Last visit was: 19 Nov 2025, 17:34 It is currently 19 Nov 2025, 17:34
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
Close
GMAT Club Daily Prep
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
User avatar
Hades
User avatar
Joined: 14 May 2009
Last visit: 13 Aug 2009
Posts: 135
Own Kudos:
90
Given Kudos: 1
Schools:Stanford, Harvard, Berkeley, INSEAD
Posts: 135
Kudos: 90
If Y is a factor of Z , is X even? (1) \frac{X^{3}Z}{Y} + X 03 Jun 2009, 00:24
Kudos
Add Kudos
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
N
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

History

Date
Time
Result
Not Attempted Yet
If \(Y\) is a factor of \(Z\), is \(X\) even?

(1) \(\frac{X^{3}Z}{Y} + X\) is even

(2) \(XY\) is even



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
User avatar
Neochronic
User avatar
Joined: 15 Jan 2008
Last visit: 05 Jul 2010
Posts: 131
Own Kudos:
68
Given Kudos: 3
Posts: 131
Kudos: 68
If Y is a factor of Z , is X even? (1) \frac{X^{3}Z}{Y} + X 03 Jun 2009, 01:30
Kudos
Add Kudos
Bookmarks
Bookmark this Post
E shud be answer..

1, insufficient

as Y is a factor of Z, we know z/y = K, but k can be even or odd..

x(x^2 K + 1) is even.. this is possible with both X is even and odd.
hence inconclusive.

2, talks abt X and Y.. no conclusive infomration abt X.

combined.. they dont give enough informatin abt X.. hence conclusive..
avatar
mjGMAT
avatar
Joined: 27 May 2009
Last visit: 05 Jun 2009
Posts: 3
Own Kudos:
1
Posts: 3
Kudos: 1
If Y is a factor of Z , is X even? (1) \frac{X^{3}Z}{Y} + X 03 Jun 2009, 07:11
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Answer is C

if y is a factor of z, then z = yK, where k is some integer constant.

1. x^3.z/y + x can be written as x^3.yk + x. Both sides of + sign can be EVEN or ODD -> insufficient

2. xy is even. X can odd or even, if y is even -> not sufficient

However, when we combine 1 and 2

x^3.yk + x can be written as x^2.xy.k, which is even since, from condition 2, xy is even.

even + x = even

hence x has to even.

Answer is c.
avatar
pmenon
avatar
Joined: 28 Dec 2005
Last visit: 01 Jul 2009
Posts: 692
Own Kudos:
600
Given Kudos: 2
Posts: 692
Kudos: 600
If Y is a factor of Z , is X even? (1) \frac{X^{3}Z}{Y} + X 03 Jun 2009, 09:28
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I think E for this one.

From stat 2, you know that either x or y can be even. insuff.

From stat 1, you can deduce that both terms have to be either both odd or both even to get an even sum. So case 1 is Z/Y is even, which means that for the sum to be even, X (and therefore X^3) are even as well. Case 2 is Z/Y being odd, then X (and therefore X^3) must be odd as well to make the sum even. X can be even or odd, so insuff.

Together, you know X can be even or odd, as can Y ... if Y is even, then Y/Z can be even or odd (ie 10/2) or even (12/2). Depending on what the quotient is , X can be even or odd
User avatar
Hades
User avatar
Joined: 14 May 2009
Last visit: 13 Aug 2009
Posts: 135
Own Kudos:
90
 [1]
Given Kudos: 1
Schools:Stanford, Harvard, Berkeley, INSEAD
Posts: 135
Kudos: 90
 [1]
If Y is a factor of Z , is X even? (1) \frac{X^{3}Z}{Y} + X 03 Jun 2009, 15:46
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hades
If \(Y\) is a factor of \(Z\), is \(X\) even?

(1) \(\frac{X^{3}Z}{Y} + X\) is even

(2) \(XY\) is even
Show more


Question:\((X\) even\()\)?

(1) \(\frac{X^{3}Z}{Y} + X\) is even

\(\longrightarrow X(\frac{X^{2}Z}{Y} + 1)\) is even

\(\longrightarrow X\) even OR \(\frac{X^{2}Z}{Y} + 1\) even

If \(X\) even then we have a YES, but if \(X\) not even then:

\(\longrightarrow \frac{X^{2}Z}{Y} + 1\) even

\(\longrightarrow \frac{X^{2}Z}{Y}\) odd

\(\longrightarrow \frac{XZ}{Y}\) odd

\(\longrightarrow X odd & \frac{Z}{Y}\) odd

(2) \(XY\) even
\(\longrightarrow (X\) even, \(Y\) odd) or (\(Y\) even, \(X\) odd) or (\(X & Y\) even)

So we have a YES case & a NO case \(\longrightarrow INSUFFICIENT\)

(1&2) Combining

Look at (1) and look at the case \(X odd\). From (2) we know that \(Y even\). But (1) can still be true because \(Z=MY\) where \(M odd\) and \(Y even\), and everything holds.

NO case (X odd)
ie \(X=1\), \(Y=2\), \(Z=6\).
\(XY = 2\) (even-- 2 is satsified)
\(\frac{X^{3}Z}{Y} + X = \frac{1^{3}6}{2} + 1 = \frac{6}{2} + 1 = 3 + 1 = 4\) (even)

YES case (X even)
ie \(X=2\), \(Y=2\), \(Z=6\).
\(XY = 4\) (even-- 2 is satsified)
\(\frac{X^{3}Z}{Y} + X = \frac{2^{3}6}{2} + 2 = \frac{48}{2} + 2 = 24 + 2 = 26\) (even)

YES & NO\(\longrightarrow INSUFFICIENT\)


\(\longrightarrow INSUFFICIENT\)

Final Answer, \(E\).
User avatar
lahoosaher
User avatar
Joined: 16 Jan 2009
Last visit: 20 Apr 2018
Posts: 236
Own Kudos:
1,031
Given Kudos: 16
Concentration: Technology, Marketing
Schools: Ross '16 (D) Tepper '16 (D) McCombs '16 (D) ISB '15 (D) Marshall '16 (WL) McDonough '16 (WL) Goizueta '16 (WL) Kelley '16 (D) Kenan-Flagler '16 (D) Rotman '16 (S)
GMAT 1: 700 Q50 V34
GPA: 3
WE:Sales (Telecommunications)
Schools: Ross '16 (D) Tepper '16 (D) McCombs '16 (D) ISB '15 (D) Marshall '16 (WL) McDonough '16 (WL) Goizueta '16 (WL) Kelley '16 (D) Kenan-Flagler '16 (D) Rotman '16 (S)
GMAT 1: 700 Q50 V34
Posts: 236
Kudos: 1,031
If Y is a factor of Z , is X even? (1) \frac{X^{3}Z}{Y} + X 03 Jun 2009, 16:13
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello mjGMAT,

if
mjGMAT
if y is a factor of z, then z = yK, where k is some integer constant
Show more

z/y=k I think you have used z/y = yk
mjGMAT
x^3.yk + x can be written as x^2.xy.k, which is even since, from condition 2, xy is even.
Show more
User avatar
lahoosaher
User avatar
Joined: 16 Jan 2009
Last visit: 20 Apr 2018
Posts: 236
Own Kudos:
1,031
Given Kudos: 16
Concentration: Technology, Marketing
Schools: Ross '16 (D) Tepper '16 (D) McCombs '16 (D) ISB '15 (D) Marshall '16 (WL) McDonough '16 (WL) Goizueta '16 (WL) Kelley '16 (D) Kenan-Flagler '16 (D) Rotman '16 (S)
GMAT 1: 700 Q50 V34
GPA: 3
WE:Sales (Telecommunications)
Schools: Ross '16 (D) Tepper '16 (D) McCombs '16 (D) ISB '15 (D) Marshall '16 (WL) McDonough '16 (WL) Goizueta '16 (WL) Kelley '16 (D) Kenan-Flagler '16 (D) Rotman '16 (S)
GMAT 1: 700 Q50 V34
Posts: 236
Kudos: 1,031
If Y is a factor of Z , is X even? (1) \frac{X^{3}Z}{Y} + X 03 Jun 2009, 16:16
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Amazing problem and explanation Hades.
+1



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
Moderators:
Bunuel
Math Expert
105390 posts
GMATBusters
GMAT Tutor
1924 posts