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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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06 Oct 2016, 06:12
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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)

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

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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 )
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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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06 Oct 2016, 06:59
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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.

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

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

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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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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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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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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.

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

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