If ∆ x = x for x ≥ 0 and 2x for x

Question

If ∆ x = x for x ≥ 0 and 2x for x < 0,  \frac{∆30}{∆(-5)}

A. −12
B. −6
C. −3
D. 6
E. 30

saswata4s · Answer

∆ x = x for x ≥ 0; Therefore, ∆30 = 30;
Again,
∆ x = 2x for x < 0; Therefore, ∆ (-5) = -10;

so, ∆30/∆ (-5) = 30/(-10) = -3;

Answer C.

BrentGMATPrepNow · Answer

∆x = x for x ≥ 0  
In other words, IF x is  greater than or equal to 0 , then ∆x = x
So, for example, ∆5 = 5, and ∆11 = 11, and ∆0 = 0, since 5, 11 and 0 are all  greater than or equal to 0 
Likewise,  ∆30 = 30

∆x = 2x for x < 0  
In other words, IF x is  less than 0 , then ∆x = 2x
So, for example, ∆(-3) = 2(-3) = -6, and ∆(-1) = 2(-1) = -2, and ∆(-9) = 2(-9) = -18, since -3, -1 and -9 are all  less than 0 
Likewise,  ∆(-5) = 2(-5) = -10

So....
 ∆30 / ∆(-5)  =  30 / (-10)  = -3

Answer: C

Cheers,
Brent

BrushMyQuant · Answer

Given that ∆ x = x for x ≥ 0 and 2x for x < 0 and we need to find the value of  \frac{∆30}{∆(-5)}

∆30 = 30 (because ∆ x = x for x ≥ 0)
∆(-5) = 2*-5 = -10 (because ∆ x = 2x fo)

=>  \frac{∆30}{∆(-5)}  =  \frac{30}{-10}  = -3

So,  Answer will be C 
Hope it helps!

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

https://www.youtube.com/watch?v=b7JoMX0gk8M

If ∆ x = x for x ≥ 0 and 2x for x < 0,

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