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# For all numbers s and t, the operation * is defined by s*t =

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Re: For all numbers s and t, the operation * is defined by s*t = [#permalink]
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Option B.
(-2)*x=-12
(-2-1)(x+1)=-12
x+1=4
x=3
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Re: For all numbers s and t, the operation * is defined by s*t = [#permalink]
SOLUTION

For all numbers s and t, the operation * is defined by s*t = (s - 1)(t + 1). If (-2)*x = -12, then x =

(A) 2
(B) 3
(C) 5
(D) 6
(E) 11

Since $$s*t = (s - 1)(t + 1)$$, then $$(-2)*x = (-2-1)(x+1)=-3(x+1)$$.

So, we are given that $$-3(x+1)=-12$$ --> $$x+1=4$$ -> $$x=3$$.

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Re: For all numbers s and t, the operation * is defined by s*t = [#permalink]
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Can I please get an explaination to this? Completely clueless..

How do you conclude that s = -2 and t = x?
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Re: For all numbers s and t, the operation * is defined by s*t = [#permalink]
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Hi erikvm,

This is an example of a "Symbolism" question (you'll likely see one of them on Test Day). The basic concept is usually pretty simple - the prompt will "make up' a math symbol, explain to you what it "means" mathematically, then ask you to use it to perform a calculation.

Since the * symbol makes people think about multiplication, I'm going to change it to a # symbol. Here, we're told....

S#T = (S-1)(T+1)

You are meant to take the numbers that S and T represent and place them into the calculation. So, as an example, if we had...

2#3 then that would equal (2-1)(3+1) = (1)(4) = 4

Knowing that, we're given....

(-2)#X = -12 and we're asked to solve for X

Let's 'substitute in' the (-2) and the X....

(-2 - 1)(X + 1) = -12

Now, you can do the algebra....
(-3)(X + 1) = -12
(X + 1) = 4
X = 3

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Re: For all numbers s and t, the operation * is defined by s*t = [#permalink]
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erikvm wrote:
Can I please get an explaination to this? Completely clueless..

How do you conclude that s = -2 and t = x?

Check other function questions in our Special Questions Directory:

Operations/functions defining algebraic/arithmetic expressions
Symbols Representing Arithmetic Operation
Rounding Functions
Various Functions
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Re: For all numbers s and t, the operation * is defined by s*t = [#permalink]
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

For all numbers s and t, the operation * is defined by s*t = (s - 1)(t + 1). If (-2)*x = -12, then x =

(A) 2
(B) 3
(C) 5
(D) 6
(E) 11

We are given that s * t = (s - 1)(t + 1).

Since (-2) * x = -12:

(-2 - 1)(x + 1) = -12

(-3)(x + 1) = -12

-3x - 3 = -12

-3x = -9

x = 3

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Re: For all numbers s and t, the operation * is defined by s*t = [#permalink]
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

For all numbers s and t, the operation * is defined by s*t = (s - 1)(t + 1). If (-2)*x = -12, then x =

(A) 2
(B) 3
(C) 5
(D) 6
(E) 11

Problem Solving
Question: 113
Category:Algebra First-degree equations
Page: 76
Difficulty: 600

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Given: For all numbers s and t, the operation * is defined by s*t = (s - 1)(t + 1). If (-2)*x = -12

s*t = (s - 1)(t + 1)
(-2)*x = -12
(-2-1)(x+1) = -12
-3x - 3 = -12
-3x = - 9
x = 3

IMO B
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Re: For all numbers s and t, the operation * is defined by s*t = [#permalink]
Top Contributor
Given that s*t = (s - 1)(t + 1) and (-2)*x = -12 and we need to find the value of x

To find (-2)*x we need to compare what is before and after * in (-2)*x and s*t

=> We need to substitute s with -2 and t with x in s*t = (s - 1)(t + 1) to get the value of (-2)*x

=> -2*x = (-2 - 1)(x + 1) = -3 *(x+1) = -12 (given)
=> x + 1 = $$\frac{-12}{-3}$$ = 4
=> x = 4 - 1 = 3

Hope it helps!

Watch the following video to learn the Basics of Functions and Custom Characters

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