If x, y and z are consecutive, even integers...

[giovanni.gastone]

SOURCE: PrincetonReview

If x, y and z are consecutive, even integers, which of the following must be true?

I. y - z is an even integer.
II. (x + y + z) / 6 is an integer.
III. x + z = 2y

A. None
B. I only
C. I and II only
D. II and III only
E. I, II, and III

OA: E

[giovanni.gastone]

This is a pretty easy question, so my question for you guys isn't about the math.

My original answer was based on the premise that while x, y, and z are consecutive, even integers, they are not necessarily ordered in ascending order (i.e., x < y < z). So, while we can definitively prove I and II, I didn't think we could definitively prove III without knowing the order. So, my original answer was C.

My question for you guys is, on the real GMAT, when faced with a question like like with the same phrasing do I assume that the order is ascending (i.e., x < y < z), or do I not?

Thank you,

Gio

======================================
PrincetonReview's Official Explanation
======================================
Yes. Plug in more than once. If x = 2, y = 4 and z = 6, I, II, and III are all true. If x = -2, y = 0 and z = 2, I, II, and III are still all true. If x = -8, y = -6 and z = -4, I, II, and III are still all true, so the answer is E.

[vineeshp]

Veyr interesting point.

Yes you can assume I guess.

[manpsingh87]

SOURCE: PrincetonReview

If x, y and z are consecutive, even integers, which of the following must be true?

I. y - z is an even integer.
II. (x + y + z) / 6 is an integer.
III. x + z = 2y

A. None
B. I only
C. I and II only
D. II and III only
E. I, II, and III

OA: E

let three consecutive even integers x,y,z be 2k,2k+2,2k+4 respectively..!!!

lets come directly to III. as I and II can be proved easily..!!

x+z= 2k+2k+4= 2(2k+2); x+z=2y..!!!
i hope it helps..!!!!

[giovanni.gastone]

let three consecutive even integers x,y,z be 2k,2k+2,2k+4 respectively..!!!

lets come directly to III. as I and II can be proved easily..!!

x+z= 2k+2k+4= 2(2k+2); x+z=2y..!!!
i hope it helps..!!!!

manpsingh87, in your logic, you're assuming that "z" is bigger (i.e. 2k+4). But, how do you know the following is wrong?

y=2k
z=2k+2
x=2k+4

in the above case, x, y, z are still consecutive, even integers. My point was that the stem only indicates that x, y, and z are consecutive but we do not know from reading it the order is such that x < y < z.

If we can assume from reading the stem that x < y < z simply given the order in which the variables appear, then if the question were posed in such a way that it says...

"If z, y, x are consecutive, even integers, which of the following must be true?" Can we assume that z < y < x? Or, do we assume that it's x < y < z? Or, is it y < x < z?

My question is about the phrasing. I want to make sure that I don't misinterpret or over-interpret on the real GMAT. If I should take the ordering of the variables as they appear then that's fine. But, if this is a problem with the way the question is phrased, then I want to make sure I don't mis-read other similar problems.

Gio

[manpsingh87]

hi gio, interesting point and you have presented good analysis of the question. i'll try to answer your question in the best possible way i can..!!!!

you're assuming that "z" is bigger (i.e. 2k+4). But, how do you know the following is wrong?

y=2k
z=2k+2
x=2k+4

in the above case, x, y, z are still consecutive, even integers. My point was that the stem only indicates that x, y, and z are consecutive but we do not know from reading it the order is such that x < y < z

as we know x,y,z are consecutive even integers, therefore they're in a.p. having common difference of 2. i.e. y-x=z-y=2
now consider y=2k,z=2k+2 and x=2k+4; now lets just put these values in the equation y-x=2k-2k-4=-4; z-y=2k+2-2k=2; therefore x,y,z are still even integers but they are not in a.p. whereas y,z,x are in a.p.!! i.e. z-y=x-z=2; so here 2z=x+y; similarly we can also have 2x=y+z;

but since its not a Data sufficiency question therefore we have to consider the case which can be the possibility among the given set of options.!!

"If z, y, x are consecutive, even integers, which of the following must be true?" Can we assume that z < y < x? Or, do we assume that it's x < y < z? Or, is it y < x < z?

now this is a data sufficiency question, which can't be answer on the given information, off-course here we need additional information to answer the question..!!!!

[Geva@EconomistGMAT]

Giovanni, the GMAC cannot allow such ambiguity in a question - this could provide a basis for disputing the question by a test taker. So no, you do not need to assume it - the question should tell you in unambiguous terms that x<y<z, or any other way. I don't think this sort of nitpicking is the kind of issue they want to test, either, so a real GMAT question would close this loophole.

[giovanni.gastone]

Thank you Geva. This answers my question!! Thank you too manpsingh87 for your help!

[Target2009]

+1 to E