Problem Solving

BTGmoderatorDC wrote:If kSn is defined to be the product of (n + k)(n - k + 1) for all positive integers k and n, which of the following expressions represents (k + 1)S(n + 1) ?

A. (n + k)(n - k + 2)
B. (n + k)(n - k + 3)
C. (n + k + 1)(n - k + 2)
D. (n + k + 2)(n - k + 1)
E. (n + k + 2)(n - k + 3)



OA D

Source: Official Guide

GIVEN: kSn = (n + k)(n - k + 1)

For example: 5S2 = (2 + 5)(2 - 5 + 1)
= (7)(-2)
= -14

And 7S3 = (3 + 7)(3 - 7 + 1)
= (10)(-3)
= -30

Now let's answer the question....
(k+1)S(n+1) = [(n+1) + (k+1)][(n+1) - (k+1) + 1]
= (n + k + 2)(n - k + 1)

Answer: D

Cheers,
Brent

Hi All,

We're told that kSn is defined to be the product of (n + k)(n - k + 1) for all positive integers k and n. We're asked for the value of (k + 1)S(n + 1). This is a "Symbolism" question (the prompt 'makes up' a math symbol, tells us how it 'works' and asks us to perform a calculation with it) and it can be approached in a couple of different ways, including by TESTing VALUES.

IF.... K = 2 and N = 3....
then we're asked to find the value of 3S4....

According to the given formula, that would be (4+3)(4 - 3 + 1) = (7)(2) = 14. So we're looking for an answer that equals 14 when K=2 and N=3. There's only one answer that matches...

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

BTGmoderatorDC wrote:If kSn is defined to be the product of (n + k)(n - k + 1) for all positive integers k and n, which of the following expressions represents (k + 1)S(n + 1) ?

A. (n + k)(n - k + 2)
B. (n + k)(n - k + 3)
C. (n + k + 1)(n - k + 2)
D. (n + k + 2)(n - k + 1)
E. (n + k + 2)(n - k + 3)



OA D

Source: Official Guide

Note that this question is a defined function question, where the letter S simply defines a relationship between two variables k and n, and the formula that relates them is (n + k)(n - k + 1).

Here is a simple example of this defined function kSn. Let's calculate 3S5. This means that k = 3 and n = 5. So we have:

(5 + 3)(5 - 3 + 1)

We won't actually calculate the numerical example, as this was simply an illustration of how to use the formula.

Now, let's look at (k + 1)S(n + 1). We see that now, wherever there is a "k" in the formula, we will substitute (k + 1), and wherever there is an "n" in the formula, we will substitute (n + 1).

(k + 1)S(n + 1)

(n + 1 + k + 1) x [(n + 1 - (k + 1) + 1]

(n + k + 2) x (n - k + 1)

Answer: D