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by Brent@GMATPrepNow » Sun Aug 09, 2015 9:04 am
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

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by [email protected] » Sun Aug 09, 2015 9:06 am
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

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by theCEO » Sun Aug 09, 2015 11:46 am
Alternative way to solve

x^1/2 + x^1/4 = 20
(x^1/4)(x^1/4) + x^1/4 = 20
x^1/4(x^1/4 + 1) = 20

x^1/4(x^1/4 + 1)
here we see that these are two consecutive numbers

what two consecutive numbers when multipled together give 20: 4 and 5
therefore x^1/4 = 4 and x^1/4 + 1= 5

x^1/4 = 4
x = 4^4= 256

ans= c
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