Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: DS - Is x even? [#permalink]
28 Jul 2009, 22:14

21

This post received KUDOS

4

This post was BOOKMARKED

IMO A

1. xy + xz is an even integer - SUFFICIENT Given: xy + z is odd ...(i) xy + xz is even ...(ii)

subtracting (ii) from (i) we get xz - z, which should be odd (* since odd - even = odd) => z(x-1) is odd => both z and (x-1) is odd => since (x-1) is odd, x must be even.

2. y + xz is an odd integer -INSUFFICIENT Given: xy + z is odd ...(i) y + xz is odd ...(ii)

subtracting (ii) from (i) we get xy + z - y - xz = (x-1)(y-z) , which should be even => either (x-1) is even or (y-z) is even ....insufficient to determine _________________

Re: If x, y and z are integers and xy + z is an odd integer, is [#permalink]
19 Mar 2014, 18:41

Given condition: xy + z = odd implies either xy = odd (x =odd and y = odd) and z = even or xy = even (x or y can be odd and even respectively and vice versa) and z = odd

condition 1:

xy + xz = even; Implies x(y+z) = even which again implies the following:

i) x even and y+z = odd - where again y or z can be odd and even respectively and vice versa ii) x odd and y +z = even - where again y and z has to be both odd or both even

inconclusive

condition 2:

y + xz = odd

again inconclusive 1 + 2: Add xy + z + y + xz = odd + odd implies: (x + 1)(y+z) = even and x (y+z) is also even according to 2.. so y + z = even <y and z both even or y + z both odd>, x can be odd or even but by 1 xy + z = odd which means y and z both odd, so x is even.

Re: If x, y and z are integers and xy + z is an odd integer, is [#permalink]
20 Mar 2014, 05:09

2

This post received KUDOS

Expert's post

Mountain14 wrote:

jlgdr wrote:

Aleehsgonji wrote:

If x, y and z are integers and xy + z is an odd integer, is x an even integer?

(1) xy + xz is an even integer (2) y + xz is an odd integer

Odd/Even questions can be usually solved quite easily if one tries some operations with the statements

We want to know if x is even integer

We are given that xy+z is odd

Statement 1

xq + xz is even

Subtracting

z(x+1) is odd

Therefore, x+1 should be odd and x should be even

Sufficient

Statement 2

Not sufficient

Answer is A

Just my 2c

Cheers J

I am not clear with the red part.

When you subtract xy + z=odd from xy+xz=even you'll get: xz-z=even-odd=odd --> z(x-1)=odd. For the product of two integers to be odd, both of them must be odd --> z and x-1 are odd. If x-1=odd, then x must be even: x-1=x-odd=odd --> x=odd+odd=even.

Re: If x, y and z are integers and xy + z is an odd integer, is [#permalink]
21 Mar 2014, 19:46

Expert's post

Odd(O) Even (E) given: x,y,z integers xy+z=O so only the following scenarios can fulfill the constraints a) EO+O b) EE+O c) OE+O d) OO+E

question: x=E?

1) x(y+z)=E i. (E)(O+O) --> fits scenario a -->yes, x can be even ii. (O)(E+E) --> n/a - doesn't fit any scenarios iii. (O)(O+O) --> n/a - doesn't fit any scenarios

stop testing, x can't be odd, sufficient

2) y+xz = O i. E+(O)(O) --> fits scenario a -->yes, x can be even ii. O+(E)(E) --> n/a - doesn't fit any scenarios iii. O+(O)(E) --> fits scenario d -->no, x can be odd