Number Systems

sukhman wrote:For which of the following values of x is √{1-√[2-(√x)]} not defined as a real number?
1 2 3 4 5

Hi Mate,

E is the correct answer here. If you chose 5 as value of x then the value √[2-(√x) will be negative and the negative value of square root is not defined. √x will give value equal to more than 2( we don't need to know how much more) and when you deduct more than 2 from 2 then answer will be negative.

Square root of a negative number is imaginary (ie. not a real number.), any answer choice which tries to find the square root of a negative number is our answer

Plug in the answer choices remembering that √(of a number) on the GMAT is +ive (eg √4 is 2)

√{1-√[2-(√x)]}

x = 5
√5 > 2 --> √[2-(√x)] would be negative --> taking a sq. root would make it imaginary.
Answer 5