If x < y < z and y-x > 5, where x is an even integer and y : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 22 Jan 2017, 20:57

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 31 Oct 2011
Posts: 324
Followers: 3

Kudos [?]: 894 [2] , given: 18

If x < y < z and y-x > 5, where x is an even integer and y [#permalink]

### Show Tags

28 Mar 2012, 01:00
2
KUDOS
6
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

59% (02:11) correct 41% (01:10) wrong based on 244 sessions

### HideShow 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
[Reveal] Spoiler: OA
Manager
Joined: 12 Mar 2012
Posts: 94
Location: India
Concentration: Technology, Strategy
GMAT 1: 710 Q49 V36
GPA: 3.2
WE: Information Technology (Computer Software)
Followers: 9

Kudos [?]: 317 [1] , given: 22

Re: If x < y < z and y-x > 5, where x is an even integer and y [#permalink]

### Show Tags

28 Mar 2012, 01:24
1
KUDOS
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.
Math Expert
Joined: 02 Sep 2009
Posts: 36601
Followers: 7097

Kudos [?]: 93483 [2] , given: 10563

Re: If x < y < z and y-x > 5, where x is an even integer and y [#permalink]

### Show Tags

28 Mar 2012, 01:26
2
KUDOS
Expert's post
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.

_________________
Intern
Joined: 24 Feb 2010
Posts: 11
Followers: 0

Kudos [?]: 9 [0], given: 0

Re: If x < y < z and y-x > 5, where x is an even integer and y [#permalink]

### Show Tags

02 Aug 2012, 03:48
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
Senior Manager
Joined: 22 Nov 2010
Posts: 288
Location: India
GMAT 1: 670 Q49 V33
WE: Consulting (Telecommunications)
Followers: 5

Kudos [?]: 138 [0], given: 75

Re: If x < y < z and y-x > 5, where x is an even integer and y [#permalink]

### Show Tags

04 Aug 2012, 20:52
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
_________________

YOU CAN, IF YOU THINK YOU CAN

Intern
Joined: 31 Oct 2012
Posts: 24
Followers: 0

Kudos [?]: 5 [0], given: 4

Re: If x < y < z and y-x > 5, where x is an even integer and y [#permalink]

### Show Tags

19 Dec 2012, 00:27
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.
Math Expert
Joined: 02 Sep 2009
Posts: 36601
Followers: 7097

Kudos [?]: 93483 [0], given: 10563

Re: If x < y < z and y-x > 5, where x is an even integer and y [#permalink]

### Show Tags

19 Dec 2012, 02:54
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.
_________________
Intern
Joined: 08 Nov 2012
Posts: 3
Followers: 0

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

Re: If x < y < z and y-x > 5, where x is an even integer and y [#permalink]

### Show Tags

20 Dec 2012, 11:30
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

Senior Manager
Joined: 23 Mar 2011
Posts: 473
Location: India
GPA: 2.5
WE: Operations (Hospitality and Tourism)
Followers: 19

Kudos [?]: 215 [0], given: 59

If x < y < z and y - x > 5, where x is an even integer and y and [#permalink]

### Show Tags

23 Apr 2013, 06:33
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
_________________

"When the going gets tough, the tough gets going!"

Bring ON SOME KUDOS MATES+++

-----------------------------

My GMAT journey begins: http://gmatclub.com/forum/my-gmat-journey-begins-122251.html

Manager
Joined: 28 Jul 2013
Posts: 93
Location: India
Concentration: Marketing, Strategy
GPA: 3.62
WE: Engineering (Manufacturing)
Followers: 1

Kudos [?]: 34 [0], given: 37

Re: If x < y < z and y-x > 5, where x is an even integer and y [#permalink]

### Show Tags

28 Mar 2014, 00:46
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
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13508
Followers: 577

Kudos [?]: 163 [0], given: 0

Re: If x < y < z and y-x > 5, where x is an even integer and y [#permalink]

### Show Tags

24 Nov 2015, 09:35
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Math Forum Moderator
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 2306
Location: India
GPA: 3.5
Followers: 94

Kudos [?]: 637 [0], given: 317

If x < y < z and y-x > 5, where x is an even integer and y [#permalink]

### Show Tags

25 Nov 2015, 00:38
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
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 1904
Followers: 49

Kudos [?]: 369 [0], given: 455

Re: If x < y < z and y-x > 5, where x is an even integer and y [#permalink]

### Show Tags

08 Mar 2016, 06:35
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 .
_________________

Mock Test -1 (Integer Properties Basic Quiz) ---> http://gmatclub.com/forum/stonecold-s-mock-test-217160.html#p1676182

Mock Test -2 (Integer Properties Advanced Quiz) --->http://gmatclub.com/forum/stonecold-s-mock-test-217160.html#p1765951

Mock Test -2 (Evens and Odds Basic Quiz) --->http://gmatclub.com/forum/stonecold-s-mock-test-217160.html#p1768023

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

Re: If x < y < z and y-x > 5, where x is an even integer and y   [#permalink] 08 Mar 2016, 06:35
Similar topics Replies Last post
Similar
Topics:
4 The integers v,w,x,y and z are such that 0<v<w<x<y<z. The average of t 3 26 Sep 2016, 05:51
9 If x>0, y<0 and z<0, (|x|+|y|+|z|)^2=? 9 18 Jan 2016, 20:50
11 If y>0>x, and (3+5y)/(x−1) < −7, then which of the following 13 01 Jul 2013, 22:38
5 If x and y are integers such that x<0<y, and z is non 8 24 Jan 2012, 08:49
6 If x < y < z and y-x > 5, where x is an even integer and y a 6 07 Apr 2011, 05:26
Display posts from previous: Sort by