What is the value of x? (1) x^(1/2) = x - 2 (2) x ≠ 1.

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Competition Mode Question

What is the value of x?

(1)  \sqrt{x} = x-2

(2) x ≠ 1

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freedom128 · Accepted Answer

(1) √x = x-2 
--> x= x^2-4x+4
--> 0= (x-4)(x-1)
--> x=4 or x=1
If x=1 --> 1= -1, NO!, 
If x=4 --> 2= 2, YES!, so x=4
SUFFICIENT

(2) x≠1
Value of x can be anything other than 1.
NOT SUFFICIENT.

FINAL ANSWER IS (A)

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chetan2u · Answer

I am pretty sure that when solutions open up, C would win over A and we would learn that how important it is to CHECK the values back in the equation.

Okay so here we are..

(1)  \sqrt{x} = x-2 
The first take  x-2\geq 0 , as  \sqrt{x}\geq 0 ...So  x\geq 2 
square both sides....
 \sqrt{x} = x-2.........x=(x-2)^2=x^2-4x+4........x^2-5x+4=0......(x-4)(x-1)=0 , so x can be 1 or 4.
But we know that  x\geq 2 , so x =4
Suff

(2) x ≠ 1
Insuff

A

CrackverbalGMAT · Answer

From statement I alone, √x=x-2.

Squaring both sides, we have x =  (x-2)^2 . Opening up the RHS and simplifying, we have,

x^2  – 5x + 4 = 0, which can be factorized as (x-4) (x-1) = 0. Therefore, x has two values, 1 and 4. We need a unique value of x. Statement I alone is insufficient.

Answer options can be B, C or E. Answer options A and D can be eliminated.

From statement II alone, x≠1. This is not sufficient to find the value of x. 
Answer option B can be eliminated.

Combining statements I and II, we have the following:

From statement I, x = 1 or 4. From statement II, x≠1. 
This means, x = 4. The combination of statements is sufficient. Answer option E can be eliminated.

The correct answer option is C .

Hope that helps!

Archit3110 · Answer

solve for #1
we get 
x=(x-2)^2
or say 
x^2-5x+4=0
so x= 4 or 1
but since LHS is +ve so 1 is not possible at square root value at RHS
x=4 sufficient
#2
x ≠ 1
insufficient
Option A

What is the value of x?

(1) x√=x−2

(2) x ≠ 1

exc4libur · Answer

(1) √x=x−2   sufic

|x|=(x-2)^2
|x|=x^2+4-4x
x≥0: x=x^2+4-4x, x^2-5x-4=0, (x-4)(x-1)=0; x=4,1
x=1: √1=1-2, 1=-1=invalid
x=4: √4=4-2, 2=2=valid

(2) x ≠ 1   insufic

Ans (A)

unraveled · Answer

What is the value of x?

(1) √x = x−2
 x = x^2 + 4 - 4x 
 x^2 + 4 - 5x = 0 
(x-4)(x-1) = 0
x = 4 OR 1

INSUFFICIENT.

(2) x ≠ 1
Any value is possible.

INSUFFICIENT.

Together 1 and 2
x = 4 only

SUFFICIENT.

Answer C.

ostrick5465 · Answer

(1)   \sqrt{x}=x−2  after solved => x=1 or x=4
but   \sqrt{1}=1−2 = -1  => nonsense => x=1 was eliminated
=> x=4
=> (1) suff

(2) not suff

=> Choice A

minustark · Answer

(1) x can be either 1 or 4. not sufficient.

(2) x can be any number except 1. not sufficient.

Together, x is 4. sufficient.

eakabuah · Answer

We are to determine the value of x.
1. √x=x-2
x=x^2-4x+4
x^2-5x+4=0
(x-1)(x-4)=0
x=1, x=4
Statement 1 alone is insufficient.

2. x≠1
Not sufficient. Infinite possibilities.

1+2
sufficient. x=4.

The answer is C.

madgmat2019 · Answer

(1) √x=x−2......FROM THIS WE GET X=4,1....Insufficient
(2) x ≠ 1....Clearly insufficient

Combining both we get x=4

OA:C

gvijaygvk · Answer

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

\sqrt{x}=x-2

x=x^2-4x+4 
 0=x^2-5x+4 
0=(x-1)(x-4)

so must be x=1 or x=4

as Per (2) ≠ 1

SO X = 4

nishantt7 · Answer

Both statements are required

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gokulbalaji20 · Answer

As x is perfect square we can say x>0 but how root(x)>0. Can you please help.

chetan2u · Answer

Square root is always positive. 
 \sqrt{X}  is always non negative.

maitryyadav · Answer

This cant be a 700-750 level question

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Bunuel · Answer

We do not assign the difficulty level manually. The difficulty level of a question on the site is determined automatically based on various parameters collected from users' attempts, such as the percentage of correct answers and the time taken to answer the question. You can find the difficulty level of a question and its related statistics in the first post.

Hope it clarifies.

mysterymanrog · Answer

X=?

1)
 \sqrt{x}=x-2

0=x-\sqrt{x}-2

Let  y=\sqrt{x}

y^2-y-2=0

(y-2)(y+1)=0

y=2  or  y=-1

Recall that y is the square root of x, which must take a positive value. Therefore, we can discard the solution y=-1. We are left with y=2, which gives us a value of x=4. Sufficient.

2) Clearly ins.

A.

What is the value of x? (1) x^(1/2) = x - 2 (2) x ≠ 1.

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GMAT Data Sufficiency (DS) Questions

What is the value of x? (1) x^(1/2) = x - 2 (2) x ≠ 1.

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