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easy- medium OG 2016 #63

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by danielheulensen » Thu Jul 13, 2017 11:05 am
any better explanations other than the book?

#63 OG 2016 Problem Solving


63. The function f is defined by f(x) = rootx -10 for all positive numbers x. If u =f(t) for some positive numbers t and u, what is t in terms of u?
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by GMATGuruNY » Thu Jul 13, 2017 11:47 am
When you post a problem, please include the answer choices.

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Let t = 4.
Then u = f(t) = √t - 10 = √4 - 10 = 2 - 10 = -8.
The question stem asks for the value of t=4. This is our target.
Now plug u=-8 into the answer choices to see which yields our target value of 4.
Only D works:
(u + 10)² = (-8 + 10)² = 2² = 4.

The correct answer is D.
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by Ian Stewart » Thu Jul 13, 2017 12:01 pm
f(x) = √x - 10

To find f(t), just replace 'x' with 't' on the right side above:

f(t) = √t - 10

We know u = f(t) so

u = √t - 10
u + 10 = √t
(u + 10)^2 = t
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by Jay@ManhattanReview » Thu Jul 13, 2017 8:55 pm
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The correct answer is D.
We know that f(x) = √x - 10

=> f(t) = √t - 10; replacing x with t

=> u = √t - 10; it is gven that u = f(t)

=> √t = u + 10

=> t = (u +10)^2; squaring both the sides

The correct answer: D

Hope this helps!

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by danielheulensen » Sat Jul 15, 2017 3:25 pm
Thanks everyone!
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Re: easy- medium OG 2016 #63

by Scott@TargetTestPrep » Fri Feb 21, 2020 7:35 am
danielheulensen wrote: ↑
Thu Jul 13, 2017 11:05 am
 any better explanations other than the book?

#63 OG 2016 Problem Solving


63. The function f is defined by f(x) = rootx -10 for all positive numbers x. If u =f(t) for some positive numbers t and u, what is t in terms of u?
We are given the function defined by f(x) = √x – 10, and we also see that f(t) = u. First, let's determine what f(t) looks like and then set the result equal to u.

f(t) = √t – 10

√t – 10 = u

To finish, we need to get t in terms of u.

√t = u + 10

t = (u + 10)^2

Answer: (u + 10)^2

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