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Is the integer n even? (1) n – 5 is an odd integer (2) n/5 is an even
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Author:  Orange08 [ 11 Sep 2010, 14:21 ]
Post subject:  Is the integer n even? (1) n – 5 is an odd integer (2) n/5 is an even

Is the integer n even?

(1) n – 5 is an odd integer.
(2) n/5 is an even integer.

From 1, shouldn't the value of n be counted as 0?
n = 0, 2,4,6, etc.
Thus, can't tell if n is even for all values. 0 isn't considered even

From 2, n = 10, 20, 30 etc. and thus n is always even. sufficient.

Please correct me if I am wrong in my understanding for statement 1.

Author:  Bunuel [ 11 Sep 2010, 14:28 ]
Post subject:  Re: Is the integer n even? (1) n – 5 is an odd integer (2) n/5 is an even

Orange08 wrote:
Is the integer n even?
(1) n – 5 is an odd integer.
(2) n/5 is an even integer.

From 1, shouldn't the value of n be counted as 0?
n = 0, 2,4,6, etc.
Thus, can't tell if n is even for all values. 0 isn't considered even

From 2, n = 10, 20, 30 etc. and thus n is always even. sufficient.

Please correct me if I am wrong in my understanding for statement 1.


Given: \(n=integer\). Question: is \(n=even\)?

(1) \(n-5=odd\) --> \(n-odd=odd\) --> \(n=odd+odd=even\). Sufficient.

(2) \(\frac{n}{5}=even\) --> \(n=5*even=even\). Sufficient.

Answer: D.

P.S. Zero is an even number:

Zero is an even integer, though it's neither positive nor negative.

An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder.
An even number is an integer of the form \(n=2k\), where \(k\) is an integer.

So for \(k=0\) --> \(n=2*0=0\).

An odd number is an integer that is not evenly divisible by 2.
An odd number is an integer of the form \(n=2k+1\), where \(k\) is an integer.

Hope it helps.

Author:  saxenashobhit [ 11 Sep 2010, 14:28 ]
Post subject:  Re: Is the integer n even? (1) n – 5 is an odd integer (2) n/5 is an even

zero is a even number. any number that is multiple of 2 is even so 2* zero is zero.

Answer D

Author:  BrentGMATPrepNow [ 21 Nov 2017, 09:25 ]
Post subject:  Is the integer n even? (1) n – 5 is an odd integer (2) n/5 is an even

Orange08 wrote:
Is the integer n even?

(1) n – 5 is an odd integer.
(2) n/5 is an even integer.


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

5. (ODD)(ODD) = ODD
6. (ODD)(EVEN) = EVEN
7. (EVEN)(EVEN) = EVEN


Target question: Is integer n even?

Statement 1: n – 5 is an odd integer
Since 5 is ODD, statement 1 is saying: n - ODD = ODD
From rule #2 above, we can conclude that n is EVEN
So, the answer to the target question is "YES, n IS even"
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: n/5 is an even integer.
First multiply both sides by 5 to get: n = (5)(some EVEN integer)
Since 5 is ODD, we statement 2 is saying: n = (ODD)(EVEN)
From rule #6 above, we can conclude that n is EVEN
So, the answer to the target question is "YES, n IS even"
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

Author:  bumpbot [ 19 May 2021, 01:12 ]
Post subject:  Re: Is the integer n even? (1) n – 5 is an odd integer (2) n/5 is an even

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