Require solution (Powerplay problem)

[mafaisal]

1. Two positive numbers are to be selected from a set of 10 different numbers in which half of the numbers are even and half are odd. How many of the possible 45 selections consist of one even and one odd?
a. 5
b. 10
c. 20
d. 23
e. 25

2. A certain money market bank account that had a balance of $48,000 during all of last month earned $360 in interest for the month. At what simple annual interest rate did the account earn interest last month?
a. 7%
b. 7.5%
c. 8%
d. 8.5%
e. 9%

[Curly213]

For the 2 nd question:
360 = 48000 *x*1/12
360 = 4000*x
x = 9/100 = 9 percent
the formula is Interest= Amount * time * Percent ... and for the first ... idk how to answer this kind of question because i think everyone know how to get 45 .. but the way to split the combination in odd or equal or odd and equal... hope that s.o. can solve it!

[Curly213]

For the first question i got 15 just wrote all of the combinations down and counted 15 c`to have one odd and one even .. so i would choose b because i aint seein anything near 15 besides 10 or 20

[jess_84]

Originally Posted by mafaisal

1. Two positive numbers are to be selected from a set of 10 different numbers in which half of the numbers are even and half are odd. How many of the possible 45 selections consist of one even and one odd?
a. 5
b. 10
c. 20
d. 23
e. 25

I think QA would be e.25
Because 5 are even and 5 are odd
so, {5c1 * 5c1}=25
Let see the example,
A={1,2,3,4,5,6,7,8,9,10}
B={2,4,6,8,10}
C={1,3,5,7,9}
so, D={(2,1),(2,3)............(2,9)}=5
{(4,1),(4,3)............(4,9)}=5
{(6,1),(6,3)............(6,9)}=5
...................................=5
.................................. =5
........
25

[mafaisal]

Thanks Curly and Jess.

@Jess I have also get the solution in this way. But in this way, I could not make any relation with " How many of the possible 45 selections consist of one even and one odd" with 25.

[Curly213]

Yep thx jess for providing the second ... and thx mafaisal for posting these questions!

[totymody]

Q-1
Answer is : e (25)

the 45 selection given at the question represents the total possibilities for selecting any 2 numbers from the 10 , and can be calculated as follows:
=10!/(2!)(10-2)! = 45

But we want to select one odd number and one even number,

So if we put the 10 numbers at the following form:
(odd1, odd2, odd3, odd4, odd5, even1, even2, even3, even4, even5)

try to make combinations of one odd number with one even number.
so each odd numbers has 5 combinations:
for odd1 we have:
(odd1,even1),(odd1,even2),(odd1,even3),(odd1,even4 ),(odd1,even5)

the same for each number , so we have 25 possibilities.