GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 26 Apr 2019, 01:22

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# x^(n^2−n+2)/x^(n−2)(n+1)=?

Author Message
TAGS:

### Hide Tags

Manager
Joined: 17 May 2017
Posts: 130
Schools: ESSEC '20
GPA: 3

### Show Tags

Updated on: 04 Jul 2017, 11:56
00:00

Difficulty:

45% (medium)

Question Stats:

64% (01:34) correct 36% (01:38) wrong based on 88 sessions

### HideShow timer Statistics

$$\frac{x^{n^2−n+2}}{x^{(n−2)(n+1)}} = ?$$

(1) $$n=5$$
(2) $$x=2$$

Originally posted by haardiksharma on 04 Jul 2017, 03:55.
Last edited by Bunuel on 04 Jul 2017, 11:56, edited 1 time in total.
Edited the question.
Intern
Joined: 11 Aug 2016
Posts: 47
Location: India
Concentration: Operations, General Management
Schools: HBS '18, ISB '17, IIMA
GMAT 1: 710 Q49 V38
GPA: 3.95
WE: Design (Manufacturing)

### Show Tags

04 Jul 2017, 07:26
1
haardiksharma wrote:
x^(n^2−n+2)/x^((n−2)(n+1))=?

1) n=5
2) x=2

$$\frac{x^(n^2-n+2)}{x^(n-2)(n+1)}$$
=$$\frac{x^(n^2-n+2)}{x^(n^2-n-2)}$$
=$$x^(n^2-n+2-n^2+n+2)$$
=$$x^4$$

So we only need the value of x to determine the answer.

Statement 1:
As we found out above, the value is independent of the value of n. We do not know that value of x. If x=1 then answer is 1 and if x=2 answer is 16.
Not sufficient

Statement 2:
This directly gives us the value of x and the answer will be $$2^4 =16$$.
Sufficient.

Hit kudos if you like the explanation.
Current Student
Joined: 04 Jan 2016
Posts: 43
Location: United States
Concentration: General Management
Schools: Tuck '20 (M)
GMAT 1: 750 Q48 V44
WE: Management Consulting (Consulting)

### Show Tags

04 Jul 2017, 11:52
1
Formatted correctly otherwise this is very confusing:

$$\frac{x^{n^2−n+2}}{x^{(n−2)(n+1)}} = ?$$

(1) $$n=5$$
(2) $$x=2$$

To solve, take the equation and simplify by first multiplying out the denominator:

$$= \frac{x^{n^2-n+2}}{x^{n^2-n-2}}$$

Separate out the X using rules of exponents:

$$= \frac{(x^{n^2})( x^{-n}) (x^{2})}{(x^{n^2}) ( x^{-n}) (x^{-2})}$$

Flip the negative exponents:

$$= \frac{(x^{n^2})( x^{n}) (x^{2})(x^{2})}{(x^{n^2}) ( x^{n})}$$

Cancel out and simplify:

$$= \frac{(x^{2})(x^{2})}{1}$$

$$= x^{4}$$

Thus if we know $$x$$, we will have solved the problem.
Retired Moderator
Joined: 19 Mar 2014
Posts: 931
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5

### Show Tags

04 Jul 2017, 12:42
$$\frac{x^{n^2−n+2}}{x^{(n−2)(n+1)}} = ?$$

$$\frac{x^{n^2−n+2}}{x^{(n^2+n-2n-2)}}$$

$$\frac{x^{n^2−n+2}}{x^{(n^2-n-2)}}$$

$$x^(n^2−n+2 - n^2+n+2)$$

$$x^(2+2)$$

$$x^(4)$$

Which means if we have the value of x we should be able to find the answer.

(1) $$n=5$$

Clearly not sufficient as we are not aware of the value of x

Hence, (1) =====> is NOT SUFFICIENT

(2) $$x=2$$

$$x=2$$

Substitute this value in above equation.

$$x^(4)$$

$$2^(4)$$

$$= 16$$

Hence, (2) =====> is SUFFICIENT

_________________
"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475
Director
Joined: 04 Dec 2015
Posts: 750
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)

### Show Tags

04 Jul 2017, 13:02
haardiksharma wrote:
$$\frac{x^{n^2−n+2}}{x^{(n−2)(n+1)}} = ?$$

(1) $$n=5$$
(2) $$x=2$$

Lets simplify the fraction : $$\frac{x^{(n^2-n+2)}}{x^{(n-2)(n+1)}}$$

$$\frac{x^{(n^2-n+2)}}{x^{(n^2-n-2)}}$$

$$x^{(n^2-n+2)-(n^2-n-2)}$$

$$x^{(n^2-n+2- n^2+n+2)}$$

$$x^4$$

So we just need the value of $$x$$.

(1) $$n=5$$

Does not provide value of $$x$$. Hence I is Not Sufficient.

(2) $$x=2$$

Gives the value of x.

$$x^4 = 2^4 = 16$$

Hence II is Sufficient.

_________________
Please Press "+1 Kudos" to appreciate.
Re: x^(n^2−n+2)/x^(n−2)(n+1)=?   [#permalink] 04 Jul 2017, 13:02
Display posts from previous: Sort by