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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## If f(a*b) = f(a) + f(b), what is the value of f(1)? tagged by: Max@Math Revolution ##### This topic has 5 expert replies and 0 member replies ### GMAT/MBA Expert ## If f(a*b) = f(a) + f(b), what is the value of f(1)? ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [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 _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only Worldâ€™s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$149 for 3 month Online Course
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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
$$f\left( {ab} \right) = f\left( a \right) + f\left( b \right)\,\,\,\,\,\left( * \right)$$
$$? = f\left( 1 \right)$$
$$f\left( 1 \right) = f\left( {1 \cdot 1} \right)\mathop = \limits^{\left( * \right)} f\left( 1 \right) + f\left( 1 \right)$$
$$f\left( 1 \right) = 2 \cdot f\left( 1 \right)\,\,\,\,\, \Rightarrow \,\,\,\,? = f\left( 1 \right) = 0$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

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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
Let a=1 and b=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).

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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
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.

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)

Cheers,
Brent

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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.

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Only $149 for 3 month Online Course Free Resources-30 day online access & Diagnostic Test Unlimited Access to over 120 free video lessons-try it yourself Email to : info@mathrevolution.com ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2852 messages Followed by: 18 members Upvotes: 43 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 We can let both a and b be 1, and thus we have: 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 _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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