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# If j and k are even integers and j < k, which of the following equals

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Math Expert
Joined: 02 Sep 2009
Posts: 51218
If j and k are even integers and j < k, which of the following equals  [#permalink]

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09 May 2018, 00:36
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Difficulty:

35% (medium)

Question Stats:

66% (01:11) correct 34% (01:07) wrong based on 203 sessions

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If j and k are even integers and j < k, which of the following equals the number of even integers that are greater than j and less than k ?

A. $$\frac{(k -j -2)}{2}$$

B. $$\frac{(k -j -1)}{2}$$

C. $$\frac{(k -j )}{2}$$

D. $$k -j$$

E. $$k -j -1$$

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Posts: 883
Concentration: Accounting, Finance
GPA: 3.68
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Re: If j and k are even integers and j < k, which of the following equals  [#permalink]

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09 May 2018, 01:12
Bunuel wrote:
If j and k are even integers and j < k, which of the following equals the number of even integers that are greater than j and less than k ?

A. $$\frac{(k -j -2)}{2}$$

B. $$\frac{(k -j -1)}{2}$$

C. $$\frac{(k -j )}{2}$$

D. $$k -j$$

E. $$k -j -1$$

1. k and j are both even integers.
2. j<k

let's assume that j=2 and k=20

so, the even integers that are greater than j and less than k are : 4 6 8 10 12 14 16 18 . In total we have 8 integers.

check option A. this the option that meets our demand.

A) (20-2-2)/2 = 8

someone can take other range of vales such as k= 10 , j=4. or k=16, j= 6.

Thus option A is the best answer.
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Posts: 35
Location: India
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If j and k are even integers and j < k, which of the following equals  [#permalink]

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18 Aug 2018, 10:12
Greater than J less than K means all even numbers in the range except j and k. Hence, minus 2, and even so divided by 2. I realised after clicking the wrong answer.
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Joined: 22 May 2016
Posts: 2211
If j and k are even integers and j < k, which of the following equals  [#permalink]

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19 Aug 2018, 07:42
1
Bunuel wrote:
If j and k are even integers and j < k, which of the following equals the number of even integers that are greater than j and less than k ?

A. $$\frac{(k -j -2)}{2}$$

B. $$\frac{(k -j -1)}{2}$$

C. $$\frac{(k -j )}{2}$$

D. $$k -j$$

E. $$k -j -1$$

Assign values. Let $$j=4$$ and $$k=12$$

4, 6, 8, 10, 12, so
The # of even integers between $$j$$ and $$k$$ = 3

Using $$k=12$$ and $$j=4$$, find the answer that yields $$3$$

Eliminate D and E immediately. Too great.

A. $$\frac{(k -j -2)}{2}=\frac{(12-4-2)}{2}=\frac{6}{2}=3$$ KEEP

B. $$\frac{(k -j -1)}{2}=\frac{(12 -4 -1)}{2}=\frac{7}{2}$$ REJECT

C. $$\frac{(k-j)}{2}=\frac{(12 -4 )}{2}=\frac{8}{2}=4$$ REJECT

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Re: If j and k are even integers and j < k, which of the following equals  [#permalink]

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19 Aug 2018, 07:56
1
lets assume j=2, k=10
there are 3 even integers between j=2 and k=10.
now test each option to get 3.

A) 6/3 = 3
B) 7/2 =not integer
C) 8/2 = 4
D) 10-2 = 8
E) 10-2-1 = 7

_________________

Hasnain Afzal

"When you wanna succeed as bad as you wanna breathe, then you will be successful." -Eric Thomas

Intern
Joined: 25 Feb 2016
Posts: 11
Re: If j and k are even integers and j < k, which of the following equals  [#permalink]

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23 Aug 2018, 01:10
Hey guys

How do I know which values to choose for substitution because I tried j=2 and k=4 and couldn't get the right answer.
Senior SC Moderator
Joined: 22 May 2016
Posts: 2211
If j and k are even integers and j < k, which of the following equals  [#permalink]

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23 Aug 2018, 09:05
1
Bunuel wrote:
If j and k are even integers and j < k, which of the following equals the NUMBER OF [how many] even integers that are greater than j and less than k ?

A. $$\frac{(k -j -2)}{2}$$

B. $$\frac{(k -j -1)}{2}$$

C. $$\frac{(k -j )}{2}$$

D. $$k -j$$

E. $$k -j -1$$

onyx12102 wrote:
Hey guys

How do I know which values to choose for substitution because I tried j=2 and k=4 and couldn't get the right answer.

onyx12102 , whoops! I think you misread the question. Easy mistake. I can't tell which part of the prompt you misread.

See highlight. Meaning: How many other even integers are between one even integer ("$$j$$") and another even integer that is greater than j, i.e. "$$k$$"?

I believe in whatever works. Maybe a number line?

Even integers:
<--(-2)---0---2---4---6---8---10--->

$$j$$ is one of those integers. So too is $$k$$. And k > j

You picked j = 2, k = 4

<-(-2)---0---2---4---6---8---10--->

How many EVEN integers are greater than $$j$$ and less than $$k$$ (between)? None.

So to choose values for j and k:
1) choose something small for j (not 0, tho' it works) and something greater for k;
2) Put some distance between j and k. You need the quantity of OTHER even integers before you get to the answer choices

Try j = 2, k = 14
<--0---2---{4---6---8---10---12}---14-->

WHICH even integers are greater than j and smaller than k
(Identify them): {4, 6, 8, 10, 12}

How many? (Count them.) There are 5
Now plug in.
-- Use k = 14, j = 2
The set {4, 6, 8, 10, 12} has 5 even integers

Hope that helps.

*There are 5 even integers that are greater than J and smaller than k.
Intern
Joined: 25 Feb 2016
Posts: 11
Re: If j and k are even integers and j < k, which of the following equals  [#permalink]

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23 Aug 2018, 22:38
Bunuel

Thank you so much that really helps
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Re: If j and k are even integers and j < k, which of the following equals  [#permalink]

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26 Aug 2018, 18:13
Bunuel wrote:
If j and k are even integers and j < k, which of the following equals the number of even integers that are greater than j and less than k ?

A. $$\frac{(k -j -2)}{2}$$

B. $$\frac{(k -j -1)}{2}$$

C. $$\frac{(k -j )}{2}$$

D. $$k -j$$

E. $$k -j -1$$

We can let j = 0 and k = 4, we see that there is 1 even integer, namely 2, that is greater than j and less than k.

Since (4 - 0 - 2)/2 = 1, answer A is correct.

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Intern
Joined: 14 Feb 2018
Posts: 15
Re: If j and k are even integers and j < k, which of the following equals  [#permalink]

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09 Dec 2018, 14:09
generis wrote:
Bunuel wrote:
If j and k are even integers and j < k, which of the following equals the NUMBER OF [how many] even integers that are greater than j and less than k ?

A. $$\frac{(k -j -2)}{2}$$

B. $$\frac{(k -j -1)}{2}$$

C. $$\frac{(k -j )}{2}$$

D. $$k -j$$

E. $$k -j -1$$

onyx12102 wrote:
Hey guys

How do I know which values to choose for substitution because I tried j=2 and k=4 and couldn't get the right answer.

onyx12102 , whoops! I think you misread the question. Easy mistake. I can't tell which part of the prompt you misread.

See highlight. Meaning: How many other even integers are between one even integer ("$$j$$") and another even integer that is greater than j, i.e. "$$k$$"?

I believe in whatever works. Maybe a number line?

Even integers:
<--(-2)---0---2---4---6---8---10--->

$$j$$ is one of those integers. So too is $$k$$. And k > j

You picked j = 2, k = 4

<-(-2)---0---2---4---6---8---10--->

How many EVEN integers are greater than $$j$$ and less than $$k$$ (between)? None.

So to choose values for j and k:
1) choose something small for j (not 0, tho' it works) and something greater for k;
2) Put some distance between j and k. You need the quantity of OTHER even integers before you get to the answer choices

Try j = 2, k = 14
<--0---2---{4---6---8---10---12}---14-->

WHICH even integers are greater than j and smaller than k
(Identify them): {4, 6, 8, 10, 12}

How many? (Count them.) There are 5
Now plug in.
-- Use k = 14, j = 2
The set {4, 6, 8, 10, 12} has 5 even integers

Hope that helps.

*There are 5 even integers that are greater than J and smaller than k.

I also misread the prompt and chose the wrong numbers to test with. Any suggestions on how to get better at picking smart numbers?
Re: If j and k are even integers and j < k, which of the following equals &nbs [#permalink] 09 Dec 2018, 14:09
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