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a very easy DS question yet it perplexes me very much so.

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a very easy DS question yet it perplexes me very much so.

by hongwang9703 » Fri Mar 26, 2010 2:24 pm
OG pg 282, question 106

If x and y are integers, is xy even?

1. x=y+1

2. x/y is an even integer.


answer: D

however, from 1. X could be 0, and y could be -1, which 0 x -1 = 0, which is neither even nor odd. 0 is an integer, and so is -1, so no rules are violated and it makes statement 1 a maybe, thus answer should be B!

please explain....i must be missing an important peice of information somewhere!
i got utterly defeated by the gmat.
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by MrE2All » Fri Mar 26, 2010 8:56 pm
Your number properties are flawed. 0 is an even number.
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by rockeyb » Fri Mar 26, 2010 11:34 pm
hongwang9703 wrote:OG pg 282, question 106

If x and y are integers, is xy even?

1. x=y+1

2. x/y is an even integer.


answer: D

however, from 1. X could be 0, and y could be -1, which 0 x -1 = 0, which is neither even nor odd. 0 is an integer, and so is -1, so no rules are violated and it makes statement 1 a maybe, thus answer should be B!

please explain....i must be missing an important peice of information somewhere!

Lets not get in to 0 is odd or even argument .

Here is a simple way to solve this problem :
=========================================
If x and y are integers, is xy even?

1. x=y+1

2. x/y is an even integer.
=========================================
we are given x and y are integers .

We need to know if xy = even .

For xy to be even we need to find if either x or y is even .

So the question is - IS any of the numbers x OR y even ?

Lets look at the statements .

1. x=y+1

x - y = 1 Rephrase x - y = odd .

Rule : Even +/- Odd = Odd .

So we can tell any one of x or y is odd and the other even.

Thus we can say xy will be even .

Sufficient .

Now lets look at statement 2 .

x/y is an even integer .

x/ y = even .

Multiply y both sides .

x= even(y).

Rephrase x = even .

Thus we can say xy will be even .

Sufficient .

Hence D .

======================================

Now to answer the 0 is odd or even .

0 is considered even . Why?

Reason : Integers range from 0 , 1, 2, ......... N .

Similarly integers can be - ve also -N ...............-3,-2,-1,0,1,2........N

Property Of Integers : Integers alternate between odd and even numbers .

That is ever alternate digit will be Odd or Even depending upon the starting digit .

So keeping this in mind -1 is odd so 0 should be even .

And 1 is odd , 2 is even so 0 should be even .

Hope this helps.
"Know thyself" and "Nothing in excess"
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by hongwang9703 » Sat Mar 27, 2010 5:15 pm
ohh helps very much, thank you

i DID NOT know that 0 is an even number!! I just thought of a scenario that made the state a maybe but your explanation cleared it up for me.
i got utterly defeated by the gmat.
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by rockeyb » Sat Mar 27, 2010 10:00 pm
welcome mate :) ,

and dont worry English is also not my first language .
"Know thyself" and "Nothing in excess"
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by eaakbari » Mon Mar 29, 2010 7:01 am
Stem :
for xy to be even
either x is even or y is even or both are even.

Statement one x = y +1
This implies x and y are consecutive numbers, hence one is even and one is odd. Hence sufficient

Statement two x/y is even
Implies one of them is even to get an even result

or x = even number * y

which makes one of them even . sufficient

Hence D
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