Well, from x^n = x^(n+2) we get that x^(n+2) - x^n = x^n(x^2 - 1) = 0. This is equivalent to x^n(x - 1)(x + 1) = 0. This happens only when x^n = 0 (so x = 0), x = -1 or x = 1.
1. This equation is equivalent to x^2 - x -2 = 0. And this one basically means that (x - 2)(x + 1) = 0. This is only true when x is either 2 or -1. Since only x = -1 fits the inital restriction, then x is indeed -1, which is smaller than 0. So 1 is sufficient.
2. 2x < x^5 is equivalent to x^5 - 2x > 0. Now let's just use the numbers we've narrowed down in our intial restriction.
a. x = 0, then x^5 - 2x = 0, which is not consistent with x^5 - 2x > 0. So 0 is out.
b. x = 1. x^5 - 2x = -1, which again is not greater than 0. So -1 is out as well.
c. x = -1 and x^5 - 2x = 1 > 0 . So -1 is the only one that fits.
2 is sufficient as well.
So the answer is D
BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course
Redeem
Featured Course
Target Test Prep GMAT OnDemand
Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.
- 715+ score guarantee — highest in the industry (99th percentile)
- 52 chapters · 1,500+ lessons · 4,000+ practice questions
- 400 hours of video · 1,500+ instructor-led HD smartboard lessons
- 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
- 24/7 live support + weekly Zoom office hours with GMAT instructors
- TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
- 1,200+ flashcards + AI-powered study assistant & daily calendar
- OnDemand, LiveTeach & GMAT Bootcamp formats available
- Also: GRE, SAT Math & Executive Assessment courses
- MBA Admissions Consulting now available
- 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
- 200,000+ students served
- 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★
5.0
(559 reviews)
130-pt guarantee
$0 to start
then $127/mo
Exponents
Source: Beat The GMAT — Data Sufficiency |
-
sureshbala
- Master | Next Rank: 500 Posts
- Posts: 319
- Location: Delhi
- Thanked: 84 times
Given x^n = x^n+2.
i.e x^n = x^n . x^2
i.e x^n(x^2-1) = 0
i.e x^n = 0 or x^2-1 = 0
So x =0 or x^2 = 1
Thus from the given question itself we know that x =0 or 1 or -1.
Statement 1: x= x^2-2 . Since we have the value of x as 0 or 1 or -1, only -1 satisfies this equation. Hence x=-1. Thus x<0
Hence statement 1 alone is sufficient.
Statement 2: 2x<x^5. Since from the question we have x = 0 or 1 or -1, this condition is satisfied only when x = -1. Thus x<0.
Hence statement 2 alone is sufficient.
So C must be the answer
i.e x^n = x^n . x^2
i.e x^n(x^2-1) = 0
i.e x^n = 0 or x^2-1 = 0
So x =0 or x^2 = 1
Thus from the given question itself we know that x =0 or 1 or -1.
Statement 1: x= x^2-2 . Since we have the value of x as 0 or 1 or -1, only -1 satisfies this equation. Hence x=-1. Thus x<0
Hence statement 1 alone is sufficient.
Statement 2: 2x<x^5. Since from the question we have x = 0 or 1 or -1, this condition is satisfied only when x = -1. Thus x<0.
Hence statement 2 alone is sufficient.
So C must be the answer
Mr sureshbala,
in statement 1 ---- 2 also satisfies the equation .......
how it could be right....
hence it is insufficient right...coz once x<0 and once x>0
detailed explanation will be appreciated .....
in statement 1 ---- 2 also satisfies the equation .......
how it could be right....
hence it is insufficient right...coz once x<0 and once x>0
detailed explanation will be appreciated .....
-
hardik.jadeja
- Legendary Member
- Posts: 535
- Thanked: 87 times
- GMAT Score:730
If you solve x^n = x^(n+2), u get two solutions. Either x^n=0 (means x=0) or x^2=1 (means x could be 1 or -1). We have 3 possible solutions here -1,0 and 1.
1) x = (x^2) - 2
if u solve this equation you get x=-1 or x=2
but there is only one value that satisfies both the equations x = (x^2) - 2 and x^n = x^(n+2) and that value is -1. So x=-1 meaning x<0.
A alone is sufficient.
2) 2x<x^5
The above equation holds true for -1 and all the numbers >= 2.
But again there is only one value that satisfies both the equations 2x<x^5 and x^n = x^(n+2) and that value is -1.
So B alone is also sufficient.
So Answer is D.
1) x = (x^2) - 2
if u solve this equation you get x=-1 or x=2
but there is only one value that satisfies both the equations x = (x^2) - 2 and x^n = x^(n+2) and that value is -1. So x=-1 meaning x<0.
A alone is sufficient.
2) 2x<x^5
The above equation holds true for -1 and all the numbers >= 2.
But again there is only one value that satisfies both the equations 2x<x^5 and x^n = x^(n+2) and that value is -1.
So B alone is also sufficient.
So Answer is D.
naaga: Solving the initial equation of x^n = x^(n+2) yields 3 answers: 0, 1 and -1. It is true that in stmt 1 you have two solutions, 2 and -1, but since only -1 is also in the list of solutions for the inital euqtion, then this means that only -1 fits.
Dana - Would statement 2 fail if x=0 were one of the solutions for 2x < x^5?DanaJ wrote:Well, from x^n = x^(n+2) we get that x^(n+2) - x^n = x^n(x^2 - 1) = 0. This is equivalent to x^n(x - 1)(x + 1) = 0. This happens only when x^n = 0 (so x = 0), x = -1 or x = 1.
1. This equation is equivalent to x^2 - x -2 = 0. And this one basically means that (x - 2)(x + 1) = 0. This is only true when x is either 2 or -1. Since only x = -1 fits the inital restriction, then x is indeed -1, which is smaller than 0. So 1 is sufficient.
2. 2x < x^5 is equivalent to x^5 - 2x > 0. Now let's just use the numbers we've narrowed down in our intial restriction.
a. x = 0, then x^5 - 2x = 0, which is not consistent with x^5 - 2x > 0. So 0 is out.
b. x = 1. x^5 - 2x = -1, which again is not greater than 0. So -1 is out as well.
c. x = -1 and x^5 - 2x = 1 > 0 . So -1 is the only one that fits.
2 is sufficient as well.
So the answer is D
beater wrote:Dana - Would statement 2 fail if x=0 were one of the solutions for 2x < x^5?DanaJ wrote:Well, from x^n = x^(n+2) we get that x^(n+2) - x^n = x^n(x^2 - 1) = 0. This is equivalent to x^n(x - 1)(x + 1) = 0. This happens only when x^n = 0 (so x = 0), x = -1 or x = 1.
1. This equation is equivalent to x^2 - x -2 = 0. And this one basically means that (x - 2)(x + 1) = 0. This is only true when x is either 2 or -1. Since only x = -1 fits the inital restriction, then x is indeed -1, which is smaller than 0. So 1 is sufficient.
2. 2x < x^5 is equivalent to x^5 - 2x > 0. Now let's just use the numbers we've narrowed down in our intial restriction.
a. x = 0, then x^5 - 2x = 0, which is not consistent with x^5 - 2x > 0. So 0 is out.
b. x = 1. x^5 - 2x = -1, which again is not greater than 0. So -1 is out as well.
c. x = -1 and x^5 - 2x = 1 > 0 . So -1 is the only one that fits.
2 is sufficient as well.
So the answer is D
x^n= x^(n+2) --> (1)
st 1:
x=x^2-2
say n=0 from (1) x^2=x^0 =1
x= 1-2=-1
sufficient
st 2:
from equ (1) x^5 = x^3 = x
2x < x^5 --> 2x<x --> x<0
sufficient.
D
