GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 24 May 2019, 02:14 ### 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. ### Request Expert Reply # If m is an even integer, v is an odd integer, and m > v> 0, which of

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

### Hide Tags

Board of Directors D
Joined: 01 Sep 2010
Posts: 3390
If m is an even integer, v is an odd integer, and m > v> 0, which of  [#permalink]

### Show Tags

2
Top Contributor
26 00:00

Difficulty:   35% (medium)

Question Stats: 70% (01:41) correct 30% (01:45) wrong based on 836 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. $$m-v$$

_________________
##### Most Helpful Community Reply
SVP  V
Joined: 26 Mar 2013
Posts: 2182
If m is an even integer, v is an odd integer, and m > v> 0, which of  [#permalink]

### Show Tags

4
1
3
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

Answer: B
##### General Discussion
Intern  B
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

The fastest way is plugging in some numbers.

Can someone show how to solve the problem algebraically?
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6228
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

3
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.

Answer: B
_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Manager  B
Joined: 13 Apr 2017
Posts: 82
Location: India
Concentration: General Management, International Business
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

1
1
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  B
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

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  B
Joined: 13 Apr 2017
Posts: 82
Location: India
Concentration: General Management, International Business
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

3
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  B
Joined: 21 Jun 2017
Posts: 83
Re: If m is an even integer, v is an odd integer, and m > v> 0, which of  [#permalink]

### Show Tags

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  B
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

2
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)
=> The answer is B
Intern  B
Joined: 20 Sep 2016
Posts: 24
Re: If m is an even integer, v is an odd integer, and m > v> 0, which of  [#permalink]

### Show Tags

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  B
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

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

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
Please help me to explain these situations. Thank you
Senior SC Moderator V
Joined: 22 May 2016
Posts: 2759
If m is an even integer, v is an odd integer, and m > v> 0, which of  [#permalink]

### Show Tags

3
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 an 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
Please help me to explain these situations. Thank you

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. Not a value.

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.

We need the number of numbers between yet two other numbers on a number line.

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 exist that 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 an even integer, x can only be (B) or (D).

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

If we pick values, in one case, the number of integers will be even.
If we increase m, the number of integers will be odd.
Count how many integers there are between your chosen values.
When you plug in your $$m$$ and $$v$$
Option B will always give you that quantity, that number of integers.

• Let's use the numbers in your quote, m = 8, v = 3

<----(v = 3)-----4-----5-----6-----7-----(m=8)----->

Between the integer 3 and the integer 8, there are two even integers: 4 and 6.
How many even integers?
Two: (1) the number four; and (2) the number six.

The number of even numbers is 2.

Answer B) $$\frac{(m-v-1)}{2}$$
Plug in your numbers:
$$\frac{(8-3-1)}{2}=\frac{4}{2}=2$$
Perfect.

That is, on the number line, between 8 and 3, there are two 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 see that fact yourself.

• Case #2: Your numbers: m = 10, v = 3

<----(v = 3)----4----5----6----7----8-----9-----(m=10>

Between 10 and 3, there are, just as you calculated from B, three 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 "new" choices into (B) to find out which even integers they are.
If you choose different values for the variables, although B's answer or output will change,
it will still match your answer -- your new answer, which has also changed.

v is any odd number. m is any even number. m > v > 0

I could use m = 100 and v = 7. The answer will be B.

The number of numbers will change depending on what you plug in for m and v,
but option B will "spit out" the number of numbers that matches the values you choose.

Hope that helps. _________________
SC Butler has resumed!
Get two SC questions to practice, whose links you can find by date, here.
Intern  B
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

1
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  B
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

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

Answer: B

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 V
Joined: 02 Aug 2009
Posts: 7685
Re: If m is an even integer, v is an odd integer, and m > v> 0, which of  [#permalink]

### Show Tags

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

Answer: B

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
_________________
Intern  B
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

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

Thanks in advance. IIMA, IIMC School Moderator V
Joined: 04 Sep 2016
Posts: 1339
Location: India
WE: Engineering (Other)
If m is an even integer, v is an odd integer, and m > v> 0, which of  [#permalink]

### Show Tags

Bunuel niks18 pushpitkc chetan2u VeritasPrepKarishma

Usually in a PS if I take numbers satisfying the property given in question stem
(here even/odd) I am usually left with only one answer choice. Here as suggested by
ScottTargetTestPrep I had to further narrow down my options from 2 to 1 by taking more
set of numbers. Is there any other time efficient way to come to OA?
_________________
It's the journey that brings us happiness not the destination.

Feeling stressed, you are not alone!!
Math Expert V
Joined: 02 Aug 2009
Posts: 7685
Re: If m is an even integer, v is an odd integer, and m > v> 0, which of  [#permalink]

### Show Tags

1
adkikani wrote:
Bunuel niks18 pushpitkc chetan2u VeritasPrepKarishma

Usually in a PS if I take numbers satisfying the property given in question stem
(here even/odd) I am usually left with only one answer choice. Here as suggested by
ScottTargetTestPrep I had to further narrow down my options from 2 to 1 by taking more
set of numbers. Is there any other time efficient way to come to OA?

to find the number of items between x and y inclusive, it is x-y+1..
say between 2 and 7... 7-2+1=6..... 2,3,4,5,6,7
so if we have consecutive numbers starting with O/E and finishing with E/O... half of them will be odd and half even
so here m is even so m-1 is odd and v is odd so v+1 will be even..
numbers between m-1 and v+1 = m-1-(v+1)+1 = m-1-v-1+1=m-v-1..
half will be even and half odd
so $$\frac{m-v-1}{2}$$
_________________
SVP  V
Joined: 26 Mar 2013
Posts: 2182
Re: If m is an even integer, v is an odd integer, and m > v> 0, which of  [#permalink]

### Show Tags

adkikani wrote:
Bunuel niks18 pushpitkc chetan2u VeritasPrepKarishma

Usually in a PS if I take numbers satisfying the property given in question stem
(here even/odd) I am usually left with only one answer choice. Here as suggested by
ScottTargetTestPrep I had to further narrow down my options from 2 to 1 by taking more
set of numbers. Is there any other time efficient way to come to OA?

Hi adkikani
Actually, this comes with lot of training and number sense. In some questions, picking easy number could lead you with 2-3 potential solutions. So you will try another set to narrow down the the right choice. In my example above, I opened the range of m & v because Scott's first data set most probably will yield number =1 which GMAT test maker know how people will rush to choose small numbers to generate easy numbers.

I hope it helps Re: If m is an even integer, v is an odd integer, and m > v> 0, which of   [#permalink] 02 Aug 2018, 05:01

Go to page    1   2    Next  [ 27 posts ]

Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne 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®.

#### MBA Resources  