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

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If n is an integer, is n - 1 even?  [#permalink]

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06 Dec 2015, 12:09
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5% (low)

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95% (00:41) correct 5% (01:25) wrong based on 159 sessions

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

(1) n - 2 is odd

(2) n + 1 is even

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Re: If n is an integer, is n - 1 even?  [#permalink]

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06 Dec 2015, 12:16
(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.

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Re: If n is an integer, is n - 1 even?  [#permalink]

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08 Dec 2015, 08:39
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
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Re: If n is an integer, is n - 1 even?  [#permalink]

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09 Dec 2015, 09:01
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
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Re: If n is an integer, is n - 1 even?  [#permalink]

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10 Dec 2015, 01:19
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.

* 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.
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Re: If n is an integer, is n - 1 even?  [#permalink]

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22 Aug 2016, 02:21
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
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Re: If n is an integer, is n - 1 even?  [#permalink]

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27 Dec 2016, 07:13
Bunuel wrote:
If n is an integer, is n - 1 even?

(1) n - 2 is odd

(2) n + 1 is even

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
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Re: If n is an integer, is n - 1 even?  [#permalink]

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08 May 2018, 11:02
Top Contributor
Bunuel wrote:
If n is an integer, is n - 1 even?

(1) n - 2 is odd

(2) n + 1 is even

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

Cheers,
Brent
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Re: If n is an integer, is n - 1 even?   [#permalink] 08 May 2018, 11:02
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