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# If the operation x&y is defined by the equation x&y=x·y/(x+y) for all

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Math Expert
Joined: 02 Sep 2009
Posts: 50670
If the operation x&y is defined by the equation x&y=x·y/(x+y) for all  [#permalink]

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21 Mar 2017, 08:18
00:00

Difficulty:

5% (low)

Question Stats:

92% (00:57) correct 8% (02:02) wrong based on 78 sessions

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If the operation x&y is defined by the equation x&y=x·y/(x+y) for all x≠−y, then (18)&(9)=

A. 2
B. 3
C. 6
D. 9
E. 12

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Re: If the operation x&y is defined by the equation x&y=x·y/(x+y) for all  [#permalink]

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21 Mar 2017, 10:13
Bunuel wrote:
If the operation x&y is defined by the equation x&y=x·y/(x+y) for all x≠−y, then (18)&(9)=

A. 2
B. 3
C. 6
D. 9
E. 12

(18)&(9) = 18*9/(18+9) = 18*9/27 = 6

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If the operation x&y is defined by the equation x&y=x·y/(x+y) for all  [#permalink]

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21 Mar 2017, 10:23
Bunuel wrote:
If the operation x&y is defined by the equation x&y=x·y/(x+y) for all x≠−y, then (18)&(9)=

A. 2
B. 3
C. 6
D. 9
E. 12

$$x&y=x·y/(x+y)$$

Or, $$\frac{(18)&(9) = 18*9}{( 18 + 9 )}$$

Or, $$(18)&(9) = \frac{162}{27}$$

Or, $$(18)&(9) = 6$$

Thus, answer must be (C) 6
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Re: If the operation x&y is defined by the equation x&y=x·y/(x+y) for all  [#permalink]

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21 Mar 2017, 14:49
This one is ridiculously easy.

18 x 9/18 +9
162/27
6

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Joined: 31 May 2015
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Re: If the operation x&y is defined by the equation x&y=x·y/(x+y) for all  [#permalink]

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23 Oct 2017, 00:09
Does anyone get why does statement mentions x≠−y.
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Re: If the operation x&y is defined by the equation x&y=x·y/(x+y) for all  [#permalink]

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23 Oct 2017, 00:17
sony1000 wrote:
Does anyone get why does statement mentions x≠−y.

Because if x = -y, the operation x&y=x·y/(x+y) becomes undefined. In this case, the denominator becomes x + y = 0, and we cannot divide by 0.
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Re: If the operation x&y is defined by the equation x&y=x·y/(x+y) for all  [#permalink]

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26 Oct 2017, 14:31
Bunuel wrote:
If the operation x&y is defined by the equation x&y=x·y/(x+y) for all x≠−y, then (18)&(9)=

A. 2
B. 3
C. 6
D. 9
E. 12

(18)&(9) = (18 * 9)/(9 + 18) = (18 * 9)/27 = (2 * 9)/3 = 2 * 3 = 6

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Re: If the operation x&y is defined by the equation x&y=x·y/(x+y) for all &nbs [#permalink] 26 Oct 2017, 14:31
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