If X and Y are positive integers , is y odd ? (1) : GMAT Data Sufficiency (DS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

It is currently 08 Dec 2016, 10:13
GMAT Club Tests

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.

Close

Request Expert Reply

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If X and Y are positive integers , is y odd ? (1)

  post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Manager
Manager
avatar
Joined: 25 Dec 2010
Posts: 84
Followers: 0

Kudos [?]: 78 [0], given: 2

If X and Y are positive integers , is y odd ? (1) [#permalink]

Show Tags

New post 02 Oct 2011, 14:02
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

26% (03:17) correct 74% (02:38) wrong based on 35 sessions

HideShow timer Statistics

If X and Y are positive integers , is y odd ?

(1) \((y+2)!\)/ \(x!\) is odd integer
(2) \((y+2)!\)/ \(x!\) is greater than 2

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-and-y-are-positive-integers-is-y-odd-128602.html
[Reveal] Spoiler: OA

Last edited by shashankp27 on 04 Oct 2011, 10:53, edited 1 time in total.
1 KUDOS received
Math Forum Moderator
avatar
Joined: 20 Dec 2010
Posts: 2021
Followers: 162

Kudos [?]: 1670 [1] , given: 376

Re: If X and Y are positive integers , is y odd ? (1) [#permalink]

Show Tags

New post 03 Oct 2011, 02:24
1
This post received
KUDOS
shashankp27 wrote:
If X and Y are positive integers , is y odd ?

(1) \((y+2)!\)/ \(x!\) is odd integer
(2) \((y+2)!\)/ \(x!\) is greater than 2


1)
x=4; y=2
x=3; y=1
Not Sufficient.

2)
x=1; y=1
x=1; y=2
Not Sufficient.

Combining both;
y = odd integer greater than 0;
x = y+1
Sufficient.

Ans: "C"
_________________

~fluke

GMAT Club Premium Membership - big benefits and savings

BSchool Forum Moderator
User avatar
Joined: 12 Aug 2015
Posts: 1524
Followers: 33

Kudos [?]: 276 [0], given: 365

GMAT ToolKit User CAT Tests
If X and Y are positive integers , is y odd ? (1) [#permalink]

Show Tags

New post 20 Nov 2016, 09:27
This is a great Question.
Testing our knowledge on factorial theory.

So we are given that both x and y are integers
And we need to get whether or not y is odd

Lets see
Statement 1
(y+2)!/x! => odd
99!/99!=> 1 => odd => y is odd
98!/98!=1=> odd=> y is even
Hence using test cases we can say that this statement is insufficient.
Lets look at statement 2
(y+2)!/x! is greater than 2
hmm
101!/2! is greater than 2=> y is 99 which is odd
100!/2! is also greater than 2=> y is 98 which is even
Hence insufficient
Combing the two statements
(y+2)!/x! to be a odd number >2
101!/100!=> y=99=> odd
100!/99!=> notes this is not odd
Hmm
Intersting
Here we know that every other number in the factorial series is even number.
so if y will be even then y+2 will be even too and no matter what value of x we take => (y+2)!/x! will always be even (constraints two the combining the two statements)
Hence y must be odd
Hence C

This Solution is pretty messed up for my liking.
I think Using test cases really helps in this one. Doesn't it ;)
_________________

Give me a hell yeah ...!!!!!

Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 35912
Followers: 6853

Kudos [?]: 90051 [1] , given: 10402

Re: If X and Y are positive integers , is y odd ? (1) [#permalink]

Show Tags

New post 20 Nov 2016, 09:32
1
This post received
KUDOS
Expert's post
If x and y are positive integers is y odd?

(1) (y+2)!/x! = odd. Notice that \(\frac{(y+2)!}{x!}=odd\) can happen only in two cases:

A. \((y+2)!=x!\) in this case \(\frac{(y+2)!}{x!}=1=odd\). For this case \(y\) can be even: \(y=2=even\) and \(x=4\): \(\frac{(y+2)!}{x!}=\frac{24}{24}=1=odd\);

B. \(y=odd\) and \(x=y+1\), in this case \(\frac{(y+2)!}{(y+1)!}=y+2=odd\). For example, \(y=1=odd\) and \(x=y+1=2\): \(\frac{(y+2)!}{x!}=\frac{3!}{2!}=3=odd\) (basically all the cases like: 3!/2!, 5!/4!, 7!/6!, ... --> y+2=odd, 3, 5, 7, ... --> y=odd, 1, 3, 5, ...).

Not sufficient.

(2) (y+2)!/x! is greater than 2. Clearly insufficient: consider \(y=1=odd\) and \(x=2\) OR \(y=2=even\) and \(x=1\).

(1)+(2) From (2) we cannot have case A, hence we have case B, which means \(y=odd\). Sufficient.

Answer: C.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-and-y-are-positive-integers-is-y-odd-128602.html
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

SVP
SVP
User avatar
Joined: 17 Jul 2014
Posts: 2088
Location: United States (IL)
Concentration: Finance, Economics
Schools: Stanford '19
GMAT 1: 550 Q39 V27
GMAT 2: 560 Q42 V26
GMAT 3: 560 Q43 V24
GMAT 4: 650 Q49 V30
WE: General Management (Transportation)
Followers: 18

Kudos [?]: 248 [0], given: 124

GMAT ToolKit User Premium Member Reviews Badge
Re: If X and Y are positive integers , is y odd ? (1) [#permalink]

Show Tags

New post 20 Nov 2016, 09:49
shashankp27 wrote:
If X and Y are positive integers , is y odd ?

(1) \((y+2)!\)/ \(x!\) is odd integer
(2) \((y+2)!\)/ \(x!\) is greater than 2

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-and-y-are-positive-integers-is-y-odd-128602.html



took me some time to test some additional values for x and y
1.
y=1, x=2 -> 1*2*3/1*2 = 3 - odd
y=2, x=4 -> 1*2*3*4/1*2*3*4 = 1 - odd
2 different options - not sufficient.

2.
y=1, x=2 -> 1*2*3/1*2 = 3 > 2
y=2, x=1 -> 1*2*3*4/1 = 24 > 2
2 outcomes - not sufficient.

1+2
must be odd, and greater than 2.
y=1, x=2
y=3, x=4
y=5, x=6

in all cases, y is odd.

C is the answer.
Re: If X and Y are positive integers , is y odd ? (1)   [#permalink] 20 Nov 2016, 09:49
    Similar topics Author Replies Last post
Similar
Topics:
6 Experts publish their posts in the topic If x and y are positive integers and (x + y)^2 is an odd integer, is x Bunuel 2 11 Apr 2016, 03:01
46 Experts publish their posts in the topic If x and y are positive integers is y odd? devinawilliam83 22 04 Mar 2012, 22:42
26 Experts publish their posts in the topic If x, y and z are positive integers, is x - y odd? Baten80 12 09 Mar 2011, 10:29
If x is a positive even integer, is y odd? (1) 2y + x is TheGmatTutor 5 19 Apr 2010, 14:10
213 Experts publish their posts in the topic If p, x, and y are positive integers, y is odd, and p = x^2 netcaesar 27 14 Aug 2009, 11:49
Display posts from previous: Sort by

If X and Y are positive integers , is y odd ? (1)

  post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.