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OG 13th, DS #111. is xy even?

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by Castor.kim » Sun Sep 16, 2012 4:56 am
I know that this question is already exist in 2010 solving but I have an other question to solving this problem.

111. If x and y are integers, is xy even?

(1) x = y+1
(2) x/y is an even integer.

As you already know that ..
(1) if y is odd, x is even and if y is even, x is odd
so, correct.
(2) x/y = even, x = even * y, so x is always even and xy is even too.

in (2),
if y is 0, x/y have no value (I learnd any kind of number can not devide by '0')
so x/y neither even nor odd isn't it??

the OG result is D.

please reply you opinions on here.. :)
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Sun Sep 16, 2012 6:20 am
Castor.kim wrote: if y is 0, x/y have no value (I learnd any kind of number can not devide by '0')
so x/y neither even nor odd isn't it??
Exactly. If y=0, then x/y is undefined, in which case x/y is neither even nor odd.

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by Brent@GMATPrepNow » Sun Sep 16, 2012 6:28 am
Castor.kim wrote:If x and y are integers, is xy even?
(1)
(2) x/y is an even integer.
Target question: Is xy even?

Aside: For xy to be even, we need x to be even, or y to be even (or both even).

Statement 1: x = y+1
This tells us that x is 1 greater than y.
This means that x and y are consecutive integers.
If x and y are consecutive integers, then one must be odd and the other must be even.
As such, the product xy must be even.
So, statement 1 is SUFFICIENT

Statement 2: x/y is an even integer.
If x/y is an even integer, then we can write x/y = 2k (where k is an integer)
Now take the equation and multiply both sides by y to get: x = 2ky
If k and y are both integers, we can see that 2ky (also known as x) must be even.
If x is even, then the product xy must be even.
So, statement 2 is SUFFICIENT

Answer = D

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by Brent@GMATPrepNow » Sun Sep 16, 2012 6:30 am
Castor.kim,
When posting questions, please use the spoiler function to hide the correct answer.
This will allow others to attempt the question without seeing the solution.

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by Castor.kim » Sun Sep 16, 2012 6:00 pm
Thanks Brent,

It's my second time posting question, so have less knowledge using board.
I'll use spoiler in next time.

return to the question,
as you said that I understand why the answer is D.

But in DS question, we should decide that the condition is true or false,
In first condition, we can answer it always 'even', so answer is 'true'
but in second condition, I can not answer it always 'even' because it can be a even, almost cases, but it can be 'nothing = neither even nor odd'

May I didn't understand about Data sufficient question algorithm?
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by Brent@GMATPrepNow » Mon Sep 17, 2012 7:55 am
Castor.kim wrote: I'll use spoiler in next time.
I believe that you can click the Edit button on the original post and add a spoiler (for anyone who still wishes to try the question)
Castor.kim wrote: But in DS question, we should decide that the condition is true or false,
In first condition, we can answer it always 'even', so answer is 'true'
Exactly. The answer to our target question will always be yes, xy is even.
Castor.kim wrote: but in second condition, I can not answer it always 'even' because it can be a even, almost cases, but it can be 'nothing = neither even nor odd'
This is not true. Here, you are not answering the target question.
The target question is: Is xy even?

Statement 2 tells us that x/y is an even integer. I believe that you are now answering a different target question (Is x/y even?). I say this because of your earlier question about whether or not x/0 can be even.
The real target questions is: Is xy even?. If we keep this in mind then we can see that statement 2 provides sufficient information to answer the target question.

For more information about Data Sufficiency, you may wish to watch our free set of video lessons on this topic: https://www.gmatprepnow.com/module/gmat-data-sufficiency

Cheers,
Brent
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by kalpita123 » Mon Sep 17, 2012 3:27 pm
Castor.kim wrote:
But in DS question, we should decide that the condition is true or false,
In first condition, we can answer it always 'even', so answer is 'true'
but in second condition, I can not answer it always 'even' because it can be a even, almost cases, but it can be 'nothing = neither even nor odd'

May I didn't understand about Data sufficient question algorithm?

Castor.kim,

In Data Sufficiency questions, we determine the sufficiency of the given statements(statements 1 & 2: individual or combined) to answer the given question (Here the question is, Is x*y= Even ?)

Addressing your query relevant to the given question-->

In the given question, lets consider the statement 2 .
Ask yourself , is x*y = Even ? ,provided that x/y is an even integer?
or, Ask yourself, is the statement 2--> "x/y is an even integer" a sufficient condition to answer whether x*y=Even?
As it is already given in the statement 2 that x/y= even integer,therefore y must not be 0, otherwise the given statement would be invalid.isn't it? I mean to say that,we should consider the statements as valid and establish their sufficiency with respect to the question in hand.

So, our task is to see whether the data given in the statement 2 is sufficient to answer [the answer can be either "yes" or "no" . Either of the answers will be sufficient ] the question .
Here this is very much sufficient.So, answer is D.

Hope this helps!
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by Castor.kim » Mon Sep 17, 2012 6:23 pm
Oops!!
I fully understand it.

Thanks Brent and kalpita123.
I hope that could be a helpful for other people.. :)
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by pinkpetal » Tue Sep 18, 2012 2:47 pm
what if y=0 and x is 1 ?
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by Brent@GMATPrepNow » Tue Sep 18, 2012 2:52 pm
pinkpetal wrote:what if y=0 and x is 1 ?
For statement 1, it is quite possible that y=0 and x=1, since x = y+1
In this case xy = 0, which is even.
For statement 1, it is also possible that y=1 and x=2, since x = y+1
In this case xy = 2, which is also even.
In fact, statement 1 ensures that xy is always even.

Now onto statement 2 (at this point, we can disregard statement 1)
For statement 2, y cannot equal 0, because we're told that x/y is an even integer, and 1/0 is not an even integer.
For us to consider any values for x and y, those values must be such that x/y is even.

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by pinkpetal » Tue Sep 18, 2012 2:59 pm
Cool Thanks :))
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