If x is a positive integer, what is the value of x ?

Question

(1)  x^2=\sqrt{x}

(2)  \frac{n}{x} = n  and  n
eq 0

(DS08306)

AkshdeepS · Answer

Given x > 0 (integer) Statement 1: x^2 = \sqrt{x} Squaring both sides: x^4 = x x^4 - x = 0 --- x (x^3 - 1) = 0 Solving for x x= 0 or x = 1 , As x can't be 0 as x is positive as per question stem, the only valid value is "1" Sufficient. Statement 2: \frac{n}{x} = n & n eq{0} x can only be "1" for statement-2 to be true. Sufficient. IMO Answer is (D). Updated answer (forgot to consider the question stem :-D

)

acegmat123 · Answer

x is a positive integer. So we can eliminate 0.

Answer is D

Sent from my iPhone using  GMAT Club Forum mobile app

Vinayak Shenoy · Answer

x is a positive integer (given)

From statement 1
 x^2=\sqrt{x} 
squaring and re arranging we get x^4-x=0, x=0,1
As x is a positive integer x=1

From statement 2
n/x=n
for this to be true x=1

Hence D

@p00rv@ · Answer

x is a positive integer (given)

From statement 1
x^2=√x --> x^4=x --> x^4-x=0 --> x(x^3-1)=0 -->Since x is a positive integer x^3=1 --> x=1. Hence Sufficient.

From statement 2
n/x=n --> n{(1/x) -1} =0 -->Since n!=0, (1/x)-1=0 -->1/x=1 -->x=1. Hence sufficient.

Hence D

Ndkms · Answer

Another approach for those that they are quite confident with exponents:

1)Squaring both sides of X^2 = sqrt(X) you get X^4 = X. Now divide both sides with X and you get X^3 = 1 (You can divide by x as x>0). Now the tricky thing comes in...you have to raise both sides to 1/3 power in order to get

(X^3) ^ 1/3 = 1^(1/3) which give X = 1^(1/3). The positive 1 is equal to 1 if is raised to any positive power which is the case. Hence Sufficient.

2) VERY Straightforward 
Multiply both sides by X so you can get n = x*n and then divide both sides by n in order to get n/n = (n*x) / n which will give x =1. Hence Sufficient.

I am not sure why I went one step further with statement (1). I am quite suprised that all of you did the x(x^3-1) = 0 ... Can you please explain why you stopped there?

Salsanousi · Answer

First we square both sides of statement 1)

x^4 = x  then it becomes  x^4 - x = 0  and taking x as a common factor it becomes  x (x^3 - 1) = 0  from the question stem we know x is a positive integer so it cannot be 0

x = 1  sufficient.

Eliminate B/C/E

check statement 2)

\frac{n}{x} = n

xn = n  then  xn - n = 0  then  n (x-1) = 0 we know n cannot be zero so x = 1 sufficient.

Answer choice D

rafa06 · Answer

Hi Bunuel, if we want to follow a factorizarion method I got stucked in the last term when factorizing x (x^3-1) could you advice?

Kinshook · Answer

If x is a positive integer, what is the value of x ?

(1)  x^2=\sqrt{x} 
x = 1
SUFFICIENT

(2)  \frac{n}{x} = n  and  n
eq 0 
x=1 
SUFFICIENT

IMO D

ScottTargetTestPrep · Answer

Solution:

Question Stem Analysis:

We need to determine the value of x, given that it is a positive integer.

Statement One Alone:

The only positive integer (and actually the only positive number) whose square is equal to its square root is 1. Therefore x = 1. Statement one alone is sufficient.

Statement Two Alone:

Multiplying both sides of the equation by x (since it is not 0), we have:

n = nx

Since n is also not 0, dividing both sides by n, we have:

1 = x

Statement two alone is sufficient. 
 
 Answer: D

KanikaJain · Answer

If x is a positive integer, what is the value of x ?

(1) x^2=√x
(2) n/x=n and n≠0

x is a positive number - thus x>0

Statement 1:
x^4 = x
x^4 - x = 0
x(x^3 - 1) = 0
x = 0, 1. but x>0 thus x = 1

Statement 2:
as n is not equal to 0
thus:
1/x=1 
x = 1

thus D

If x is a positive integer, what is the value of x ?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards