Welcome back! Today, we’ll go over Tuesday’s Brain Twister problem.

## 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

## Answer and Explanation

There are a few ways to flub this question. One is to think that there is no way to know the value of ‘n’ or ‘x’ and then to blithely mark (E) as the answer. The reality is that one of the variables is a known, based on the relationship between the two sides of the equation.

Notice how there are three ‘x^n’ values on the left and on the right side of the equation we have x^(n + 1). Therefore, ‘x’ has to be ‘3’, since we are adding one more ‘x’ (remember the (n+1)).

Another way to miss this question is by forgetting the case for where x could equal n. So if we know that ‘x’ has to be three and we make n = 3, then Condition III is not true.

Therefore, the answer is (D).

See you again soon!

Hi Chris,What about if x equals zero and n equals (for instance) 1? Then the equation is satisfied: on the left side, each of the terms equals zero (0 to the 1st power), so their sum equals the term on the right (0 to the 2nd power). Since the equation has a solution where x does not equal 3, answer choice D must be incorrect and answer choice E must be correct. Do you see any problems with my reasoning here?

So, we get x=3 and n= 1 . Am I correct ?

Hi,

Your answer should be D, II only, right?

Thanks!

Yes, my answer was supposed to be (D). I made a typo :).

don’t you mean the correct answer is D?

The answer should be ‘D’ as condition 3 only holds true.

Answer is D.

what if ‘x’ equals zero.

or can you please explain why ‘x’ can not be equal to zero.

Chris, The answer can’t be A.

If the answer is A,

then it will be evaluated to 3 * x ^2 = x ^ (3)

If x is valued as 1, there is inequalities on the both side.

Therefore, It can’t be A.

Yes, that was a typo on my part :). I meant (D), not (A).

“Therefore, the answer is (A).”

Sorry, I meant the answer is D.

Yes, yes :)…that was a typo on my part.

A? o.O. Lele, Is it a typo or am I missing something important in this seemingly easy question?

I rather hope not!

Hi Vinod,

No, you are not missing anything :). And yes, that was a typo 🙂

Hi Chris,

I think answer should be (D)

Yes, it should be (D). That was a typo 🙂

Hii..

I don’t understand how u could conclude n=2 when the question is 3*x^n= x^(n+1) if n=2 exponent on lhs is 2 and on rhs is 3

Hey Chris,

I solved till x=3 and marked answer D as the correct one. However, per your explanation there is one more condition x=n. I’m totally lost how this condition is considered in this problem. Could you please elaborate ?

Regards,

Ridhi

Sorry about that! Rereading my explanation, I too am initially confused. I will rework that explanation so that it makes more sense!

Hi Chris,

In the explanation you have mentioned that x has to be 3 in order to satisfy the equation. Thus, answer should be option D not A.

Yes, that was a typo 🙂

Hey 🙂 Shouldn’t the answer be D?

Yep, that was a typo on my part 🙂