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

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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]
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]
BrentGMATPrepNow 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

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