x^1/2

nahid078 wrote:x^1/2 + x^1/4 = 20
Then x = ?

a) 196
b) 254
c) 256
d) 312
e) 512

Note: x^(1/2) = √x and x^(1/4) = ∜x
So, we have the equation √x + ∜x = 20

This is a great candidate for plugging in the answer choices.

NOTE: if the square root of a number is not an integer, then it is likely a very UGLY number, in which case it is highly unlikely that, when it's added to the fourth root of a value will yield a nice integer value (like 20).

So, let's weed out any answer choice that does not have a nice integer square root.

a) 196: √196 = 14 NICE. However, ∜196 does not equal 6 (which is required to get a sum of 20) ELIMINATE A

b) 254: √254 is not an integer. SKIP for now.

c) 256: √256 = 16 NICE. ∜256 = 4. PERFECT.
So, √256 + ∜256 = 16 + 4 = 20

Answer: C

Cheers,
Brent

Hi nahid078,

This question can be solved by TESTing THE ANSWERS.

We're told that X^(1/2) + X^(1/4) = 20

While the '4th-root' might seem like a 'scary' concept, it's based on the same idea that square-roots are based on:

X^(1/2) means 'what positive number, multiplied by itself, equals X?'

eg.
4^(1/2) = 2 because (2)(2) = 4

With a 4th-root, you're looking for a positive number, multiplied by itself 3 more times, that equals X...

16^(1/4) = 2 because (2)(2)(2)(2) = 16

Knowing all of that, we can TEST THE ANSWERS by plugging in values until we find the one that totals 20. Based on the prompt, we should look for a number that is a PERFECT SQUARE...

256 = (16)(16), so let's start there...

256^(1/2) = 16

256^(1/4) = (4)(4)(4)(4) = 4

16+4 = 20

This is a MATCH, so this must be the answer.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich