NEW HERE? LEARN MORE
closeclose
Last visit was: 23 Apr 2024, 21:28 It is currently 23 Apr 2024, 21:28
Decision Tracker
My Rewards
New posts
New comers' posts

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

If x < y < z and y - x > 5, where x is an even integer and y and z are

SORT BY:
Date
Kudos
 1   2   
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
eybrj2
Manager
Manager
Joined: 31 Oct 2011
Posts: 201
Own Kudos [?]: 7793 [116]
Given Kudos: 18
Send PM
If x < y < z and y - x > 5, where x is an even integer and y and z are [#permalink] New post   28 Mar 2012, 02:00
11
Kudos
105
Bookmarks
00:00
A
B
C
D
E

Difficulty:

35% (medium)

Question Stats:

70% (01:49) correct 30% (01:52) wrong based on 2677 sessions
Hide Show timer Statistics
If x < y < z and y - x > 5, where x is an even integer and y and z are odd integers, what is the least possible value of z - x?

A. 6
B. 7
C. 8
D. 9
E. 10

PS25302.01
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14816
Own Kudos [?]: 64887 [20]
Given Kudos: 426
Location: Pune, India
Send PM
Re: If x < y < z and y - x > 5, where x is an even integer and y and z are [#permalink] New post   02 Jun 2017, 09:07
10
Kudos
10
Bookmarks
Expert Reply
eybrj2 wrote:
If x < y < z and y-x > 5, where x is an even integer and y and z are odd integers, what is the least possible value of z - x?

A. 6
B. 7
C. 8
D. 9
E. 10



Think about it this way: x < y < z
Difference between y and x is more than 5 so it is at least 6. But x is even and y is odd so their difference would be odd. Hence the diff between them will be at least 7.
Now z is greater than y by at least 2 (since z is odd too), hence diff between x and z is at least 9.

Answer (D)
avatar
Abhii46
Manager
Manager
Joined: 12 Mar 2012
Posts: 66
Own Kudos [?]: 523 [12]
Given Kudos: 22
Location: India
Concentration: Technology, Strategy
Schools: ISB '15 HKUST '16 Kelley '16 NUS '15 Duke '16
GMAT 1: 710 Q49 V36
GPA: 3.2
WE:Information Technology (Computer Software)
Send PM
Re: If x < y < z and y - x > 5, where x is an even integer and y and z are [#permalink] New post   28 Mar 2012, 02:24
7
Kudos
5
Bookmarks
y-x is >5. y is odd and x is even then y-x will be odd. Lowest possible value of y-x is 7.
For lowest possible value of z-x, y and z should be close, it means y and z are consecutive odd integers or z = y + 2.
Hence z-x = y + 2 - x = 7 + 2 = 9.
General Discussion
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92883
Own Kudos [?]: 618624 [4]
Given Kudos: 81563
Send PM
CAT Tests Forum Quiz Mode
Re: If x < y < z and y - x > 5, where x is an even integer and y and z are [#permalink] New post   28 Mar 2012, 02:26
2
Kudos
2
Bookmarks
Expert Reply
eybrj2 wrote:
If x < y < z and y-x > 5, where x is an even integer and y and z are odd integers, what is the least possible value of z - x?

A. 6
B. 7
C. 8
D. 9
E. 10


We want to minimize \(z-x\), so we need to maximize \(x\).

Say \(z=11=odd\), then max value of \(y\) will be 9 (as \(y\) is also odd). Now, since \(y-5>x\) --> \(9-5>x\) --> \(4>x\), then max value of \(x\) is 2 (as \(x\) is even).

Hence, the least possible value of \(z-x\) is 11-2=9.

Answer: D.
avatar
palsays
Intern
Intern
Joined: 24 Feb 2010
Posts: 7
Own Kudos [?]: 19 [6]
Given Kudos: 0
Send PM
Re: If x < y < z and y - x > 5, where x is an even integer and y and z are [#permalink] New post   02 Aug 2012, 04:48
4
Kudos
2
Bookmarks
If x < y < z and y-x > 5, where x is an even integer and y and z are odd integers, what is the least possible value of z - x?

A. 6
B. 7
C. 8
D. 9
E. 10

Y is odd and X is even, so (y - x) has to be odd. ( Y - X ) > 5 means ( Y - X ) can have a value of 7.

Y - X = 7; Y = X + 7

Main equation will become,
X < X + 7 < Z

Subtract X from all,

0 < 7 < Z - X

Since Z is odd and X is even, (Z - X) has to be odd.

As (Z - X) > 7, the least possible value of Z-X will be 9. ANSWER.


- Ravender Singh
User avatar
greatps24
Manager
Manager
Joined: 22 Nov 2010
Posts: 202
Own Kudos [?]: 497 [0]
Given Kudos: 75
Location: India
GMAT 1: 670 Q49 V33
WE:Consulting (Telecommunications)
Send PM
Re: If x < y < z and y - x > 5, where x is an even integer and y and z are [#permalink] New post   04 Aug 2012, 21:52
eybrj2 wrote:
If x < y < z and y-x > 5, where x is an even integer and y and z are odd integers, what is the least possible value of z - x?

A. 6
B. 7
C. 8
D. 9
E. 10


Z-x will be odd. therefore, option A, C, E is eliminated.

y-x> 5, if x= 2 then Y> 7 (8, 9 etc). so minimum value from z-x is 9
avatar
maddyboiler
Intern
Intern
Joined: 31 Oct 2012
Posts: 20
Own Kudos [?]: 52 [0]
Given Kudos: 4
Send PM
Re: If x < y < z and y - x > 5, where x is an even integer and y and z are [#permalink] New post   19 Dec 2012, 01:27
I did it like this and i am getting 7 as the answer. Kindly tell me where i went wrong.

Given
x<y<z
y-x>5

From the first equation i subtracted x so 0<y-x<z-x
From the second equation multiply by (-1) so -y+x<-5
adding the above 2 i got 0<z-x-5 ie z-x>5
We now that z-x is odd so the next odd number is 7.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92883
Own Kudos [?]: 618624 [0]
Given Kudos: 81563
Send PM
CAT Tests Forum Quiz Mode
Re: If x < y < z and y - x > 5, where x is an even integer and y and z are [#permalink] New post   19 Dec 2012, 03:54
Expert Reply
maddyboiler wrote:
I did it like this and i am getting 7 as the answer. Kindly tell me where i went wrong.

Given
x<y<z
y-x>5

From the first equation i subtracted x so 0<y-x<z-x
From the second equation multiply by (-1) so -y+x<-5
adding the above 2 i got 0<z-x-5 ie z-x>5
We now that z-x is odd so the next odd number is 7.


You got z-x>5 but we also have y-x>5, so the least value of y-x is 7 and since z>y then the least value of z-x is 9.
avatar
Levry
Intern
Intern
Joined: 08 Nov 2012
Posts: 3
Own Kudos [?]: 7 [0]
Given Kudos: 0
Send PM
Re: If x < y < z and y - x > 5, where x is an even integer and y and z are [#permalink] New post   20 Dec 2012, 12:30
We have:
1) x<y<z
2) y-x>5
3) x=2k (x is an even number)
4) y=2n+1 (y is an odd number)
5) z=2p+1 (z is an odd number)
6) z-x=? least value

z-x=2p+1-2k=2p-2k+1=2(p-k)+1 - that means that z-x must be an ODD number. We can eliminate answer choices A, C and E
we are asked to find the least value, so we have to pick the least numbers
since y is odd and x is even, y-x must be odd. since y-x>5, the least value for y-x must be 7, the least value for x must be 2, and, thus, the least possible value for y must be 9 (y-2=7, y=9)
2<9<z, since z is odd, the least possible value for z is 11
z-x=11-2=9

Answer D
User avatar
sdas
Senior Manager
Senior Manager
Joined: 23 Mar 2011
Posts: 365
Own Kudos [?]: 637 [0]
Given Kudos: 59
Location: India
Schools: Rotman '16 Ivey '15 Queens'16 INSEAD Jan '16
GPA: 2.5
WE:Operations (Hospitality and Tourism)
Send PM
Re: If x < y < z and y - x > 5, where x is an even integer and y and z are [#permalink] New post   23 Apr 2013, 07:33
Acer86 wrote:
If x < y < z and y - x > 5, where x is an even integer and y and z are odd integers, what is the least possible value of z – x ?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10


The answer i am getting is 7..thought original answer is something else...can someone help me out :(


Question asks least possible value, thus we can substitute by least possible numbers to get to answer

A, C and E are out since they are even

Left with B and E

y-x>5 which means least value of y-x=7 (since y is odd and x is even, result will be odd)
Work back: y= 5 (least value) x= -2 (least value). thus y-x = 5 - (-2) = 7 (least possible odd integer greater than 5)

Since z> y, thus least possible value of z = 7
Therefore, z-x = 7 - (-2) = 9

Correct choice D
avatar
sayansarkar
Intern
Intern
Joined: 28 Jul 2013
Posts: 48
Own Kudos [?]: 100 [0]
Given Kudos: 37
Location: India
Concentration: Marketing, Strategy
GPA: 3.62
WE:Engineering (Manufacturing)
Send PM
Re: If x < y < z and y - x > 5, where x is an even integer and y and z are [#permalink] New post   28 Mar 2014, 01:46
ACE are out as they are even. z = odd and x is even therefore Z-X is odd. out of B or D we need to see that we have to get the minimum value of z-x so we have to minimize z and maximize x. Hence z-x is 9
User avatar
L
Abhishek009
Board of Directors
Joined: 11 Jun 2011
Status:QA & VA Forum Moderator
Posts: 6072
Own Kudos [?]: 4689 [0]
Given Kudos: 463
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Send PM
GMAT ToolKit User
Re: If x < y < z and y - x > 5, where x is an even integer and y and z are [#permalink] New post   25 Nov 2015, 01:38
eybrj2 wrote:
If x < y < z and y-x > 5, where x is an even integer and y and z are odd integers, what is the least possible value of z - x?


From where x is an even integer & least possible value of z - x?

we can have x < y as 2 < 7 , where y - x = 5

From x < y < z and y and z are odd integers

We have x < y < z = 2 < 7 < 9

So, least possible value of z - x? = 9 - 2 => 7
User avatar
D
stonecold
Alum
Joined: 12 Aug 2015
Posts: 2282
Own Kudos [?]: 3124 [0]
Given Kudos: 893
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Send PM
GMAT ToolKit User
Re: If x < y < z and y - x > 5, where x is an even integer and y and z are [#permalink] New post   08 Mar 2016, 07:35
eybrj2 wrote:
If x < y < z and y-x > 5, where x is an even integer and y and z are odd integers, what is the least possible value of z - x?

A. 6
B. 7
C. 8
D. 9
E. 10


here let y be 13 => then x will be 8 atleast and z will be 15 atleast => 9 is the difference
thus D .
avatar
mehraumang
Intern
Intern
Joined: 21 Jan 2017
Posts: 2
Own Kudos [?]: [0]
Given Kudos: 0
Send PM
Re: If x < y < z and y - x > 5, where x is an even integer and y and z are [#permalink] New post   02 Jun 2017, 11:38
Since y-x>5; let us assume x to be -4 (even no); such that we get the least value of y.
Hence y has to be either 1 or 3, but since y=1 give y-x=5, this. Ant be right. Thus we can conclude y to be 3
Therefore next available odd integer is z=5
Z-x = 5-(-4)=9


Sent from my iPhone using GMAT Club Forum
avatar
S
AD2GMAT
Manager
Manager
Joined: 30 Jul 2014
Status:MBA Completed
Affiliations: IIM
Posts: 91
Own Kudos [?]: 97 [0]
Given Kudos: 107
Send PM
Reviews Badge
Re: If x < y < z and y - x > 5, where x is an even integer and y and z are [#permalink] New post   04 Sep 2017, 02:40
x=0; y=5; z=7 - if we take this set of values, then all the conditions satisfy and the answer becomes 7.
Where did I go wrong?
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14816
Own Kudos [?]: 64887 [1]
Given Kudos: 426
Location: Pune, India
Send PM
Re: If x < y < z and y - x > 5, where x is an even integer and y and z are [#permalink] New post   04 Sep 2017, 04:33
1
Kudos
Expert Reply
DAakash7 wrote:
x=0; y=5; z=7 - if we take this set of values, then all the conditions satisfy and the answer becomes 7.
Where did I go wrong?


y - x needs to be greater than 5.
If x = 0, y = 5, then y - x = 5

So this set of values does not satisfy the conditions.
User avatar
B
gps5441
Manager
Manager
Joined: 04 May 2014
Posts: 114
Own Kudos [?]: 72 [0]
Given Kudos: 126
Location: India
WE:Sales (Mutual Funds and Brokerage)
Send PM
Re: If x < y < z and y - x > 5, where x is an even integer and y and z are [#permalink] New post   23 Oct 2017, 05:11
Easy one. Not sure if it is a 700 level question.
Given x < y < z and y-x > 5 and x is even and y&z are odd.
y-x>5. Now y is odd and x is even, therefore, Y can be 7, 9, 11.... and x is even and can be 0,2,4...
let us plug in a set of values
7-0>5
9-0>5
9-2>5
One more condition mentioned is z>y and is odd therefore z can be 9, 11, 13....
we now have
0<7<9 and z-x=9-0=9
2<9<11 and z-x=11-2=9 Answer D
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18753
Own Kudos [?]: 22042 [1]
Given Kudos: 283
Location: United States (CA)
Send PM
Re: If x < y < z and y - x > 5, where x is an even integer and y and z are [#permalink] New post   23 Jan 2020, 11:36
1
Kudos
Expert Reply
eybrj2 wrote:
If x < y < z and y - x > 5, where x is an even integer and y and z are odd integers, what is the least possible value of z - x?

A. 6
B. 7
C. 8
D. 9
E. 10

PS25302.01


Since y < z and y and z are odd integers, the smallest value that z can be, in terms of y, is z = y + 2.


We know that y - x > 5, so we might think that the minimum difference between y and x would be 6. However, this is impossible. Since x is even and y is odd, their difference cannot be an even number (because even – odd = odd). Thus, we see that the smallest difference between even number x and odd number y is not 6, but rather it is 7. So we have y - x = 7.

Therefore, the smallest difference between z and x is:

z - x = (y + 2) - x = (y - x) + 2 = 7 + 2 = 9.

Answer: D
avatar
B
babloorudra
Intern
Intern
Joined: 26 Jun 2019
Posts: 13
Own Kudos [?]: 5 [1]
Given Kudos: 9
Send PM
Re: If x < y < z and y - x > 5, where x is an even integer and y and z are [#permalink] New post   30 May 2020, 01:25
1
Kudos
eybrj2 wrote:
If x < y < z and y - x > 5, where x is an even integer and y and z are odd integers, what is the least possible value of z - x?

A. 6
B. 7
C. 8
D. 9
E. 10

PS25302.01

Please correct me if my process is wrong:

x= even , Y & Z are Odd. Z-X has to be Odd. y>x+5. So Y has to be 7 & or 7+ (considering smallest even value for x,i.e 0). To obtain the least value of Z-x, Z has to be reduced and X has to be maximised. Since Z > Y, Min value for Z is 9. thus 9-0= 9.
User avatar
P
Pritishd
UNC Kenan Flagler Moderator
Joined: 18 Jul 2015
Posts: 238
Own Kudos [?]: 247 [0]
Given Kudos: 120
GMAT 1: 530 Q43 V20
WE:Analyst (Consumer Products)
Send PM
GMAT ToolKit User
Re: If x < y < z and y - x > 5, where x is an even integer and y and z are [#permalink] New post   14 Aug 2020, 11:44
eybrj2 wrote:
If x < y < z and y - x > 5, where x is an even integer and y and z are odd integers, what is the least possible value of z - x?

A. 6
B. 7
C. 8
D. 9
E. 10
PS25302.01


1. \(x\) = even, \(y\) = odd and \(z\) = odd
2. \(x\), \(y\) and \(z\) are integers
3. Subtracting \(x\) in \(x < y < z\) yields \(0 < y - x < z - x\) (Why? because we are asked to find the value of \(z - x\))
4. Re-arranging \(y - x > 5\) to \(y > x + 5\)
5. Least value that \(x\) can take is \(0\)
6. Substitute in 4 and we get that the least value of \(y - x\) will be \(7\)
7. Substitute \(y - x\) in 3 to get \(0 < 7 < z - x\)
8. Now z (odd) - x (even) will be odd so the smallest odd \(>7\) is \(9\) (Why? because we are asked for the least value)
9. \(0 < y - x < z - x\) is \(0 < 7 < 9\)

Ans D
GMAT Club Bot
gmatclubot
Re: If x < y < z and y - x > 5, where x is an even integer and y and z are [#permalink]
14 Aug 2020, 11:44
 1   2   
Moderators:
Bunuel
Math Expert
92883 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions