For all numbers q and r, the operation Θ is defined by q Θ r = (q + 3)

Question

For all numbers q and r, the operation Θ is defined by  q Θ r = (q + 3)(r – 2) . If  1Θ z = –8 , then z is equal to which of the following?

(A) –3
(B) –2
(C) –1
(D) 0
(E) 2

pushpitkc · Answer

Given : qΘr=(q+3)(r–2)
1Θz=–8

(1+3)(z-2) = -8
z-2 = -2
x=0(Option D)

umadurga · Answer

By simple substitution
(1+3)(Z-2)=-8
4(Z-2)=-8
z-2=-2
z=0
Option D

ScottTargetTestPrep · Answer

We are given that q@r = (q + 3)(r - 2) and that 1@z = -8.

Using the given pattern, we see that q = 1 and r = z. Thus:

1@z = (1 + 3)(z - 2)

-8 = 4(z - 2)

-2 = z - 2

0 = z

Answer: D

BrushMyQuant · Answer

q Θ r = (q + 3)(r – 2) and 1 Θ z = –8

Lets start by finding the value of 1 Θ z

To find 1 Θ z we will compare what is before and after Θ in 1 Θ z and q Θ r 
=> We will replace q with 1 and r with z in q Θ r = (q + 3)(r – 2) to get the value of 1 Θ z

=>  1 Θ z  = (1 + 3)(z – 2) = -8 (Given)
=> 4 * (z - 2) = -8
=> z - 2 =  \frac{-8 }{ 4}  = -2
=> z = -2 + 2 = 0

So,  Answer will be D 
Hope it helps!

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For all numbers q and r, the operation Θ is defined by q Θ r = (q + 3)

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