Is f(n) > f(n 1)? (1) n = 8 (2) f(n) = n - 1

1. No information about the function itself. f(n) could be more or less than f(n-1). NOT SUFFICIENT
2. Gives us the general function. From this we have sufficient information to test the inequality. SUFFICIENT

ANSWER D

Target question: Is f(n) > f(n−1)?

Statement 1: n = 8
Plug n = 8 into target question to get: Is f(8) > f(8−1)?
In other words, Is f(8) > f(7)?
We cannot answer the target question with certainty, because we don't know anything about the function f.
So, statement 1 is NOT SUFFICIENT

Statement 1: f(n) = n-1
At first glance, we might assume that statement 2 is not sufficient, since we don't know the value of n.
However, now that we know how the function f behaves, we can, indeed answer the target question.
If f(n) = n-1, then...
f(n) = n - 1 and f(n - 1) = (n - 1) - 1 = n - 2
So, the original target question Is f(n) > f(n−1)? becomes Is n - 1 > n − 2?
Sure, n - 1 is definitely greater than n - 2
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1) : n = 8
Since f(n) is not determined, condition 1) is not sufficient.

Condition 2) : f(n) = n - 1
Since f(n) = n - 1, we have f(n-1) = (n-1)-1 = n-2.
Since n - 1 > n - 2, f(n) > f(n-1).
Thus, the condition 2) is sufficient.

Therefore, B is the answer.

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.

(1) We can rephrase the question as \(f(8)>f(7)\)?

However, we have no information regarding the function. INSUFFICIENT.

(2) We have \(n - 1 > (n - 1) - 1\)
\(n - 1 > n -2\)

SUFFICIENT.

BrentGMATPrepNow in ST 1 , f(8) > f(7)? what do you mean "because we don't know anything about the function f." we know what "n" is.... Can you give example how in this case function may behave

i thought St 1 is sufficient ... i just wrote 8>7

Any videos on functions ?

Here's an example:

f(n) = 2 - n
(1) n = 8
So, f(n) = f(8) = 2 - 8 = -6
And f(n-1) = f(7) = 2 - 7 = -5
In this case, f(n-1) > f(n)

Now consider the function f(n) = 2n
(1) n = 8
So, f(n) = f(8) = (2)(8) = 16
And f(n-1) = f(7) = (2)(7) = 14
In this case, f(n) > f(n-1)

Does that help?

Hi BrentGMATPrepNow, For St.1 not sufficient, is it because it's being given as n = 8 and not f(n) = 8? Therefore function f is not being defined.
Could we understand it this way? Thanks Brent

That's correct.
If we don't have any information about what the function does, there's no way to answer the target question.

Brilliant thanks BrentGMATPrepNow for great explanation always.

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