(cube root x-b) = c^6, then x=

[stevenstratmann]

I appologize this is a difficult question to search for and write in english form. But the above question was on the GMAT Prep test.

answers:
a) c^2 + b
b) c^6 + b
c) c^9 + b
d) c^12 + b
e) c^18 + b

I attempted to solve by picking numbers to represent each individual letter (somewhat difficult and it did not yield the correct answer)

during review I noticed that if I made
x= 262,146
b=2
c=2 then I would get the correct answer of E)

There has got to be an easier solution. Thanks!

[shaleengaurav]

hi steven. your attempt to solving the problem was not incorrect. however you need to see what kind of answer is the question demanding. In here, the answer is already given in 2 variables (c and b) hence we dont need to take any values.
simply take a cube on both the sides.

(x-b)^1/3=c^6
taking cube
x-b = c^18 (remember (x^3)^2 = x^6)

x=c^18+b

Hope this helps

[RonPurewal]

during review I noticed that if I made
x= 262,146
b=2
c=2 then I would get the correct answer of E)

that's ... impressive.
if you know your powers of 2 really, really well, then this is actually a reasonably fast solution; if not, it's sort of ridiculous. (i have had students who have memorized all powers of 2 up to 2^32; i was, again, quite impressed.)

There has got to be an easier solution. Thanks!

ya, this is routine algebra: to undo a cube root, you cube both sides. if you aren't comfortable enough with this to do it in literally two seconds or less (not an exaggeration), then check out our Foundations of Math book, or grab an Algebra 1 book out of a public library.

given: cube root (x - b) = c^6
cube both sides: x - b = c^18
add b: gives the answer.