It is currently 20 Oct 2017, 14:52

### 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: 338

Kudos [?]: 1230 [3], given: 18

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

### Show Tags

28 Mar 2012, 02:00
3
KUDOS
11
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

59% (01:10) correct 41% (01:13) wrong based on 381 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

Kudos [?]: 1230 [3], given: 18

Manager
Joined: 12 Mar 2012
Posts: 93

Kudos [?]: 347 [1], given: 22

Location: India
Concentration: Technology, Strategy
GMAT 1: 710 Q49 V36
GPA: 3.2
WE: Information Technology (Computer Software)
Re: If x < y < z and y-x > 5, where x is an even integer and y [#permalink]

### Show Tags

28 Mar 2012, 02:24
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.

Kudos [?]: 347 [1], given: 22

Math Expert
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129029 [2], given: 12187

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

### Show Tags

28 Mar 2012, 02:26
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.

_________________

Kudos [?]: 129029 [2], given: 12187

Intern
Joined: 24 Feb 2010
Posts: 11

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, 04:48
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

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

Senior Manager
Joined: 22 Nov 2010
Posts: 287

Kudos [?]: 174 [0], given: 75

Location: India
GMAT 1: 670 Q49 V33
WE: Consulting (Telecommunications)
Re: If x < y < z and y-x > 5, where x is an even integer and y [#permalink]

### Show Tags

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
_________________

YOU CAN, IF YOU THINK YOU CAN

Kudos [?]: 174 [0], given: 75

Intern
Joined: 31 Oct 2012
Posts: 22

Kudos [?]: 11 [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, 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.

Kudos [?]: 11 [0], given: 4

Math Expert
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129029 [0], given: 12187

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

### Show Tags

19 Dec 2012, 03:54
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.
_________________

Kudos [?]: 129029 [0], given: 12187

Intern
Joined: 08 Nov 2012
Posts: 3

Kudos [?]: 3 [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, 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

Kudos [?]: 3 [0], given: 0

Senior Manager
Joined: 23 Mar 2011
Posts: 461

Kudos [?]: 279 [0], given: 59

Location: India
GPA: 2.5
WE: Operations (Hospitality and Tourism)
If x < y < z and y - x > 5, where x is an even integer and y and [#permalink]

### Show Tags

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
_________________

"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

Kudos [?]: 279 [0], given: 59

Manager
Joined: 28 Jul 2013
Posts: 85

Kudos [?]: 42 [0], given: 37

Location: India
Concentration: Marketing, Strategy
GPA: 3.62
WE: Engineering (Manufacturing)
Re: If x < y < z and y-x > 5, where x is an even integer and y [#permalink]

### Show Tags

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

Kudos [?]: 42 [0], given: 37

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16636

Kudos [?]: 273 [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, 10:35
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.
_________________

Kudos [?]: 273 [0], given: 0

Math Forum Moderator
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3003

Kudos [?]: 1088 [0], given: 325

Location: India
GPA: 3.5
If x < y < z and y-x > 5, where x is an even integer and y [#permalink]

### Show Tags

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
_________________

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 )

Kudos [?]: 1088 [0], given: 325

BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2212

Kudos [?]: 841 [0], given: 595

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

### Show Tags

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 .
_________________

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

Kudos [?]: 841 [0], given: 595

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16636

Kudos [?]: 273 [0], given: 0

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

### Show Tags

02 Jun 2017, 06:34
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.
_________________

Kudos [?]: 273 [0], given: 0

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7676

Kudos [?]: 17369 [0], given: 232

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

### Show Tags

02 Jun 2017, 09:07
Expert's post
1
This post was
BOOKMARKED
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.

_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Kudos [?]: 17369 [0], given: 232 Intern Joined: 21 Jan 2017 Posts: 2 Kudos [?]: [0], given: 0 Re: If x < y < z and y-x > 5, where x is an even integer and y [#permalink] ### Show Tags 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 Kudos [?]: [0], given: 0 Manager Joined: 30 Jul 2014 Posts: 136 Kudos [?]: 11 [0], given: 98 GPA: 3.72 Re: If x < y < z and y-x > 5, where x is an even integer and y [#permalink] ### Show Tags 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? _________________ A lot needs to be learned from all of you. Kudos [?]: 11 [0], given: 98 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7676 Kudos [?]: 17369 [0], given: 232 Location: Pune, India Re: If x < y < z and y-x > 5, where x is an even integer and y [#permalink] ### Show Tags 04 Sep 2017, 04:33 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. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Kudos [?]: 17369 [0], given: 232

Re: If x < y < z and y-x > 5, where x is an even integer and y   [#permalink] 04 Sep 2017, 04:33
Display posts from previous: Sort by