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If f(x+y) = f(x)f(y), what is the value of f(0)? 1) f(x) > 0 2) f(x) h

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5073
GMAT 1: 800 Q59 V59
GPA: 3.82
If f(x+y) = f(x)f(y), what is the value of f(0)? 1) f(x) > 0 2) f(x) h [#permalink]

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10 Nov 2017, 00:50
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Difficulty:

65% (hard)

Question Stats:

38% (00:44) correct 62% (01:00) wrong based on 60 sessions

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[GMAT math practice question]

If f(x+y) = f(x)f(y), what is the value of f(0)?

1) f(x) > 0
2) f(x) has integer values
[Reveal] Spoiler: OA

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Manager Joined: 17 Mar 2015 Posts: 121 Re: If f(x+y) = f(x)f(y), what is the value of f(0)? 1) f(x) > 0 2) f(x) h [#permalink] Show Tags 10 Nov 2017, 05:39 1 This post received KUDOS 1) Put y = 0: f(x+0) = f(x) = f(x)*f(0), Divide both sides by f(x) which is not equal to zero (so we can divide), f(0) ends up being equal to 1, sufficient. 2) f(x) can be 0, which doesn't let me do the procedure above + no info given about f(y) or any other combination, insufficient. A Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5073 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: If f(x+y) = f(x)f(y), what is the value of f(0)? 1) f(x) > 0 2) f(x) h [#permalink] Show Tags 12 Nov 2017, 19:00 => Forget conventional ways of solving math questions. In DS, VA (Variable Approach) method is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution. The first step of VA(Variable Approach) method is modifying the original condition and the question, and rechecking the number of variables and the number of equations. To find the value of f(x), we can plug in 0 for the variables x and y. Then we have $$f(0+0) = f(0) ∙ f(0) or f(0) = {f(0)}^2$$ $${f(0)}^2 - f(0) = 0$$ $$f(0) { f(0) – 1 } = 0$$ Then $$f(0) = 0 or f(0) = 1.$$ Then f(0) becomes an unknown variable and we have 1 variable. D is most likely to be the answer. Condition 1) Since f(0) > 0, we have f(0) = 1. This is sufficient. Condition 2) Both 0 and 1 are integers, f(0) = 0 or f(0) = 1. Thus, this is not sufficient. Therefore, A is the answer. Answer: A _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Re: If f(x+y) = f(x)f(y), what is the value of f(0)? 1) f(x) > 0 2) f(x) h   [#permalink] 12 Nov 2017, 19:00
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