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

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

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New post 09 May 2018, 01:36
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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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New post 09 May 2018, 02:12
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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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If j and k are even integers and j < k, which of the following equals  [#permalink]

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New post 18 Aug 2018, 11:12
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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If j and k are even integers and j < k, which of the following equals  [#permalink]

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New post 19 Aug 2018, 08:42
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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

Answer A
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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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New post 19 Aug 2018, 08:56
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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

So answer is A
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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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New post 23 Aug 2018, 02:10
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.
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If j and k are even integers and j < k, which of the following equals  [#permalink]

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New post 23 Aug 2018, 10:05
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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
-- Your answer is 5*
The set {4, 6, 8, 10, 12} has 5 even integers
-- Find the answer that matches your answer of 5

Hope that helps. :-)

*There are 5 even integers that are greater than J and smaller than k.
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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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New post 23 Aug 2018, 23:38
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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New post 26 Aug 2018, 19:13
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.

Answer: A
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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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New post 09 Dec 2018, 15:09
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
-- Your answer is 5*
The set {4, 6, 8, 10, 12} has 5 even integers
-- Find the answer that matches your answer of 5

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?
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Re: If j and k are even integers and j < k, which of the following equals   [#permalink] 09 Dec 2018, 15:09
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