If x^{n+1} - 2x^n=3x^n, then what is the value of x^n?

Question

If  x^{n+1} - 2x^n=3x^n , then what is the value of x^n?

(1)  x^{n+1}=625

(2) x=5

Skywalker18 · Answer

Hi  Bunuel  , do we need to solve for the value of n ?

x^{n+1} - 2x^n=3x^n 
 x^{n+1} = 2x^n + 3x^n = x^n (2+3) = 5 * x^n 
=> x = 5

(1)  x^{n+1}=625 = 5^4 
We can solve for the value of n
Sufficient

(2) x=5
Not sufficient as we already know x

Answer A

Bunuel · Answer

We need to find the value of x^n. Edited. Thank you.

gauravsaggis1 · Answer

from given equation x=5.
now statement 1. x^(n+1)=625. can be solved for n and then x^n. so sufficient.

statement 2- already given in the stem. so not sufficient.

ANS A.

jasimuddin · Answer

STEM: x^(n+1) - 2x^n=3x^n
or, x^n.x=5x^n
or, x=5...........(i)
x^n=?

STAT-1:x^(n+1)=625
or, 5^(n+1)=5^4
or, n+1=4
or, n=3.........sufficient

STAT-2: x=5, already given at STEM..... insufficient

ANS:A

mikemcgarry · Answer

If x^{n+1} - 2x^n = 3x^n , then what is the value of x^n ? Statement #1 : x^{n+1} = 625 Statement #2 : x = 5 One of the statements of this DS problem is a tautological statement . To find that a statement is tautological implies more than if we merely find that the statement is insufficient. For a discussion of this subtle logical issue, as well as the OE for this particular question, see: GMAT Data Sufficiency Logic: Tautological Statements Mike :-)

abhimahna · Answer

Answer should be C.

Statement 1 : x^n+1=625. We could have either 5^4=625 => x=5

or (-5)^4=625 => x=-5.

=> x^n could be either 125 or -125 -- Insufficient.

Statement 2: x=5. But we don't know the value of n.--> Insufficient.

Combining both the statements, we know x=5 and n=3 => x^n=125.

hence, answer is C

Rushilkhera · Answer

Statement 1 First of all we will solve the equation

x^(n+1)=625 then 5^(3+1) so x = 5 or x = -5 Clearly Insufficient

Statement 2 x=5 that doesn't really say anything so clearly insufficient

Combining both of them we get x=5 and n =3 so answer is C

subrataroy0210 · Answer

x^{n+1}−2x^n=3x^n 
 x^{n+1} = 5x^n  .... eq (1)

From this expression, we cannot say that  x=5  as  x  can be 0 too.

1)  x^{n+1} = 625

From this expression, we come to know that x is not equal to 0. Therefore, we can divide both the sides of eq (1) by  x^n .
Thus, we get  x=5  and therefore  n=3 .  Sufficient .

2) x=5

With this information in hand, we cannot get a definitive value for  n .  Insufficient .

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If x^{n+1} - 2x^n=3x^n, then what is the value of x^n?

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

GMAT Data Sufficiency (DS) Questions

If x^{n+1} - 2x^n=3x^n, then what is the value of x^n?

Prep Toolkit

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