It is currently 19 Feb 2018, 07:37

### 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 m is an even integer, v is an odd integer, and m > v> 0, which of

Author Message
TAGS:

### Hide Tags

Board of Directors
Joined: 01 Sep 2010
Posts: 3472
If m is an even integer, v is an odd integer, and m > v> 0, which of [#permalink]

### Show Tags

24 Jul 2017, 12:05
Top Contributor
8
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

70% (01:14) correct 30% (01:15) wrong based on 419 sessions

### HideShow timer Statistics

If m is an even integer, v is an odd integer, and m > v > 0, which of the following represents the number of even integers less than m and greater than v ?

A. $$\frac{m-v}{2} -1$$

B. $$\frac{m-v-1}{2}$$

C. $$\frac{m-v}{2}$$

D. $$m-v-1$$

E. $$m-v$$
[Reveal] Spoiler: OA

_________________
VP
Joined: 26 Mar 2013
Posts: 1427
If m is an even integer, v is an odd integer, and m > v> 0, which of [#permalink]

### Show Tags

24 Jul 2017, 14:27
1
KUDOS
1
This post was
BOOKMARKED
carcass wrote:
If m is an even integer, v is an odd integer, and m > v > 0, which of the following represents the number of even integers less than m and greater than v ?

A. $$\frac{m-v}{2} -1$$

B. $$\frac{m-v-1}{2}$$

C. $$\frac{m-v}{2}$$

D. $$m-v-1$$

E. $$m-v$$

Let m = 10 & v = 1...........There are 4 Even number less than 10 and greater than 1

A. $$\frac{10-1}{2} -1$$= Fraction number....Eliminate

B. $$\frac{10-1-1}{2}$$ = 4.........................Keep

C. $$\frac{10-1}{2}$$ = Fraction...................Eliminate

D. $$10-1-1$$ = 8........................................Eliminate

E. $$10-1$$=9.............................................Eliminate

Intern
Joined: 06 Feb 2016
Posts: 48
Location: Poland
Concentration: Finance, Accounting
GMAT 1: 730 Q49 V41
GPA: 3.5
Re: If m is an even integer, v is an odd integer, and m > v> 0, which of [#permalink]

### Show Tags

26 Jul 2017, 01:10
The fastest way is plugging in some numbers.

Can someone show how to solve the problem algebraically?
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2179
Location: United States (CA)
Re: If m is an even integer, v is an odd integer, and m > v> 0, which of [#permalink]

### Show Tags

26 Jul 2017, 15:15
1
KUDOS
Expert's post
carcass wrote:
If m is an even integer, v is an odd integer, and m > v > 0, which of the following represents the number of even integers less than m and greater than v ?

A. $$\frac{m-v}{2} -1$$

B. $$\frac{m-v-1}{2}$$

C. $$\frac{m-v}{2}$$

D. $$m-v-1$$

E. $$m-v$$

We can let m = 6 and v = 5. Since there are no (or zero) even integers less than m but greater than v, we see that the answer can be either B, (m - v - 1)/2, or D, m - v - 1, since either choice will produce 0 when we substitute m = 6 and v = 5.

Now, let’s let m = 8 and v = 5. Since there is 1 even integer (namely, 6) less than m but greater than v, we see that the answer must be choice B, since (8 - 5 - 1)/2 = 1 whereas choice D will yield 8 - 5 - 1 = 2. Thus, the correct answer choice must be B.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Manager
Joined: 13 Apr 2017
Posts: 87
Location: India
GMAT 1: 660 Q40 V41
GPA: 3.4
WE: Engineering (Energy and Utilities)
Re: If m is an even integer, v is an odd integer, and m > v> 0, which of [#permalink]

### Show Tags

27 Jul 2017, 00:28
Devbek wrote:
The fastest way is plugging in some numbers.

Can someone show how to solve the problem algebraically?

Hi Devbek,
I'll try to explain.

Number of even numbers between 2 different even numbers (eg, a,b) can be given by ((a-b)/2)+1 (1 is added to include the first even number in the series)
In the current question we need to find number of even numbers "greater than v" and "less than m".
The even number after v(which is odd) is v+1 and the even number before m(which is even) is m-2. (This step is done to exclude both v and m from the total number of even integers)
Hence the number of even numbers between v and m (excluding v and m) should be ((m-2-v-1)/2) + 1) (1 added to include the number v+1)
Upon solving you will get (m-v-1)/2

Hope you got it.
Intern
Joined: 06 Feb 2016
Posts: 48
Location: Poland
Concentration: Finance, Accounting
GMAT 1: 730 Q49 V41
GPA: 3.5
Re: If m is an even integer, v is an odd integer, and m > v> 0, which of [#permalink]

### Show Tags

27 Jul 2017, 02:06
Dkingdom wrote:
Devbek wrote:
The fastest way is plugging in some numbers.

Can someone show how to solve the problem algebraically?

Hi Devbek,
I'll try to explain.

Number of even numbers between 2 different even numbers (eg, a,b) can be given by ((a-b)/2)+1 (1 is added to include the first even number in the series)
In the current question we need to find number of even numbers "greater than v" and "less than m".
The even number after v(which is odd) is v+1 and the even number before m(which is even) is m-2. (This step is done to exclude both v and m from the total number of even integers)
Hence the number of even numbers between v and m (excluding v and m) should be ((m-2-v-1)/2) + 1) (1 added to include the number v+1)
Upon solving you will get (m-v-1)/2

Hope you got it.

Still confusing, but thanks anyway
Manager
Joined: 13 Apr 2017
Posts: 87
Location: India
GMAT 1: 660 Q40 V41
GPA: 3.4
WE: Engineering (Energy and Utilities)
Re: If m is an even integer, v is an odd integer, and m > v> 0, which of [#permalink]

### Show Tags

27 Jul 2017, 02:18
1
KUDOS
Devbek wrote:
Dkingdom wrote:
Devbek wrote:
The fastest way is plugging in some numbers.

Can someone show how to solve the problem algebraically?

Hi Devbek,
I'll try to explain.

Number of even numbers between 2 different even numbers (eg, a,b) can be given by ((a-b)/2)+1 (1 is added to include the first even number in the series)
In the current question we need to find number of even numbers "greater than v" and "less than m".
The even number after v(which is odd) is v+1 and the even number before m(which is even) is m-2. (This step is done to exclude both v and m from the total number of even integers)
Hence the number of even numbers between v and m (excluding v and m) should be ((m-2-v-1)/2) + 1) (1 added to include the number v+1)
Upon solving you will get (m-v-1)/2

Hope you got it.

Still confusing, but thanks anyway

Formula to find count of even numbers in a consecutive series between two numbers is ((a-b)/2) + 1. In this formula both a and b are included in the count.
let m = 10 (even), v = 3(odd)
What the question is asking : find the number of even numbers greater than v (3) and less than m (10).
Breaking the question down :1) We need to exclude m and v from the total count of even numbers. v obviously is out because it is odd. To exclude m we need to use an even number less than m.
Hence in order to apply the above stated formula we will use v+1 (4) and m-2 (8). (Since we need to find only the count of even numbers that's why it is easier to keep the starting and ending numbers as even digits.
Applying the formula : ((8-4)/2)+1) = 3 (i.e. 4,6,8) Remember :numbers are more than 3 and less than 10 and even.
The above equation can be written as ((m-2-v-1)/2)+1 = (m-v-1)/2
Manager
Joined: 21 Jun 2017
Posts: 77
Re: If m is an even integer, v is an odd integer, and m > v> 0, which of [#permalink]

### Show Tags

10 Sep 2017, 03:52
Devbek wrote:
The fastest way is plugging in some numbers.

Can someone show how to solve the problem algebraically?

You are better off just plugging in numbers, come the real test.
Intern
Joined: 20 Feb 2017
Posts: 3
Re: If m is an even integer, v is an odd integer, and m > v> 0, which of [#permalink]

### Show Tags

18 Sep 2017, 09:04
1
KUDOS
m is even and v is odd -> (m-v) is odd -> (m-v)/2 is not an interger => elimate A, C imidiately

SOLVE: Between m and v, we have [(m-1) - (v+1) + 1] = (m-v-1) numbers, include both odd and even -> the number of even is half of (m-v-1)
Intern
Joined: 20 Sep 2016
Posts: 26
Re: If m is an even integer, v is an odd integer, and m > v> 0, which of [#permalink]

### Show Tags

15 Oct 2017, 17:34
Hi,
when we use number picking for method for this problem, it does not give a consistent result. For ex. if m=2; v=1 then non of the answers stand true.

please let me know what am i missing here?
Intern
Joined: 20 Feb 2017
Posts: 3
If m is an even integer, v is an odd integer, and m > v> 0, which of [#permalink]

### Show Tags

15 Oct 2017, 19:54
If m is an even integer, v is an odd integer, and m > v > 0, which of the following represents the number of even integers less than m and greater than v?
We are looking for even integers x that m< x <v -> these three (m, v, x) are integers that means (m - v) cannot less than or equal to 1 (x cannot be an integer if it happens). So, m = 2 and v=1 are not the right numbers to pick.
Hope it helps!
Intern
Joined: 26 Oct 2017
Posts: 1
Re: If m is an even integer, v is an odd integer, and m > v> 0, which of [#permalink]

### Show Tags

01 Dec 2017, 05:04
Hi all,
I still don't understand.
M>v>0 and we have to find a number x which is a even integer and m>x>v>0.
Because x is a even integer, x can only be (B) or (D).
If m=8, v=3:
(m-v-1)/2=2
m-v-1= 4
2<v=3; 4>v=3
So (B) is wrong.
If m=10, v =3
(m-v-1)/2=3 is an odd integer
m-v-1=6
So (B) is wrong
VP
Joined: 22 May 2016
Posts: 1329
If m is an even integer, v is an odd integer, and m > v> 0, which of [#permalink]

### Show Tags

02 Dec 2017, 12:41
1
KUDOS
carcass wrote:
If m is an even integer, v is an odd integer, and m > v > 0, which of the following represents the number of even integers less than m and greater than v ?

A. $$\frac{m-v}{2} -1$$

B. $$\frac{m-v-1}{2}$$

C. $$\frac{m-v}{2}$$

D. $$m-v-1$$

E. $$m-v$$

Greyfield wrote:
Hi all,
I still don't understand.
M>v>0 and we have to find a number x which is a even integer and m>x>v>0.
Because x is a even integer, x can only be (B) or (D).
If m=8, v=3:
(m-v-1)/2=2
m-v-1= 4
2<v=3; 4>v=3
So (B) is wrong.
If m=10, v =3
(m-v-1)/2=3 is an odd integer
m-v-1=6
So (B) is wrong

Greyfield , it looks as if you are interpreting one little part incorrectly. The wording is terse. And to use $$x$$ can be confusing here.

We are looking for a specially defined kind of number, defined by the prompt.

The answers are supposed to tell us how many of those specially defined numbers there are -- not the actual values of those specially defined numbers.

Try rewriting this:
. . .which of the following represents the number of even integers less than m and greater than v

to THIS:

. . .which of the following represents how many even integers there are which are less than m and greater than v

You wrote
Quote:
find a number x which is a even integer and m>x>v>0.
Because x is a even integer, x can only be (B) or (D).

Mmm... no. $$x$$ is how many even integers there are.

Let's use your numbers, m = 8, v = 3

Answer B) $$\frac{(m-v-1)}{2} = 2$$

On the number line, between 8 and 3, there are two(2) even numbers: 4 and 6. Both are less than m=8 and greater than v=3. Answer B does not tell you "4 and 6." You have to discern that yourself.

Your numbers: m = 10, v = 3
Between 10 and 3, there are, just as you calculated from B, three (3) even integers: 8, 6, and 4. All are less than 10 and greater than 3.

Once you have figured out how many of those special integers there are, you cannot "go again" and plug your choices into (B) to find out which even integers they are.

Hope that helps.
_________________

At the still point, there the dance is. -- T.S. Eliot
Formerly genxer123

Intern
Joined: 26 Nov 2017
Posts: 1
Re: If m is an even integer, v is an odd integer, and m > v> 0, which of [#permalink]

### Show Tags

10 Dec 2017, 18:22
Hi,

Can you explain why are you adding 1 to v and why are you subtracting 2 to m please?

Hi Devbek,
I'll try to explain.

Number of even numbers between 2 different even numbers (eg, a,b) can be given by ((a-b)/2)+1 (1 is added to include the first even number in the series)
In the current question we need to find number of even numbers "greater than v" and "less than m".
The even number after v(which is odd) is v+1 and the even number before m(which is even) is m-2. (This step is done to exclude both v and m from the total number of even integers)
Hence the number of even numbers between v and m (excluding v and m) should be ((m-2-v-1)/2) + 1) (1 added to include the number v+1)
Upon solving you will get (m-v-1)/2

Hope you got it.[/quote][/quote]
Intern
Joined: 29 Jul 2017
Posts: 3
Re: If m is an even integer, v is an odd integer, and m > v> 0, which of [#permalink]

### Show Tags

20 Dec 2017, 06:11
Mo2men wrote:
carcass wrote:
If m is an even integer, v is an odd integer, and m > v > 0, which of the following represents the number of even integers less than m and greater than v ?

A. $$\frac{m-v}{2} -1$$

B. $$\frac{m-v-1}{2}$$

C. $$\frac{m-v}{2}$$

D. $$m-v-1$$

E. $$m-v$$

Let m = 10 & v = 1...........There are 4 Even number less than 10 and greater than 1

A. $$\frac{10-1}{2} -1$$= Fraction number....Eliminate

B. $$\frac{10-1-1}{2}$$ = 4.........................Keep

C. $$\frac{10-1}{2}$$ = Fraction...................Eliminate

D. $$10-1-1$$ = 8........................................Eliminate

E. $$10-1$$=9.............................................Eliminate

Hi, I am not really sure why are you canceling out Choice D. I thought the question require us to find an EVEN integer that is LESS than m but GREATER than v? If you use m =10, v=1, isn't 8 fulfill this condition as well? since 8 is an even integer <10 but >1?
Math Expert
Joined: 02 Aug 2009
Posts: 5651
Re: If m is an even integer, v is an odd integer, and m > v> 0, which of [#permalink]

### Show Tags

20 Dec 2017, 06:30
xlgoh1992 wrote:
Mo2men wrote:
carcass wrote:
If m is an even integer, v is an odd integer, and m > v > 0, which of the following represents the number of even integers less than m and greater than v ?

A. $$\frac{m-v}{2} -1$$

B. $$\frac{m-v-1}{2}$$

C. $$\frac{m-v}{2}$$

D. $$m-v-1$$

E. $$m-v$$

Let m = 10 & v = 1...........There are 4 Even number less than 10 and greater than 1

A. $$\frac{10-1}{2} -1$$= Fraction number....Eliminate

B. $$\frac{10-1-1}{2}$$ = 4.........................Keep

C. $$\frac{10-1}{2}$$ = Fraction...................Eliminate

D. $$10-1-1$$ = 8........................................Eliminate

E. $$10-1$$=9.............................................Eliminate

Hi, I am not really sure why are you canceling out Choice D. I thought the question require us to find an EVEN integer that is LESS than m but GREATER than v? If you use m =10, v=1, isn't 8 fulfill this condition as well? since 8 is an even integer <10 but >1?

HI..

we rae looking for NUMBERS of even numbers between v and m..
if v=1 and m=10, even integers are 2,4,6,8.. HOW many 4

so our answer should be 4

8 is ONE of the even integer BUT we are looking for NUMBERS of even integers between v and m
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

BANGALORE/-

Intern
Joined: 25 Jan 2016
Posts: 18
Location: India
GPA: 3.9
WE: Engineering (Consulting)
Re: If m is an even integer, v is an odd integer, and m > v> 0, which of [#permalink]

### Show Tags

11 Jan 2018, 09:50
Bunuel, Sir Can you please help me with this one ; if i am not able to get the answer after plugging the numbers.

Re: If m is an even integer, v is an odd integer, and m > v> 0, which of   [#permalink] 11 Jan 2018, 09:50
Display posts from previous: Sort by