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?