Hi Sanju,


I resolved it as n+(1/(n-1))
solution set on n looks like (all R except 1)

when n = 3 3+0.5
when n = 2 2+1 [.........3..........]
when n = 1 Out of scope
when n= 0.5 0.5+ -2
when n = 0 -1 [..........-1........]
when n = -1 -1.5

HSPA wrote:Hi Sanju,


I resolved it as n+(1/(n-1))
solution set on n looks like (all R except 1)

when n = 3 3+0.5
when n = 2 2+1 [.........3..........]
when n = 1 Out of scope
when n= 0.5 0.5+ -2
when n = 0 -1 [..........-1........]
when n = -1 -1.5

good! so what's your answer?

Ans D cannot lie between -1 and 3
just plug in numbers to see the range.

if n=-1, we get -1.5
if n=0, we get -1
if n=2, we get 3
for n=3, we get 3.5

n cannot equal 1 since that would make the denominator undefined.

therefore it is either >= +3 or <= -1 hence D

sanju09 wrote:Value of the expression (n^2 - n + 1)/ (n - 1) cannot lie between
(A) -1, -3
(B) 1, -3
(C) -1, 2
(D) -1, 3
(E) 1, 3

I am not aware the exact mathematics approach for this kind of problem, but I try to find out the solution using plug-in methodology

(n^2-n+1) / ( n-1) = (n+1)(n^2-n+1) / ( n+1)(n-1)
= (n^3 +1) / ( n^2-1)

For n=-2 , value of expression comes -2.3
For n=-1 , value of expression comes 0
For n= 0 , value of expression comes -1
For n= 1 , value of expression comes "not defined"
For n= 1.5 , value of expression comes 3.5
For n= 2 , value of expression comes 3
For n= 3 , value of expression comes 3.5

First two options are out, as we have values under that range.
We cannot have the expression value when n=1.

Last 3 options seem to be in answer choices, but which one to select.

Please guide with accurate approach.

3,-1 .. D

Correct its D. The value will never be between -1 and 3.

6983manish wrote:

sanju09 wrote:Value of the expression (n^2 - n + 1)/ (n - 1) cannot lie between
(A) -1, -3
(B) 1, -3
(C) -1, 2
(D) -1, 3
(E) 1, 3

I am not aware the exact mathematics approach for this kind of problem, but I try to find out the solution using plug-in methodology

(n^2-n+1) / ( n-1) = (n+1)(n^2-n+1) / ( n+1)(n-1)
= (n^3 +1) / ( n^2-1)

For n=-2 , value of expression comes -2.3
For n=-1 , value of expression comes 0
For n= 0 , value of expression comes -1
For n= 1 , value of expression comes "not defined"
For n= 1.5 , value of expression comes 3.5
For n= 2 , value of expression comes 3
For n= 3 , value of expression comes 3.5

First two options are out, as we have values under that range.
We cannot have the expression value when n=1.

Last 3 options seem to be in answer choices, but which one to select.

Please guide with accurate approach.

Assaulters please revise Quadratic Equations, Functions, and Inequalities.

If (n^2 - n + 1)/ (n - 1) = m, then question is simply asking for what's not within the range of m, not that of n here. Remember, in functions of the form y = f (x), we first need to derive it to the form x = f (y) in order to answer its range. In our case, we therefore need to find n in terms of m and then answer it for m. Here we go...

If (n^2 - n + 1)/ (n - 1) = m

then, (n^2 - n + 1) = m (n - 1)

or, n^2 - (m + 1) n + (m + 1) = 0

This is a quadratic in n, which may be solved by using the famous quadratic formula invented by an Indian genius Aacharya Shridhar who proved that the roots of the quadratic of the form a x^2 + b x + c = 0 can be given by

x = [-b ± √(b^2 - 4 a c)]/ (2 a)

In our case, a = 1, b = -(m + 1), and c = m + 1, using we have

n = [(m + 1) ± √[(m + 1) ^2 - 4 × 1 × (m + 1)]/ (2 × 1)

Revise the concept of Discriminant too, for real roots (m + 1) ^2 - 4 × 1 × (m + 1) can never be negative, in other words

(m + 1) ^2 - 4 × 1 × (m + 1) ≥ 0

or, (m + 1) (m - 3) ≥ 0

We can see that m can take -1 and 3, and anything more than -1 and less than 3 won't make m defined.

Hence m or (n^2 - n + 1)/ (n - 1) cannot lie between [spoiler]-1 and 3[/spoiler].

This is why [spoiler]D[/spoiler] is the correct choice.

sanju09 wrote:

6983manish wrote:

sanju09 wrote:Value of the expression (n^2 - n + 1)/ (n - 1) cannot lie between
(A) -1, -3
(B) 1, -3
(C) -1, 2
(D) -1, 3
(E) 1, 3

I am not aware the exact mathematics approach for this kind of problem, but I try to find out the solution using plug-in methodology

(n^2-n+1) / ( n-1) = (n+1)(n^2-n+1) / ( n+1)(n-1)
= (n^3 +1) / ( n^2-1)

For n=-2 , value of expression comes -2.3
For n=-1 , value of expression comes 0
For n= 0 , value of expression comes -1
For n= 1 , value of expression comes "not defined"
For n= 1.5 , value of expression comes 3.5
For n= 2 , value of expression comes 3
For n= 3 , value of expression comes 3.5

First two options are out, as we have values under that range.
We cannot have the expression value when n=1.

Last 3 options seem to be in answer choices, but which one to select.

Please guide with accurate approach.

Assaulters please revise Quadratic Equations, Functions, and Inequalities.

If (n^2 - n + 1)/ (n - 1) = m, then question is simply asking for what's not within the range of m, not that of n here. Remember, in functions of the form y = f (x), we first need to derive it to the form x = f (y) in order to answer its range. In our case, we therefore need to find n in terms of m and then answer it for m. Here we go...

If (n^2 - n + 1)/ (n - 1) = m

then, (n^2 - n + 1) = m (n - 1)

or, n^2 - (m + 1) n + (m + 1) = 0

This is a quadratic in n, which may be solved by using the famous quadratic formula invented by an Indian genius Aacharya Shridhar who proved that the roots of the quadratic of the form a x^2 + b x + c = 0 can be given by

x = [-b ± √(b^2 - 4 a c)]/ (2 a)

In our case, a = 1, b = -(m + 1), and c = m + 1, using we have

n = [(m + 1) ± √[(m + 1) ^2 - 4 × 1 × (m + 1)]/ (2 × 1)

Revise the concept of Discriminant too, for real roots (m + 1) ^2 - 4 × 1 × (m + 1) can never be negative, in other words

(m + 1) ^2 - 4 × 1 × (m + 1) ≥ 0

or, (m + 1) (m - 3) ≥ 0

We can see that m can take -1 and 3, and anything more than -1 and less than 3 won't make m defined.

Hence m or (n^2 - n + 1)/ (n - 1) cannot lie between [spoiler]-1 and 3[/spoiler].

This is why [spoiler]D[/spoiler] is the correct choice.

Thanks Sanju for clarification.

Your most welcome 6983manish. Please re read it as...

We can see that m can take -1 and 3, and anything more than -1 and less than 3 won't make n (not m) defined.

Regards

force5 wrote:Correct its D. The value will never be between -1 and 3.

Then the question is worded horribly.

If the value cannot lie between -1 and 3, then it also cannot lie between (c) -1 and 2 and (e) 1 and 3.

Accordingly, C, D and E are all correct answers to this question.

I face similar problem in CRs.. they ask to choose the best option with 3 choices in agreement with the question. I always "try" to choose the "best"...

HSPA wrote:I face similar problem in CRs.. they ask to choose the best option with 3 choices in agreement with the question. I always "try" to choose the "best"...

Here's a fundamental principle of the GMAT: every question has 1 answer that's correct and 4 that are wrong.

So, if it seems like there's more than 1 correct answer, there are a few possibilities:

1) the question is ambiguous or poorly designed (should rarely if ever happen if you get your questions from a reliable source);

2) you misread/misunderstood the question;

3) you misread/misunderstood the background information (e.g. the stimulus in a CR question or the statements in a DS questions); and/or

4) you misread/misunderstood the answer choice(s).

Since each of those issues has a different solution, it's essential to identify exactly what mistakes you're making on each question - just another reason why thorough review is the key to score improvement on the GMAT!

Stuart Kovinsky wrote:

force5 wrote:Correct its D. The value will never be between -1 and 3.

Then the question is worded horribly.

If the value cannot lie between -1 and 3, then it also cannot lie between (c) -1 and 2 and (e) 1 and 3.

Accordingly, C, D and E are all correct answers to this question.

That's absolutely correct, choices are not designed properly, or may be the question is failing to ask the closed interval [a, b] specifically. Even both reasons are possible to prove that the source of this question is bogus. One student of mine, studying in a less known GMAT training center has come up with this problem a week ago. But the concept that it's testing is certainly not out of GMAT, and it could well be a 720+ question on the real test if tailored well.