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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
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Kudos [?]: 3125 [0], given: 0

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:

75% (hard)

Question Stats:

35% (00:54) correct 65% (01:06) wrong based on 48 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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Kudos [?]: 3125 [0], given: 0

Manager
Joined: 17 Mar 2015
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Kudos [?]: 57 [1], given: 4

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]

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10 Nov 2017, 05:39
1
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

Kudos [?]: 57 [1], given: 4

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4451

Kudos [?]: 3125 [0], given: 0

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]

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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.

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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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