If f(n) = xa^n, what is the value of f(5) ?

Question

If  f(n) = xa^n , what is the value of  f(5)  ?

(1)  f(0) = 3 
(2)  f(4) = 48

BrentGMATPrepNow · Accepted Answer

Target question :    What is the value of f(5)?

Given : f(n) = xa^n

Statement 1 : f(0) = 3   
In other words, x(a^0) = 3
Since a^0 = 1, we can write: (x)(1) = 3
This tells us that x = 3
So, our function now looks like this: f(n) = 3a^n 
Since we still don't know the value of a,  this is NOT enough information to determine the value of f(5) 
Since we cannot answer the  target question  with certainty, statement 1 is SUFFICIENT

Statement 2 : f(4) = 48  
In other words, x(a^4) = 48
There are several values of x and a that satisfy statement 2. Here are two: 
Case a: x = 3 and a = 2. Notice that x(a^4) = 48 turns into 3(2^4) = 48, which works. In this case  f(5) = 3(2^5) = 96 
Case b: x = 3 and a = -2. Notice that x(a^4) = 48 turns into 3  = 48, which works. In this case  f(5) = 3  = -96 
Since we cannot answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined    
Statement 1 tells us that x = 3
Statement 2 tells us that, when x = 3, either a = 2 or a = -2
In other words, we still have 2 possible cases that satisfy BOTH statements: 
Case a: x = 3 and a = 2. Notice that x(a^4) = 48 turns into 3(2^4) = 48, which works. In this case  f(5) = 3(2^5) = 96 
Case b: x = 3 and a = -2. Notice that x(a^4) = 48 turns into 3  = 48, which works. In this case  f(5) = 3  = -96 
Since we cannot answer the  target question  with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Chethan92 · Answer

Please correct me if I'm wrong. combining both gives 3a^4 =48. a^4 = 16. Then the fourth power of a is 2. Since GMAT doesn't consider -2 for the even powers. Then combining both works, isn't it?

BrentGMATPrepNow · Answer

It all comes down to NOTATION.

If x² = 9, then x = 3 or -3
However, with √9, the square root notation tells us to take the POSITIVE root of 9
So, √9 = 3
To generalize, if x² = k, then x = √k or -√k, where √k represents the POSITIVE square root of k, and -√k represents the NEGATIVE square root of k

The same applies to fourth roots. 
Of x⁴ = 16, then x = 2 or x = -2
However, when it comes to ∜16, the 4th root NOTATION tells us to take the POSITIVE value.

Does that help?

Cheers,
Brent

Chethan92 · Answer

Yes, thanks. Is it only in GMAT that it's considered like this or in general?

BrentGMATPrepNow · Answer

No, it's not just the GMAT. This is a general concept. More here: https://www.mathsisfun.com/square-root.html Cheers, Brent

CounterSniper · Answer

(1) f(0) = 3
so,
3=x a^0 
x=3
f(5)=3 a^5 
a=?
insufficient

(2) f(4) = 48
so,
48=3 a^4 
 a^4 =16
a= +- 2
f(5)=3( 2^5 )=96 or 3( -2^5 ) = -96 
insufficient

using both , still insufficient

E

Kimberly77 · Answer

Hi  BrentGMATPrepNow , x⁴ = 16, then x = 2 or x = -2. So this will apply to all even exponent power x^6, x^8....etc? Thanks Brent

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

If f(n) = xa^n, what is the value of f(5) ?

Prep Toolkit

Top 5 GMAT Debrief Videos

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

GMAT Data Sufficiency (DS) Questions

If f(n) = xa^n, what is the value of f(5) ?

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