If f(x) = 12 - x^2/2 and f(2k) = 2k, what is one possible value for k?

Question

If  f(x) = 12 - \frac{x^2}{2}  and  f(2k) = 2k , what is one possible value for k?

A. 2
B. 3
C. 4
D. 6
E. 8

peachfuzz · Answer

12 - ( 2k)^2/2 = 2k
4k = 24 - 4k^2
(k-2)(k+3) = 0
k = 2 
k = -3

Answer : A

KarishmaB · Answer

Once you form the equation f(2k) =  12 - (2k)^2/2 = 2k 
 12 - 2k^2 = 2k , you don't even need to solve it. Note that 12 is a small number and when you subtract twice of a square from it, you still get a positive number 2k (all values of k given in the options are positive). So k must be very small --> k^2 must be less than 6 so k can only be 2 from the given options.

Verify:  12 - 2*2^2 = 2*2  - Correct

Answer (A)

EMPOWERgmatRichC · Answer

Hi all,

While this question looks 'technical', the math involved is actually pretty straight-forward. You can solve this by TESTing THE ANSWERS.

We're given the function....

f(X) = 12 - X^2/2

We're asked which of the answer COULD be the value of K if f(2K) = 2K

Let's TEST Answer A: K = 2.....

Does f(4) = 4?

Plugging 4 in for X, we get:

12 - 4^2/2 = 
12 - 16/2 = 
12 - 8 = 
4

So f(4) DOES = 4. This MUST be the answer.

Final Answer:  A

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

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION:

First of all, see this  GMAT blog post  and check the related lesson linked below for some background on function notation.

We can plug anything in for x and get a result. You can find f(1), for example, by plugging in 1 where x is, and you would get 12 - 1/2 = 11.5. Or we could find f(2), which would be 12 - 4/2 = 10.

So the notation f(2k) means that we are going to plug a 2k in for x everywhere in the formula for f(x). That would be:

f(2k) = 12 - (2k)^2/2 = 12 - 2k^2.

Remember that we have to square both the 2 and the k, to get 4k2. Now, this expression, the output, we will set equal to 2k.

12 - 2k^2 = 2k --> k = -3 or k = 2.

All the answers are positive, so we choose k = 2.

Answer = A

PareshGmat · Answer

f(x) = 12 - \frac{x^2}{2}

f(2k) = 12 - \frac{4k^2}{2} = 2k

k^2 + k - 6 = 0

k = 2 or k = -3 (Ignore -ve value)

Answer = A

If f(x) = 12 - x^2/2 and f(2k) = 2k, what is one possible value for k?

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GMAT Problem Solving (PS) Questions

If f(x) = 12 - x^2/2 and f(2k) = 2k, what is one possible value for k?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards