C bcos the sign is powered to N...

There is a convention tho that we always take it as if it X (or any number) had the () and then the number and then the sign were both powered to N... Maybe here is where I am going wrong: Once I see X, when I substitute it's both, the number and sign that are powered..

Do you see where I am coming from??? THANK YOU!!
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by HSPA » Tue Mar 15, 2011 4:25 am
(-2)^2 = 4
-2^2= -4
Where did you get this ... square of any non zero integer number is always positive...

Kindly PM an expert for better explanations on this..
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by lolap4 » Tue Mar 15, 2011 4:33 am
well, as far as I know that is a basic Maths rule..

But I think I know where I am going wrong here when I do the problem I write it like this:
-3*x^n and then that rule stands (again I think.. clearly not an expert) In this case same as -2^2 =-4 you only power the number not the sign..

but what I should do is when I substitute the X I should power THE X( NUMBER AND SIGN) and thus write it like this:
-3*(-2)^n and then when number and sign are powered to N I do need to know N's value ... C

Thanks anayway! If there is an expert around would appreciate insight on the norm stated!!!

THANKS!
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by GMATGuruNY » Tue Mar 15, 2011 6:24 am
lolap4 wrote:If n is an integer is -3x^n positive ?

(1) x is negative
(2) n is odd

My answer was A bcos it doesnt have parentheses so x would keep the negative sign no matter what n was. Thus -3*-x = would al ways yield > 0 RIGHTT???
-3x^n = (-3)(x^n).
(-3x)^n = (-3)^n * x^n.

Statement 1: x<0
If x = -1 and n=2, -3(x^n) = -3*(-1)² = -3*1 = -3.
If x = -1 and n=3, -3(x^n) = -3*(-1)³ = -3*-1 = 3.
Insufficient.

Statement 2: n is odd
If x = -1 and n=3, -3(x^n) = -3*(-1)³ = -3*-1 = 3.
If x = 1 and n=3, -3(x^n) = -3*(1³) = -3*1 = -3.
Insufficient.

Statements 1 and 2 together:
If x<0 and n is odd, then x^n < 0. (A negative number raised to an odd power stays negative.)
Thus, -3(x^n) = negative * negative = positive.
Sufficient.

The correct answer is C.

To confirm the notation used on the GMAT (and in all of math):
-2² = -(2²) = -(2*2) = -4.
(-2)² = (-2)*(-2) = 4.
Last edited by GMATGuruNY on Tue Mar 15, 2011 6:32 am, edited 1 time in total.
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by lolap4 » Tue Mar 15, 2011 6:28 am
Yeh def I wasnt writting it like that with the ()--> -3(x^n)-- everything is powered.. basic I guess..!

Thanks a lot!
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