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

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If x is a positive integer, what is the value of x ?  [#permalink]

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New post 06 Oct 2016, 06:12
2
13
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

70% (01:05) correct 30% (01:06) wrong based on 577 sessions

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Re: If x is a positive integer, what is the value of x ?  [#permalink]

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New post Updated on: 06 Oct 2016, 07:08
1
Bunuel wrote:
If x is a positive integer, what is the value of x ?

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

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


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: \(\frac{n}{x}\) \(= n\) & \(n\neq{0}\)

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 )
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Originally posted by AkshdeepS on 06 Oct 2016, 06:44.
Last edited by AkshdeepS on 06 Oct 2016, 07:08, edited 2 times in total.
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Re: If x is a positive integer, what is the value of x ?  [#permalink]

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New post 06 Oct 2016, 06:59
2
GMATantidote wrote:
Bunuel wrote:
If x is a positive integer, what is the value of x ?

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

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


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 , Not sufficient

Statement 2: \(\frac{n}{x}\) \(= n\) & \(n\neq{0}\)

x can only be "1" for statement-2 to be true.

Sufficient. IMO Answer is (B)



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

Answer is D


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Re: If x is a positive integer, what is the value of x ?  [#permalink]

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New post 06 Oct 2016, 08:08
Bunuel wrote:
If x is a positive integer, what is the value of x ?

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

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



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
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Re: If x is a positive integer, what is the value of x ?  [#permalink]

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New post 06 Oct 2016, 10:45
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
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Re: If x is a positive integer, what is the value of x ?  [#permalink]

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New post 20 Jan 2017, 09:39
Bunuel wrote:
If x is a positive integer, what is the value of x ?

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

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



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?
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Re: If x is a positive integer, what is the value of x ?  [#permalink]

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New post 19 Oct 2018, 10:02
Bunuel wrote:
If x is a positive integer, what is the value of x ?

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

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


(DS08306)


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
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Re: If x is a positive integer, what is the value of x ?  [#permalink]

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New post 15 Nov 2018, 20:30
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?
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Re: If x is a positive integer, what is the value of x ?   [#permalink] 15 Nov 2018, 20:30
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