If j and k are even integers and j

Question

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

KSBGC · Answer

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.

dumbodingo · Answer

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.

generis · Answer

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

hasnain3047 · Answer

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

onyx12102 · Answer

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.

generis · 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.

onyx12102 · Answer

Bunuel

Thank you so much that really helps

ScottTargetTestPrep · Answer

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

justgottamakeit1592 · Answer

I also misread the prompt and chose the wrong numbers to test with. Any suggestions on how to get better at picking smart numbers?

HoudaSR · Answer

Picking up numbers here is definitely the quicker method to solve.

But if you want the algebraic solution, here it is:

J is the first term of an arithmetic progression, which has d=2 and k is the last term in this arithmetic progression. We are asked to find the number of terms in this AP minus 2: (n-2).

Using the following formula for an AP: An=A1+ (n-1)d

we get, k=j+ (n-1)x2

Solving for n we get n=(k-j+2)/2.

But we want n-2. 
n-2= (k-j-2)/2

Correct answer is A

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

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