miscbelle wrote:For which of the following functions is f(a + b) = f(a) + f(b) for all positive numbers a and b?
a. f(x) = x^2
b. f(x) = x + 1
c. f(x) = sq. root of x
d. f(x) = 2/s
e. f(x) = -3x
Like many GMAT number property problems, we can attack this one through picking numbers or by applying principles.
Most people find picking numbers to be the quickest approach. Of course, before we can pick numbers we need to understand the question.
Step 1 of the Kaplan Method for PS: study the Q stem and the choices.
We see that we have a function question with functions in the choices as well. We also see a "which of the following" question; in problem solving, "which of the following" questions have a disproportionate number of (D) and (E) correct answers.
Step 2 of the Kaplan Method for PS: identify the exact question.
We're looking for an answer choice for which F(a + b) = F(a) + F(b) for all values of a and b.
Step 3 of the Kaplan Method for PS: choose the best approach.
If you're really up on your number properties, you'd have noticed that the question is really asking about the distributive principle. To what operation does the distributive principle apply? That's right, multiplication! So, we would simply look for a function in the choices that's multiplication: choose (e).
Alternatively, if you didn't see that, you wouldn't give up! Function questions are made for picking numbers, so we'd jump in and get our hands a bit dirty.
Let's keep our numbers simple:
a = 1
b = 2
and, therefore
a + b = 3
So, now the question becomes:
for which of the following functions is f(3) = f(1) + f(2)?
Plugging in (starting with (e) because of "WOTF"):
e) -3(3) = -3(1) + -3(2)... -9 = -3 + -6.. -9 = -9... yay!
Now it's possible that (e) just worked as a fluke for that specific set of numbers. If we're in a rush we should just pick (e) and take our chances; if we have the time we should quickly check the remaining choices.
d) 2/3 = 2/1 + 2/2... nope
c) root3 = root1 + root2... nope
b) 3 + 1 = (1+1) + (2+1)... nope
a) 9 = 1 + 4... nope
and now we're 100% sure that (e) is the correct choice.
HOWEVER... we should never forget:
Step 4 of the Kaplan Method for PS: double check the question.
Taking a very quick look back, yes we read it correctly and solved properly: ok, choose (e)!
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