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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Which of the following is equivalent to (a^100-b^100)/(a^50-b^50)

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

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Difficulty:   15% (low)

Question Stats: 74% (00:54) correct 26% (01:18) wrong based on 135 sessions

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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.

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

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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: 150
Re: Which of the following is equivalent to (a^100-b^100)/(a^50-b^50)  [#permalink]

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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.

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

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

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

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

Intern  B
Joined: 31 May 2014
Posts: 5
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]

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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]

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[(a^50 - b^50)(a^50 + b^50)] / (a^50 - b^50)

Answer is (a^50 + b^50) = C
GMAT Club Legend  V
Joined: 11 Sep 2015
Posts: 4999
GMAT 1: 770 Q49 V46
Re: Which of the following is equivalent to (a^100-b^100)/(a^50-b^50)  [#permalink]

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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

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If you enjoy my solutions, you'll love my GMAT prep course.  Re: Which of the following is equivalent to (a^100-b^100)/(a^50-b^50)   [#permalink] 03 Oct 2018, 09:26

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