If (2 + x) 2x which of the following must be true?

Question

If (2 + √x) > 2√x which of the following must be true?

A x < 2
B x < 3
C x < 1
D x < 4
E None of these

Bunuel · Answer

2 + √x > 2√x

2 > √x

4 > x

Answer: D.

shihab7944 · Answer

The given answer is E, saying "0  ≤x ≤ 4 (x cannot take any negative values since you cannot root a negative number)"

Bunuel · Answer

No. The inequality holds for 0 ≤ x < 4. The question asks “which of the following must be true?” For any value of x in this range, x will always be less than 4. So the correct answer is D.

This question belongs to a type of question that tends to be very confusing for many. Therefore, I recommend practicing similar questions from the following collection:  Trickiest Inequality Questions Type: Confusing Ranges .

Hope it's clear.

manassikri · Answer

In GMAT and other competitive tests it is understood we shall always take only real numbers into considerations and not imaginary.
Here if we are given an equation involving the term √x that means we are talking about all real values of x. For this term to be valid x>=0 .

In such situations it is implicit that x>=0.

If (2 + x) > 2x which of the following must be true?

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