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The positive integers x, y, and z are such that x is a [#permalink]
 17 Oct 2009, 14:15
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The positive integers x, y, and z are such that x is a factor of y and y is a factor of z. Is z even? (1) xz is even (2) y is even.
Last edited by Bunuel on 25 Feb 2012, 02:35, edited 1 time in total.
Added the OA
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Re: positive integers [#permalink]
17 Oct 2009, 14:32
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amitgovin wrote: The positive integers x, y, and z are such that x is a factor of y and y is a factor of z. Is z even?
(1) xz is even
(2) y is even. Given: x is a factor of y --> y=mx, for some non-zero integer m; y is a factor of z --> z=ny, for some non-zero integer n; So, z=mnx. Question: is z even? Note that z will be even if either x or y is even (1) xz even --> either z even, so the answer is directly YES or x is even (or both). But if x is even and as z=mnx then z must be even too (one of the multiples of z is even, so z is even too). Sufficient. (2) y even --> as z=ny then as one of the multiples of z even --> z even. Sufficient. Answer: D.
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Re: positive integers [#permalink]
19 Oct 2009, 23:18
amitgovin wrote: The positive integers x, y, and z are such that x is a factor of y and y is a factor of z. Is z even?
1) xz is even
2) y is even.
Please explain. thanks. y/x = k where k is an integer. y = xk ....................i z/y = m where m is an integer. z = ym = xkm .....................ii If a factor is even, then the source of the factor must be even. 1) If xz is even, z must be even because x may or may not be an even because x is a factor of z but z must be even. SUFF. 2) If y is even, z must be even because y is a factor of z. SUFF.. D..
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Re: positive integers [#permalink]
02 Dec 2010, 11:16
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amitgovin wrote: The positive integers x, y, and z are such that x is a factor of y and y is a factor of z. Is z even?
1) xz is even
2) y is even.
Please explain. thanks. Though Bunuel has provided the solution, I would just like to bring to your notice a train of thought. When we say, "The positive integers x, y, and z are such that x is a factor of y and y is a factor of z.", it implies that if x or y is even, z will be even. e.g. x = 4. Since x is a factor of y, y will be a multiple of 4 and will be even. Since z is a multiple of y, it will also be even. So, in a way, the 2 in x will drive through the entire sequence and make everything even. Once this makes sense to you, it will take 10 secs to arrive at the solution. Stmnt 1: Either x or z (or both which will happen if x is even) is even. In either case, z is even. Stmnt 2: y is even, so z must be even
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Re: positive integers [#permalink]
12 Dec 2010, 10:22
Bunuel, you always try to solve the questions algebraically, don't you?
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Re: positive integers [#permalink]
12 Dec 2010, 10:48
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metallicafan wrote: Bunuel, you always try to solve the questions algebraically, don't you? Not at all. There are certain GMAT questions which are pretty much only solvable with plug-in or trial and error methods (well at leas in 2-3 minutes). Also many questions can be solved with logic and common sense much quicker than with algebraic approach. So you shouldn't always rely on algebra. Having said that I must add that there are of course other types of questions which are perfect for algebraic approach, plus I often use algebra just to explain a solution.
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Re: positive integers [#permalink]
12 Dec 2010, 19:36
I like to thing of the boxes method. If you draw them out, then x is inside y which is inside z.
zx, a 2 will exist inside the box of either z or x (which is itself inside z) so YES
y a 2 will exist inside the box of y which is itself z so YES
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Re: positive integers [#permalink]
26 Dec 2010, 17:37
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VeritasPrepKarishma wrote: amitgovin wrote: The positive integers x, y, and z are such that x is a factor of y and y is a factor of z. Is z even?
1) xz is even
2) y is even.
Please explain. thanks. Though Bunuel has provided the solution, I would just like to bring to your notice a train of thought. When we say, "The positive integers x, y, and z are such that x is a factor of y and y is a factor of z.", it implies that if x or y is even, z will be even. e.g. x = 4. Since x is a factor of y, y will be a multiple of 4 and will be even. Since z is a multiple of y, it will also be even. So, in a way, the 2 in x will drive through the entire sequence and make everything even. Once this makes sense to you, it will take 10 secs to arrive at the solution. Stmnt 1: Either x or z (or both which will happen if x is even) is even. In either case, z is even. Stmnt 2: y is even, so z must be even awesome. your explanations and bunuel as well, are amazing  thanks
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Re: positive integers [#permalink]
30 Dec 2010, 10:23
answer:D
1 xz is even- sufficient
2 y is even-sufficient
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Re: positive integers [#permalink]
17 Mar 2011, 23:07
Easy if you realize the following:
When a is a factor of b
AND b is a factor of c
THEN a is a factor of c as well.
Hence when either one of these numbers is even, the other has to be even too..
D
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Re: positive integers [#permalink]
17 Mar 2011, 23:52
z = ky y = mx so z = (km)xy (1) -> xz is eve means at least x or z is even, and if x = even, then z is also even as it has an even factor. 2 -> y is even so z having an even factor is even too. Answer D
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Re: positive integers [#permalink]
15 Apr 2011, 05:24
At first, mistook "factor" for "multiple" came with answer E.
Later, understood that the problem was so easy...just plug and play !!
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Re: The positive integers x, y, and z are such that x is a [#permalink]
24 Feb 2012, 10:06
if we plug and play, why can't we test X = 1? then y/n..
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Re: The positive integers x, y, and z are such that x is a [#permalink]
24 Feb 2012, 10:46
The positive integers x, y, and z are such that x is a factor of y and y is a factor of z. Is z even?
1) xz is even
2) y is even.
Please explain. thanks.[/quote]
Ans. let us take any 3 numbers, say x=3,y=18,z=54,
or x=2,y=4,z=20
1)if xz is even then it means that either x or z is even,say that x is even, now there is no even number which is a factor of odd number, so z is definitely even, now if x is odd as in the above case, still then we can point out that z is even.
2)if y is even then it is clear that z will be even.
Thus this question could be answered by any of the two questions.
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if x,y,z are positive integers such that x is a factor of y and y is a factor of Z. Is Z even?
I XZ is even
II y is even
How is the OA D?
According to me A is NS
if xz is even it means atleast 1 is even so z may be even or odd.. pl explain
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Re: The positive integers x, y, and z are such that x is a [#permalink]
27 Feb 2012, 05:20
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dchow23 wrote: if we plug and play, why can't we test X = 1? then y/n.. Plug in method would be far more painful for this question (and most other questions in my opinion). Think how you would go about it: Checking whether stmnt 1 is enough: xz is even If x = 1, y = 1 and z = 2 (so that xz is even), then z is even. If x = 2, y = 2 and z = 4, z is again even. Then you start thinking if you can take some values such that xz is even but z is not... Now you start using logic... Wouldn't you say it is far better to use logic in the first place itself?
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Re: The positive integers x, y, and z are such that x is a [#permalink]
29 Feb 2012, 13:29
I think you are right
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Re: The positive integers x, y, and z are such that x is a [#permalink]
22 Jan 2013, 22:49
amitgovin wrote: The positive integers x, y, and z are such that x is a factor of y and y is a factor of z. Is z even?
(1) xz is even
(2) y is even.
What is given? z = y*Ny = x*R1. xz = 2*IIf x is even, then z is even since z = x*RIf z is even, then z is even. SUFFICIENT! 2. y = 2*I ==> z = 2*I*N Definitely EVEN SUFFICIENT! Answer: D
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Re: The positive integers x, y, and z are such that x is a
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22 Jan 2013, 22:49
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