If c is a nonnegative constant, how many real number values for x sat

Question

If c is a nonnegative constant, how many real number values for x satisfy the equation \(\sqrt{c - x} = \sqrt{c} - \sqrt{x}\)

A. 0

B. 1

C. 2

D. 3

E. Infinitely many

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Official Answer

C

Bunuel · Accepted Answer

Squaring the given expression, we obtain:

\sqrt{c - x} = \sqrt{c} - \sqrt{x}

c - x =c - 2\sqrt{cx} + x

x = \sqrt{cx}

Now, square again:

x^2 = cx

x^2 - cx = 0

x(x - c) = 0

The above equation has two solutions, x = 0 and x = c.

Answer: C.

unraveled · Answer

Hi Bunuel, 
As x = c so any nonnegative value of c is value of x. Thu,
Should not the answer be E then?
 
Thanks.

sachi-in · Answer

Ans is B  2

c has a finite fixed value choosen from a infinite range ( it may take any value between 0 to Inf ) , but once the constant is decided like let's say c = 3

then the equation

\sqrt{(c - x)}  =  \sqrt{c} - \sqrt{x} 
 \sqrt{(3 - x)}  =  \sqrt{3} - \sqrt{x}

will have only two values as root.

c - x = c + x - 2\sqrt{(c*x)}   only when  x = \sqrt{(c*x)} 
that is possible only when x = c or x = 0  , here value of x will be 0 or 3.

Oppenheimer1945 · Answer

x=0 and x=c are 2 solutions.

Bunuel · Answer

c there is a fixed constant, not a variable. So it has one fixed value, say 10 or 12.

unraveled · Answer

c there is a fixed constant, not a variable. So it has one fixed value, say 10 or 12. 
yes, i realised it later after a couple of minutes of posting the question. Silly me. 
Only that if someone tries testing numbers on hit and trial basis, he/she is going to get wrong answer.

KrishnaVamsiP · Answer

Since Zero is also nonnegative, When C = 0, X has only 1 possible solution and in other cases it has 2 solutions. Isn't the question ambiguous?

Bunuel · Answer

Yes, in the general case, the equation has two solutions for x. However, in the specific case where c = 0, it has only one solution, x = 0.

Blackcrow1972 · Answer

To this extent it is surely ambiguous.

Shlokzanwar · Answer

Yes this question is a test question in the practice test of gmat official mock tests
I got the question wrong on the test but still got a Q90 in the mock

KarishmaB · Answer

Yes, there is a problem here. They needed to give that "c takes a positive constant value" (not non negative). Then the answer will be a clean 2.

Dream009 · Answer

but for any value of c this will be true - so won't answer be infinitely many?

Bunuel · Answer

c  could  be any number but it stands for only one.

meilimeagan · Answer

The question asks how many real number values for x satisfy the equation. As stated above x = 0 or x = c. This means that there are two real number values 0 and c.

MrinmoyNegel · Answer

C is non-negative. Which means C can be 0. So it may well be the solution is 0 .... ( that is only 1 solution ) . IDeally the question should have been C is a positive constant... Otherwise it brings in ambiguity. 
Though I marked C (2 solutions)

If c is a nonnegative constant, how many real number values for x sat

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If c is a nonnegative constant, how many real number values for x sat