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# If kSn is defined to be the product of (n + k)(n – k + 1) for all posi

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Re: If kSn is defined to be the product of (n + k)(n – k + 1) for all posi [#permalink]
Dillesh4096 wrote:
gmatt1476 wrote:
If $$kS_n$$ 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 $$k + 1S_n + 1$$ ?

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)

PS79302.01

$$k + 1S_n + 1$$ can be interpreted in more than 1 way: (k + 1)$$S_n$$ + 1 or $$(k + 1)S_{n + 1}$$ or k + $$1S_n$$ + 1

There is not brackets there, so it's k + $$1S_n$$ + 1
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Re: If kSn is defined to be the product of (n + k)(n – k + 1) for all posi [#permalink]
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Bunuel wrote:
Dillesh4096 wrote:
gmatt1476 wrote:
If $$kS_n$$ 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 $$k + 1S_n + 1$$ ?

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)

PS79302.01

$$k + 1S_n + 1$$ can be interpreted in more than 1 way: (k + 1)$$S_n$$ + 1 or $$(k + 1)S_{n + 1}$$ or k + $$1S_n$$ + 1

There is not brackets there, so it's k + $$1S_n$$ + 1

But that gives k + $$1S_n$$ + 1 as
k + (n + 1)(n - 1 + 1) + 1
= k + (n + 1)*n + 1
= n^2 + n + k + 1
Which is NOT equal to D.

Only if I take it as $$(k + 1)S_{n + 1}$$
= (n + 1 + k + 1)((n + 1) - (k + 1) + 1)
= (n + k + 2)(n - k + 1)
Which gives me option D.

So, in my opinion the representation in the question is not clear

Posted from my mobile device
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Re: If kSn is defined to be the product of (n + k)(n – k + 1) for all posi [#permalink]
1
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Dillesh4096 wrote:
Bunuel wrote:
Dillesh4096 wrote:

$$k + 1S_n + 1$$ can be interpreted in more than 1 way: (k + 1)$$S_n$$ + 1 or $$(k + 1)S_{n + 1}$$ or k + $$1S_n$$ + 1

There is not brackets there, so it's k + $$1S_n$$ + 1

But that gives k + $$1S_n$$ + 1 as
k + (n + 1)(n - 1 + 1) + 1
= k + (n + 1)*n + 1
= n^2 + n + k + 1
Which is NOT equal to D.

Only if I take it as $$(k + 1)S_{n + 1}$$
= (n + 1 + k + 1)((n + 1) - (k + 1) + 1)
= (n + k + 2)(n - k + 1)
Which gives me option D.

So, in my opinion the representation in the question is not clear

Posted from my mobile device

Dillesh4096 you are totally right. It's (k + 1)S(n + 1). Edited. By bad. Thank you.
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Re: If kSn is defined to be the product of (n + k)(n – k + 1) for all posi [#permalink]
given function ; kSn = (n + k)(n – k + 1)
so for
(k + 1)S(n + 1)= (n+1+k+1)(n+1-k-1+1) ; (n + k + 2)(n – k + 1)
IMO D

gmatt1476 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)

PS79302.01
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Re: If kSn is defined to be the product of (n + k)(n – k + 1) for all posi [#permalink]
1
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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...

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Re: If kSn is defined to be the product of (n + k)(n – k + 1) for all posi [#permalink]
2
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gmatt1476 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)

PS79302.01

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)

The formula is: (n + k)(n - k + 1), so our substitutions are:

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

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

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If kSn is defined to be the product of (n + k)(n – k + 1) for all posi [#permalink]
1
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gmatt1476 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)

PS79302.01

I received a request that I comment.

Let k=2 and n=3.

Which of the following expressions represents (k + 1)S(n + 1)?
(k + 1)S(n + 1) = (2 + 1)S(3 + 1) = 3S4

kSn is defined as: (n + k)(nk + 1)
Thus:
3S4 = (4 + 3)(4 - 3 + 1) = 7*2 = 14

The correct answer must yield 14 when k=2 and n=3.

A: (n + k)(n – k + 2)
B: (n + k)(n – k + 3)

n+k = 3+2 = 5, which is not a factor of 14.
Eliminate A and B.

C: (n + k + 1)(n – k + 2)
n+k+1 = 3+2+1 = 6, which is not a factor of 14.
Eliminate C.

D: (n + k + 2)(n – k + 1)
(n + k + 2)(n – k + 1) = (3 + 2 + 2)(3 - 2 + 1) = 7*2 = 14

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Re: If kSn is defined to be the product of (n + k)(n – k + 1) for all posi [#permalink]
Just take k+1 = a
n+1 = b

(a+b)(b-a+1)

input and solve
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Re: If kSn is defined to be the product of (n + k)(n – k + 1) for all posi [#permalink]
Can someone let me know where I’m getting it wrong?

Let N=3, K=2
NKS = (N+K)(N-K+1)
6S = 10
S = 5/3

(K+1)(S)(N+1) = (3)(5/3)(4) = 20

Only option B equates to 20. Why is the answer D?
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Re: If kSn is defined to be the product of (n + k)(n – k + 1) for all posi [#permalink]
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jonathantanzy wrote:
Can someone let me know where I’m getting it wrong?

Let N=3, K=2
NKS = (N+K)(N-K+1)
6S = 10
S = 5/3

(K+1)(S)(N+1) = (3)(5/3)(4) = 20

Only option B equates to 20. Why is the answer D?

Hi jonathantanzy,

In "Symbolism" questions, the symbol is NOT a variable (re: it does not have a value attached to it; for example 2 x 10 = 20..... not 20x). In this question, the S is only a symbol and not something that you are supposed to solve for. Thus, your calculation should be...

k = 2, n = 3
kSn = (n + k)(n - k + 1)
2S3 = (3 + 2)(3 - 2 + 1) = (5)(2) = 10

The question asks for the value of (k+1)S(n+1). In the context of the prior calculations, that would be...

(k+1) = 3
(n+1) = 4

(4 + 3)(4 - 3 + 1) = (7)(2) = 14. When you plug in your original values for k and n (re: k = 2, n = 3), only one of the answers matches...

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If kSn is defined to be the product of (n + k)(n – k + 1) for all posi [#permalink]
EMPOWERgmatRichC wrote:
jonathantanzy wrote:
Can someone let me know where I’m getting it wrong?

Let N=3, K=2
NKS = (N+K)(N-K+1)
6S = 10
S = 5/3

(K+1)(S)(N+1) = (3)(5/3)(4) = 20

Only option B equates to 20. Why is the answer D?

Hi jonathantanzy,

In "Symbolism" questions, the symbol is NOT a variable (re: it does not have a value attached to it; for example 2 x 10 = 20..... not 20x). In this question, the S is only a symbol and not something that you are supposed to solve for. Thus, your calculation should be...

k = 2, n = 3
kSn = (n + k)(n - k + 1)
2S3 = (3 + 2)(3 - 2 + 1) = (5)(2) = 10

The question asks for the value of (k+1)S(n+1). In the context of the prior calculations, that would be...

(k+1) = 3
(n+1) = 4

(4 + 3)(4 - 3 + 1) = (7)(2) = 14. When you plug in your original values for k and n (re: k = 2, n = 3), only one of the answers matches...

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

Thanks! How do we recognise when we’re facing a “symbolism” question? Since in most cases, we’re conditioned to think in terms of algebraic variables.
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Re: If kSn is defined to be the product of (n + k)(n – k + 1) for all posi [#permalink]
Hi jonathantanzy,

I'm going to assume that you know all of the typical math symbols (addition, subtraction, etc.) and specialty symbols (absolute value, exponents, etc.). If you read a Quant question that includes a math symbol that's used in a way that you've never seen before, then it's likely that you are looking at a Symbolism question. In addition, Symbolism questions have to explain to you how the Symbol "works" (often with math symbols that you already know), so that you can properly use the Symbol to answer whatever question is asked.

For example, in this question, "kSn" is immediately followed by a description of the math that you actually have to do (and the 'k' and 'n' are substituted into specific spots in the calculation).

GMAT assassins aren't born, they're made,
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Re: If kSn is defined to be the product of (n + k)(n – k + 1) for all posi [#permalink]
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) ?

(k + 1)S(n + 1) = $$(n+1 + k + 1)[(n+1) - (k+1) + 1)]$$

= $$(n+1 + k + 1)[(n+1) - (k+1) + 1)]$$
= $$(n+k+2)(n + 1 - k - 1 + 1)$$
= $$(n+k+2)(n - k + 1)$$

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Re: If kSn is defined to be the product of (n + k)(n – k + 1) for all posi [#permalink]
BrentGMATPrepNow wrote:
gmatt1476 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)

PS79302.01

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

For example: 5S2 = (2 + 5)(25 + 1)
= (7)(-2)
= -14

And 7S3 = (3 + 7)(37 + 1)
= (10)(-3)
= -30

(k+1)S(n+1) = [(n+1) + (k+1)][(n+1)(k+1) + 1]
= (n + k + 2)(n - k + 1)

Cheers,
Brent

Straightforward...once you understand that S means multiply and not a variable. Will GMAT define these things?
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Re: If kSn is defined to be the product of (n + k)(n – k + 1) for all posi [#permalink]
Hi CEdward,

If you read a Quant question that includes a math symbol that you've never seen before, then it's likely that you are looking at a Symbolism question. In addition, Symbolism questions have to explain to you how the Symbol "works" (often involving basic Arithmetic or Algebra), so that you can properly use the Symbol to answer whatever question is asked.

For example, in this question, "kSn" is immediately followed by a description of the math that you actually have to do (and the 'k' and 'n' are substituted into specific spots in the calculation).

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