If [x] is defined as x^2 – 1 for all integers x, then [x + 1] - [x] =

Question

If   is defined as x^2 – 1 for all integers x, then   -   =

A. 0
B. x
C. x + 2
D. 2x
E. 2x + 1

PS21179

BrentGMATPrepNow · Accepted Answer

Given:   = x² - 1 
So, for example,   5 ] =  5 ² - 1 = 25 - 1 = 24 
And   7 ] =  7 ² - 1 = 49 - 1 = 48 
Likewise,   3k ] = ( 3k )² - 1 = 9k² - 1

So...... 
  x + 1 ] = ( x + 1 )² - 1 = (x² + 2x + 1) - 1 = x² + 2x 
And   x ] =  x ² - 1 = x² - 1

So,   -   = ( x² + 2x ) - ( x² - 1 ) = 2x +1

Answer: E

Cheers, 
Brent

GMATinsight · Answer

= x^2 – 1

Let,  x = 2 ,   = x^2 – 1 = 2^2 - 1 = 3

Let, x+1 = 3,   = (x+1)^2 – 1 = 3^2 - 1 = 8

-   = 8-3 = 5

A. 0  WRONG 
B. x  WRONG 
C. x + 2 = 2+2 = 4  WRONG 
D. 2x = 2*2 = 4  WRONG 
E. 2x + 1 = 2*2+1 = 5  CORRECT

Answer: Option E

Basshead · Answer

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

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

Answer is E.

KarishmaB · Answer

We can solve it by plugging in numbers too. Say x = 2, then x + 1 = 3

-   = (3^2 - 1) - (2^2 - 1) = 5

Put x = 2 in the options. Only (E) satisfies.

BrushMyQuant · Answer

= x^2 – 1

=>   -   =  (x+1)^2 - 1 - ( x^2 - 1)  =  x^2 + 2x + 1 -1 - x^2 + 1  = 2x + 1

So,  Answer will be E 
Hope it helps!

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

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

DanTheGMATMan · Answer

Straightforward function- keep each expression in parentheses to be safe:

https://www.youtube.com/watch?v=g_Nms3800aQ

Apk641 · Answer

Step 1: Use the definition of 
The problem defines  as:

\  = x^2 - 1
\]

This tells you that whenever you see , you can replace it with $x^2 - 1$.

Step 2: Apply the function to 
Now you need to apply the same definition to . This means, wherever you have $x + 1$, you replace it into the function $x^2 - 1$:

\  = (x + 1)^2 - 1
\]

Now, expand $(x + 1)^2$:

\

So:

\  = (x^2 + 2x + 1) - 1 = x^2 + 2x
\]

Step 3: Now subtract  from

We already know from the definition that:

\  = x^2 - 1
\]

So now, subtract  from :

\  -   = (x^2 + 2x) - (x^2 - 1)
\]

Step 4: Simplify

Now, simplify this expression:

\

Final Result:

The result of $  -  $ is:

\

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If [x] is defined as x^2 – 1 for all integers x, then [x + 1] - [x] =

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If [x] is defined as x^2 – 1 for all integers x, then [x + 1] - [x] =

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards