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
vto THIS:
...which of the following represents
how many even integers
exist that are less than
m and greater than
vYou 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 > 0I 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.
_________________
Any fool can know. The point is to understand. — Albert Einstein