If n is an integer, is n - 1 even?

Question

(1) n - 2 is odd

(2) n + 1 is even

Skywalker18 · Answer

(1) n - 2 is odd
n-1 = n-2 + 1
 = Odd + 1
 = Even

Sufficient.

(2) n + 1 is even
n+1=n+1-2
 = even - 2
 = even
Sufficient.

Answer D

mango aadmi · Answer

n is integer, n-1 =even ?

1) n-2 is odd

n= odd +2 =odd
so, n is odd..

n-1 = even ( S)

2) n+1 = even
 n= even-1
 so, n = odd

therefore , n-1 = even (S)

D

nipunjain14 · Answer

n - 1 will be even if n is odd. Thus we need to prove is n is odd

(1) n - 2 is odd
odd-even = odd
Thus n = odd
Sufficient

(2) n + 1 is even 
odd+odd= even
thus n is odd
Sufficient

Ans: D

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

3) If n is an integer, is n - 1 even?

(1) n - 2 is odd

(2) n + 1 is even

-> When you modify the original condition and question, it becomes n-1=even? --> n=even-1=odd?. There is 1 variable(n), which should match with the number of equations. So, 1 equation is needed. That is, for 1) 1 equation, for 2) 1 equation, which is likely to make D the answer. 
1) n-2=odd, n=odd+2=odd -> yes, which is sufficient.
2) n+1=even, n=even-1=odd -> yes, which is sufficient.
Therefore, the answer is D.

* For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

stonecold · Answer

To check => n-1 = even i.e if n is odd or not
Statement 1 = n-2=odd => n=odd+even = odd => suff
statement 2 => n+1=even => n=even -odd = odd => suff

Smash that D

Sirakri · Answer

1)
The consecutive number of n-2=odd is always even.
2)
The consecutive number of n+1=even, n is odd and n-1 is EVEN.

D

BrentGMATPrepNow · Answer

Some important rules: 
1. ODD +/- ODD = EVEN
2. ODD +/- EVEN = ODD
3. EVEN +/- ODD = ODD
4. EVEN +/- EVEN = EVEN

Target question :    Is n - 1 even?

Statement 1 : n - 2 is odd  
In other words, we can write n - 2 = ODD
Add 1 to both sides to get: n - 2 + 1 = ODD + 1
Simplify: n - 1 = ODD + 1
1 is ODD, so we can write: n - 1 = ODD + ODD
From   rule #1  , we can write: n - 1 = EVEN
So,  the answer to the target question is YES, n-1 IS even 
Since we can answer the  target question  with certainty, statement 1 is SUFFICIENT

Statement 2 : n + 1 is even 
In other words, we can write n + 1 = EVEN
Subtract 2 from to both sides to get: n + 1 - 2 = EVEN - 2
Simplify: n - 1 = EVEN - 2
2 is EVEN, so we can write: n - 1 = EVEN - EVEN
From   rule #4  , we can write: n - 1 = EVEN
So,  the answer to the target question is YES, n-1 IS even 
Since we can answer the  target question  with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

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 n is an integer, is n - 1 even?

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 Data Sufficiency (DS) Questions

If n is an integer, is n - 1 even?

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