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

 It is currently 19 Oct 2018, 11:11

### 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
Your Progress

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

# Which of the following is equivalent to (a^100-b^100)/(a^50-b^50)

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50002
Which of the following is equivalent to (a^100-b^100)/(a^50-b^50)  [#permalink]

### Show Tags

23 Sep 2015, 22:46
00:00

Difficulty:

15% (low)

Question Stats:

78% (00:45) correct 22% (00:48) wrong based on 90 sessions

### HideShow timer Statistics

Which of the following is equivalent to $$\frac{{{a}^{100}}-{{b}^{100}}}{{{a}^{50}}-{{b}^{50}}}$$ for all values of a and b for which the expression is defined?

(A) a^2+b^2
(B) a^2-b^2
(C) a^50+b^50
(D) a^50-b^50
(E) (ab)^2

Kudos for a correct solution.

_________________
Manager
Joined: 10 Aug 2015
Posts: 103
Which of the following is equivalent to (a^100-b^100)/(a^50-b^50)  [#permalink]

### Show Tags

24 Sep 2015, 01:26
1
Bunuel wrote:
Which of the following is equivalent to $$\frac{{{a}^{100}}-{{b}^{100}}}{{{a}^{50}}-{{b}^{50}}}$$ for all values of a and b for which the expression is defined?

(A) a^2+b^2
(B) a^2-b^2
(C) a^50+b^50
(D) a^50-b^50
(E) (ab)^2

Kudos for a correct solution.

Solution:
$$\frac{{{a}^{2*50}}-{{b}^{2*50}}}{{{a}^{50}}-{{b}^{50}}}$$ = $$\frac{({{a}^{50}}-{{b}^{50}})({{a}^{50}}+{{b}^{50}})}{{{a}^{50}}-{{b}^{50}}}$$ = $${{a}^{50}}+{{b}^{50}}$$

Option C
Manager
Joined: 29 Jul 2015
Posts: 159
Re: Which of the following is equivalent to (a^100-b^100)/(a^50-b^50)  [#permalink]

### Show Tags

24 Sep 2015, 06:54
Bunuel wrote:
Which of the following is equivalent to $$\frac{{{a}^{100}}-{{b}^{100}}}{{{a}^{50}}-{{b}^{50}}}$$ for all values of a and b for which the expression is defined?

(A) a^2+b^2
(B) a^2-b^2
(C) a^50+b^50
(D) a^50-b^50
(E) (ab)^2

Kudos for a correct solution.

$$\frac{{{a}^{100}}-{{b}^{100}}}{{{a}^{50}}-{{b}^{50}}}$$

= $$\frac{(a^{50})^2 - (b^{50})^2}{a^{50}-b^{50}}$$

= $$\frac{(a^{50}+b^{50})(a^{50}-b^{50})}{a^{50}-b^{50}}$$

= $$a^{50}+b^{50}$$

Answer:- C
Intern
Joined: 31 May 2014
Posts: 3
Location: India
Concentration: Technology, Strategy
GMAT 1: 700 Q47 V39
GPA: 3.2
Re: Which of the following is equivalent to (a^100-b^100)/(a^50-b^50)  [#permalink]

### Show Tags

25 Sep 2015, 23:49
1
Bunuel wrote:
Which of the following is equivalent to $$\frac{{{a}^{100}}-{{b}^{100}}}{{{a}^{50}}-{{b}^{50}}}$$ for all values of a and b for which the expression is defined?

(A) a^2+b^2
(B) a^2-b^2
(C) a^50+b^50
(D) a^50-b^50
(E) (ab)^2

Kudos for a correct solution.

To solve this we have to remember the basic formula : $$a^2 - b^2 = (a+b)(a-b)$$

Here the numerator $$a^{100}-b^{100}$$ Can be changed to $$(a^{50})^2 -(b^{50})^2$$

Clearly this can now be re written as $$({a}^{50}+{b}^{50})({a}^{50}-{{b}^{50})$$

Simplify this with the denominator whats left is $${a}^{50}+{b}^{50}$$ and thus the Answer is C
Intern
Joined: 04 Jun 2008
Posts: 6
Re: Which of the following is equivalent to (a^100-b^100)/(a^50-b^50)  [#permalink]

### Show Tags

27 Sep 2015, 00:22
1
[(a^50 - b^50)(a^50 + b^50)] / (a^50 - b^50)

Answer is (a^50 + b^50) = C
CEO
Joined: 12 Sep 2015
Posts: 3016
Location: Canada
Re: Which of the following is equivalent to (a^100-b^100)/(a^50-b^50)  [#permalink]

### Show Tags

03 Oct 2018, 10:26
Top Contributor
Bunuel wrote:
Which of the following is equivalent to $$\frac{{{a}^{100}}-{{b}^{100}}}{{{a}^{50}}-{{b}^{50}}}$$ for all values of a and b for which the expression is defined?

(A) a^2+b^2
(B) a^2-b^2
(C) a^50+b^50
(D) a^50-b^50
(E) (ab)^2

Kudos for a correct solution.

The numerator has a nice difference of squares, which can be factored
Note: a^100 = (a^50)²

So, (a^100 - b^100)/(a^50 - b^50) = (a^50 + b^50)(a^50 - b^50)/(a^50 - b^50)
= a^50 + b^50

Answer: C

RELATED VIDEO FROM OUR COURSE

_________________

Brent Hanneson – GMATPrepNow.com

Sign up for our free Question of the Day emails

Re: Which of the following is equivalent to (a^100-b^100)/(a^50-b^50) &nbs [#permalink] 03 Oct 2018, 10:26
Display posts from previous: Sort by

# Which of the following is equivalent to (a^100-b^100)/(a^50-b^50)

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.