Is z even?

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Wed Apr 08, 2009 4:32 am

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) x z is even.

(2) y is even.

OA D

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
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Source: Beat The GMAT — Data Sufficiency | Wed Apr 08, 2009 4:32 am

mals24: Legendary Member; Posts: 683; Joined: Tue Jul 22, 2008 1:58 pmFollowed by: 2 members; Location: Dubai; Thanked: 73 times

by mals24 » Wed Apr 08, 2009 5:18 am

Given: x is a factor of y; y is a factor of z

St 1: x.z is even

2 cases: either x is even or z is even

case 1: x is even
X is a factor of Y and X being an even number when multiplied with another number gives an even product.
So Y is even.
Y is a factor of Z. So Z is also even.

case 2: z is even
In both cases Z is even...Suff

St 2: y is even
Y is a factor of Z, so Z is also even...Suff
[spoiler]
Answer is D[/spoiler]

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srn: Senior | Next Rank: 100 Posts; Posts: 32; Joined: Thu Feb 05, 2009 7:35 pm; Thanked: 2 times

by srn » Wed Apr 08, 2009 8:29 pm

I could not get it. Could you plz tell where I am wrong?

Given: x is a factor of y; y is a factor of z i.e y/x and z/y are integers.

1. x.z is even
The cases possible are
a. x is even z is even
b. x is odd z is even
c. x is even z is odd
If x is even, y is even and hence z should be even.
But what if x is odd, y can be odd or even..eg: 15/3 or 12/3. In that case we can't say that z is even.

2. y is even , hence z should be even.

Hence I go with B.

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cubicle_bound_misfit: Master | Next Rank: 500 Posts; Posts: 246; Joined: Mon May 19, 2008 7:34 am; Location: Texaco Gas Station; Thanked: 7 times

by cubicle_bound_misfit » Wed Apr 08, 2009 8:37 pm

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) x z is even.

(2) y is even.

Given,

Y = xK
z=yJ=xKJ

(1) XZ is even means either one of them should be even or both even

if x is even then y is even then z is even
if z is even well...

Sufficient

(2) if Y is evn then z has to be even.
Hence D.

Cubicle Bound Misfit

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sumanr84: Legendary Member; Posts: 758; Joined: Sat Aug 29, 2009 9:32 pmFollowed by: 2 members; Location: Bangalore,India; Thanked: 67 times

by sumanr84 » Wed Jul 14, 2010 9:36 am

Beauty of GMATPrep..simple but tricky..

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Wed Jul 14, 2010 10:17 pm

srn wrote:I could not get it. Could you plz tell where I am wrong?

Given: x is a factor of y; y is a factor of z i.e y/x and z/y are integers.

1. x.z is even
The cases possible are
a. x is even z is even
b. x is odd z is even
c. x is even z is odd
If x is even, y is even and hence z should be even.
But what if x is odd, y can be odd or even..eg: 15/3 or 12/3. In that case we can't say that z is even.

2. y is even , hence z should be even.

Hence I go with B.

With x is a factor of y; y is a factor of z; x is obviously a factor of z. If x z is even, z is even irrespective of what the positive integers x was. Statement 1 is hence, SUFFICIENT.

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Thu Jul 15, 2010 1:16 pm

sanju09 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) x z is even.

(2) y is even.

One of the most common mistakes people make in attacking DS questions is rushing to the statements too quickly. By taking the time to think about the question, you make working with the statements much easier. Hence:

Step 1 of the Kaplan Method for DS: Analyze the Question Stem

If x is a factor of y and y is a factor of z, then if x is even, y and z will both be even; if y is even, z will be even. So, if any of the 3 are even, we'll get a yes answer. Accordingly, let's rephrase the question:

Is at least one of the integers x, y and z even?

(1) xz is even.

The only way to get an even product from integers is to include an even integer. Accordingly, at least one of x and z is even: sufficient.

(2) y is even.

At least one of x, y and z is even: sufficient.

Each statement is sufficient alone, choose (D).

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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