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

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

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

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Originally posted by SajjadAhmad on 02 Apr 2017, 12:07.
Last edited by SajjadAhmad on 22 May 2019, 04:20, edited 2 times in total.
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Re: If f(n) = xa^n, what is the value of f(5) ?  [#permalink]

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

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

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[(-2)^4] = 48, which works. In this case f(5) = 3[(-2)^5] = -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[(-2)^4] = 48, which works. In this case f(5) = 3[(-2)^5] = -96
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

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Re: If f(n) = xa^n, what is the value of f(5) ?  [#permalink]

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GMATPrepNow wrote:

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[(-2)^4] = 48, which works. In this case f(5) = 3[(-2)^5] = -96
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

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?
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Re: If f(n) = xa^n, what is the value of f(5) ?  [#permalink]

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Afc0892 wrote:
GMATPrepNow wrote:

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[(-2)^4] = 48, which works. In this case f(5) = 3[(-2)^5] = -96
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

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?

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
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Re: If f(n) = xa^n, what is the value of f(5) ?  [#permalink]

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GMATPrepNow wrote:
Afc0892 wrote:
GMATPrepNow wrote:

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[(-2)^4] = 48, which works. In this case f(5) = 3[(-2)^5] = -96
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

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?

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

Yes, thanks. Is it only in GMAT that it's considered like this or in general?
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Re: If f(n) = xa^n, what is the value of f(5) ?  [#permalink]

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Afc0892 wrote:

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

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

Cheers,
Brent
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Re: If f(n) = xa^n, what is the value of f(5) ?  [#permalink]

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

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

(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

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Re: If f(n) = xa^n, what is the value of f(5) ?  [#permalink]

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