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# For all positive numbers x and y, the operation x ♦ y is defined by x

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Math Expert
Joined: 02 Sep 2009
Posts: 64158
For all positive numbers x and y, the operation x ♦ y is defined by x  [#permalink]

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19 Mar 2020, 08:07
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Difficulty:

15% (low)

Question Stats:

87% (01:02) correct 13% (01:53) wrong based on 39 sessions

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For all positive numbers x and y, the operation $$x ♦ y$$ is defined by $$x ♦ y = \frac{x^2 - x}{2xy}$$. If $$x ♦ 5 = 2$$, then $$x =$$

A. 1
B. 5
C. 11
D. 20
E. 21

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Location: India
GMAT 1: 690 Q50 V34
WE: Engineering (Transportation)
For all positive numbers x and y, the operation x ♦ y is defined by x  [#permalink]

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19 Mar 2020, 08:15
Bunuel wrote:
For all positive numbers x and y, the operation $$x ♦ y$$ is defined by $$x ♦ y = \frac{x^2 - x}{2xy}$$. If $$x ♦ 5 = 2$$, then $$x =$$

A. 1
B. 5
C. 11
D. 20
E. 21

Asked; For all positive numbers x and y, the operation $$x ♦ y$$ is defined by $$x ♦ y = \frac{x^2 - x}{2xy}$$. If $$x ♦ 5 = 2$$, then $$x =$$

m]x ♦ y = \frac{x^2 - x}{2xy}[/m]
$$x ♦ 5 = \frac{x^2 - x}{10x} = 2$$
$$x^2 - x = 20x$$
$$x^2 - 21x = 0$$
x(x-21) = 0
x = 21 ; Since x <>0

IMO E
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Kinshook Chaturvedi
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Joined: 12 Dec 2015
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Re: For all positive numbers x and y, the operation x ♦ y is defined by x  [#permalink]

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19 Mar 2020, 08:46
1
For all positive numbers x and y, the operation $$x ♦ y$$ is defined by $$x ♦ y = \frac{x^2 - x}{2xy}$$. If $$x ♦ 5 = 2$$, then $$x =$$

A. 1
B. 5
C. 11
D. 20
E. 21 --> correct: $$x ♦ 5 = (x^2 -x)/2*x*5= 2$$ => x^2 -x = 20x => x^2-21x = 0 => x(x-21)=0 => x >0, so x =21
Intern
Joined: 03 May 2019
Posts: 5
Re: For all positive numbers x and y, the operation x ♦ y is defined by x  [#permalink]

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20 Mar 2020, 12:39
21
x♦5=2
x^2-x/2.x.5=2
x^2-x=20x
x^2=21x
Hence x=21
Target Test Prep Representative
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Posts: 10566
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Re: For all positive numbers x and y, the operation x ♦ y is defined by x  [#permalink]

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21 Mar 2020, 14:56
Bunuel wrote:
For all positive numbers x and y, the operation $$x ♦ y$$ is defined by $$x ♦ y = \frac{x^2 - x}{2xy}$$. If $$x ♦ 5 = 2$$, then $$x =$$

A. 1
B. 5
C. 11
D. 20
E. 21

Since x * 5 = 2:

(x^2 - x) / [(2)(x)(5)] = 2

(x^2 - x) / (10x) = 2

x^2 - x = 20x

x^2 - 21x = 0

x(x - 21) = 0

x = 0 or x = 21

Since x is positive, x = 21.

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Re: For all positive numbers x and y, the operation x ♦ y is defined by x   [#permalink] 21 Mar 2020, 14:56