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

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Math Expert
Joined: 02 Sep 2009
Posts: 51215
Which of the following is equivalent to (a^100-b^100)/(a^50-b^50)  [#permalink]

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23 Sep 2015, 21:46
00:00

Difficulty:

15% (low)

Question Stats:

78% (00:45) correct 22% (00:47) wrong based on 97 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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Joined: 10 Aug 2015
Posts: 103
Which of the following is equivalent to (a^100-b^100)/(a^50-b^50)  [#permalink]

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24 Sep 2015, 00:26
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: 158
Re: Which of the following is equivalent to (a^100-b^100)/(a^50-b^50)  [#permalink]

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24 Sep 2015, 05:54
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.

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

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

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

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

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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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25 Sep 2015, 22:49
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]

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26 Sep 2015, 23:22
1
[(a^50 - b^50)(a^50 + b^50)] / (a^50 - b^50)

Answer is (a^50 + b^50) = C
CEO
Joined: 11 Sep 2015
Posts: 3237
Re: Which of the following is equivalent to (a^100-b^100)/(a^50-b^50)  [#permalink]

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03 Oct 2018, 09:26
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

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Re: Which of the following is equivalent to (a^100-b^100)/(a^50-b^50) &nbs [#permalink] 03 Oct 2018, 09:26
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