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# For all integers and b, where a is a ≠ b[/m], a £ b = |(a^2 - b^2)/(a

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Math Expert
Joined: 02 Sep 2009
Posts: 51205
For all integers and b, where a is a ≠ b[/m], a £ b = |(a^2 - b^2)/(a  [#permalink]

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03 Jul 2018, 08:55
00:00

Difficulty:

15% (low)

Question Stats:

100% (00:37) correct 0% (00:00) wrong based on 20 sessions

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For all integers and b, where a is $$a \neq b$$, $$a £ b = |\frac{(a^2 - b^2)}{(a - b)}|$$. What is the value of $$4 £ 2$$?

A. 2

B. 4

C. 6

D. 8

E. 10

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Math Expert
Joined: 02 Aug 2009
Posts: 7106
Re: For all integers and b, where a is a ≠ b[/m], a £ b = |(a^2 - b^2)/(a  [#permalink]

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03 Jul 2018, 10:35
Bunuel wrote:
For all integers and b, where a is $$a \neq b$$, $$a £ b = |\frac{(a^2 - b^2)}{(a - b)}|$$. What is the value of $$4 £ 2$$?

A. 2

B. 4

C. 6

D. 8

E. 10

$$a £ b = |\frac{(a^2 - b^2)}{(a - b)}|=|\frac{(a-b)(a+b)}{a-b}|=|a+b|$$
so $$4 £ 2 = |4+2|=6$$

C
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: For all integers and b, where a is a ≠ b[/m], a £ b = |(a^2 - b^2)/(a  [#permalink]

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03 Jul 2018, 13:57
1
Bunuel wrote:
For all integers and b, where a is $$a \neq b$$, $$a £ b = |\frac{(a^2 - b^2)}{(a - b)}|$$. What is the value of $$4 £ 2$$?

A. 2

B. 4

C. 6

D. 8

E. 10

This question is all about pattern. At first we need to analyse or break down the given pattern in order to reach our ultimate answer. Computations can be performed as follows:

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

a £ b = |$$\frac{( a+b) ( a - b)}{(a-b)}$$|

a £ b = |a + b |

we are asked to determine the value of 4 £ 2.

4 £ 2 = |4+2|
= 6

Thus the best answer is C.
Re: For all integers and b, where a is a ≠ b[/m], a £ b = |(a^2 - b^2)/(a &nbs [#permalink] 03 Jul 2018, 13:57
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