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For all numbers x and y the definition of the operation ♦ is x♦ y=xy(x

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For all numbers x and y the definition of the operation ♦ is x♦ y=xy(x  [#permalink]

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05 Feb 2020, 08:56
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68% (01:00) correct 32% (01:39) wrong based on 22 sessions

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For all numbers $$x$$ and $$y$$ the definition of the operation $$♦$$ is $$x♦ y=xy(x+4)$$. If $$(-6) ♦ a = -60,$$ then what is the value of $$a$$ ?

A. -20
B. -5
C. 2.5
D. 5
E. 10

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Posts: 10231
Location: Pune, India
Re: For all numbers x and y the definition of the operation ♦ is x♦ y=xy(x  [#permalink]

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05 Feb 2020, 20:42
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For all numbers $$x$$ and $$y$$ the definition of the operation $$♦$$ is $$x♦ y=xy(x+4)$$. If $$(-6) ♦ a = -60,$$ then what is the value of $$a$$ ?

A. -20
B. -5
C. 2.5
D. 5
E. 10

$$x♦ y=xy(x+4)$$

$$(-6) ♦ a = -60 = (-6)a(-6 + 4) = 12a$$

a = -5

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Karishma
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Re: For all numbers x and y the definition of the operation ♦ is x♦ y=xy(x  [#permalink]

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05 Feb 2020, 22:28
We are given
• x♦y = xy(x+4)
• (−6) ♦a=−60
Required: a = ?

• (−6) ♦a=−60
or, (-6)a (-6 + 4) = -60
or, (-6a) *(-2) = -60
or, 12a = -60
or, a = -5

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Posts: 9906
Location: United States (CA)
Re: For all numbers x and y the definition of the operation ♦ is x♦ y=xy(x  [#permalink]

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09 Feb 2020, 05:22
1
For all numbers $$x$$ and $$y$$ the definition of the operation $$♦$$ is $$x♦ y=xy(x+4)$$. If $$(-6) ♦ a = -60,$$ then what is the value of $$a$$ ?

A. -20
B. -5
C. 2.5
D. 5
E. 10

(-6)*a = -60

-6a(-6 + 4) = -60

36a - 24a = -60

12a = -60

a = -5

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Re: For all numbers x and y the definition of the operation ♦ is x♦ y=xy(x   [#permalink] 09 Feb 2020, 05:22
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