[Math Revolution GMAT math practice question]
If f(a*b) = f(a) + f(b), what is the value of f(1)?
A. 1
B. -1
C. 0
D. 2
E. -2
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If f(a*b) = f(a) + f(b), what is the value of f(1)?
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Max@Math Revolution
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fskilnik@GMATH
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$$f\left( {ab} \right) = f\left( a \right) + f\left( b \right)\,\,\,\,\,\left( * \right)$$Max@Math Revolution wrote:[Math Revolution GMAT math practice question]
If f(a*b) = f(a) + f(b), what is the value of f(1)?
A. 1
B. -1
C. 0
D. 2
E. -2
$$? = f\left( 1 \right)$$
$$f\left( 1 \right) = f\left( {1 \cdot 1} \right)\mathop = \limits^{\left( * \right)} f\left( 1 \right) + f\left( 1 \right)$$
$$f\left( 1 \right) = 2 \cdot f\left( 1 \right)\,\,\,\,\, \Rightarrow \,\,\,\,? = f\left( 1 \right) = 0$$
This solution follows the notations and rationale taught in the GMATH method.
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Fabio.
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Let a=1 and b=2.Max@Math Revolution wrote:[Math Revolution GMAT math practice question]
If f(a*b) = f(a) + f(b), what is the value of f(1)?
A. 1
B. -1
C. 0
D. 2
E. -2
Plugging a=1 and b=2 into f(ab) = f(a) + f(b), we get:
f(1*2) = f(1) + f(2)
f(2) = f(1) + f(2)
0 = f(1).
The correct answer is C.
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Brent@GMATPrepNow
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To generalize Mitch's and Fabio's solutions, notice that, as long as we can get f(1) involved in the process, we'll arrive at answer choice C every time.Max@Math Revolution wrote:[Math Revolution GMAT math practice question]
If f(a*b) = f(a) + f(b), what is the value of f(1)?
A. 1
B. -1
C. 0
D. 2
E. -2
Notice that k = 1*k
Since f(a*b) = f(a) + f(b), we can write: f(1*k) = f(1) + f(k)
Simplify: f(k) = f(1) + f(k)
Subtract f(k) from both sides to get: 0 = f(1)
Answer: C
Cheers,
Brent
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Max@Math Revolution
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=>
Since 1 = 1 * 1, setting a = 1 and b = 1 yields f(1) = f(1*1) = f(1) + f(1) and f(1) = 2f(1), which is equivalent to f(1) = 0.
Therefore, the answer is C.
Answer: C
Since 1 = 1 * 1, setting a = 1 and b = 1 yields f(1) = f(1*1) = f(1) + f(1) and f(1) = 2f(1), which is equivalent to f(1) = 0.
Therefore, the answer is C.
Answer: C
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Scott@TargetTestPrep
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We can let both a and b be 1, and thus we have:Max@Math Revolution wrote:[Math Revolution GMAT math practice question]
If f(a*b) = f(a) + f(b), what is the value of f(1)?
A. 1
B. -1
C. 0
D. 2
E. -2
f(1*1) = f(1) + f(1)
f(1) = 2f(1)
Subtracting f(1) from both sides, we have:
0 = f(1)
Alternate Solution:
We can let a be 1, and thus we have:
f(1*b) = f(1) + f(b)
f(b) = f(1) + f(b)
Subtracting f(b) from both sides, we have:
0 = f(1)
Answer: C
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