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 .

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

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GMAT Data Sufficiency (DS) Questions

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

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