x^n + x^n + x^n = x^(n + 1), where x cannot equal zero. Which of the

Question

x^n + x^n + x^n = x^{(n + 1)} , where x cannot equal zero. Which of the following must be true?

I. n = 2
II. x = 3
III. n^x < x^n

(A) I only
(B) II and III
(C) I and III
(D) II only
(E) None of the above

SidJainGMAT · Accepted Answer

Its D..
As  3x^n=x^n*x  and x is not 0
so x=3 
Hence D. 
:-D

bowlalife · Answer

E for me.

A is negated because when x equals 1, n can take any value.

B is negated because x can take values other than 3. It can take 1.

C is negated by combining cases taking x equals 1 and 3 for different values of n.

E it is.

Sent from my ONE A2003 using  GMAT Club Forum mobile app

GTExl · Answer

i think it is D
 x^n + x^n + x^n = x^(n + 1)

3x^n=x*x^n

x^n(3-x)=0

as x is not equal to 0 only solution is x=3

i) we can not comment on value of n

ii) we have got x= 3

iii) n^x < x^n 
put x= 3 (only solution of x)
we get n^3 < 3^n

for n =3 condition will not hold true.

susheelh · Answer

Given :  x^n + x^n + x^n = x^{(n+1)}

=  3* x^n = x^{n+1}

= 3 =  \frac{x^{n+1}}{x^n}

=  3^1  =  x^1

Equating both sides we get x = 3. When x= 3, the value of n could be anything.

I. n = 2; n COULD be 2. And not MUST be 2. 
II. x = 3. As described above X MUST be 3. 
III.  n^x < x^n . From the stem we have x=3. Substituting we get  n^3 < 3^n  . By checking for n = +1,-1 and 0 we see the inquality holds true. But, does not hold true when n=3. So, this COULD be true.

So only II Must be true and the answer is D

rulingbear · Answer

The answer is D

Solving the equation gives x= 3, i.e 3 (x^n) = (x^n)x, x =3

Now,

For I, n does not have to be 2 for x=3 - Must not be true
For II, x=3 -  Must be true 
For III, take a case where n=3=x, this negates n^x < x^n - Must not be true

Hence answer is D.

niks18 · Answer

What if n=3. then the third statement will be  3^3<3^3  (as x=3) which is not possible and the question stem gives no constraint for "n" Hence B is doubtful

susheelh · Answer

Excellent!!! I stand corrected. Will edit the response as well. Thanks niks18 ! (How could I even overlook that! :shock:

)

MvArrow · Answer

I picked D because X^(n+1) is X(X^n) so 3X^n = X(X^n) hence X=3

devlin · Answer

We can simplify as 3x^n = x^(n+1) which equals to 3 = x for sure. So we can rid of options A, D and E. Then we need just to check statement III. Let say that n = 3. 3^3 < 3^3. Not true. Eliminating option B the remaning option is D.

ScottTargetTestPrep · Answer

Simplifying we have:

3(x^n) = x^n * x^1

3 = x

So, Roman numeral II must be true. Since the only choices involving II are B and D, we just need to test whether Roman numeral III is true.

We note that 3^n + 3^n + 3^n = 3^(n+1) is satisfied when n = 3 (which also proves Roman numeral I is not necessarily true). But then, substituting x = n = 3 in Roman numeral III, we see that 3^3 < 3^3 is not true.

Thus, among the given statements, only II must be true.

Answer: D

jmwon · Answer

I solved this by simplifying the question stem:

x^{n} + x^{n} + x^{n} = x^{n+1}  
 x^{n}(1 + 1 + 1) = x^{n+1} 
 x^{n}(3) = x^{n}(x^{1}) 
 x = 3

Since x = 3 was answer II, B and D were only items to choose from. Since I could not determine on any information regarding n, I eliminated B and went with D.

kayarat600 · Answer

Hi why can't we take x as 1 and if we can why does2 have to be true

Krunaal · Answer

x^n + x^n + x^n = x^{(n + 1)}

Simplifying the above,

=>  x^n * (1 + 1 + 1) = x^n * x

=>  x^n * 3 = x^n * x

From above, you get  x = 3

If you were to take x = 1, then LHS becomes 3, and RHS becomes 1 => and LHS is not equal to RHS, hence it would be invalid to take x = 1.

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