Respuesta :
The answer is C, 2240.
Explanation from the book makes more sense now that I've thought about it a bit more.
Let ABCD be your four digits; D has to be odd since the four-digit number is odd (5 odd digits from the sequence). A has 8 options (1 thru 9, but one of the unit is reserved for digit D); B has 8 options aswell (0 thru 9, again one digit is reserved for digit D); C has 7 options (0 thru 9; one digit accounted for D and two A and B); D has 5 options since it must be odd.
8*8*7*5 = 2240
Explanation from the book makes more sense now that I've thought about it a bit more.
Let ABCD be your four digits; D has to be odd since the four-digit number is odd (5 odd digits from the sequence). A has 8 options (1 thru 9, but one of the unit is reserved for digit D); B has 8 options aswell (0 thru 9, again one digit is reserved for digit D); C has 7 options (0 thru 9; one digit accounted for D and two A and B); D has 5 options since it must be odd.
8*8*7*5 = 2240
We want to use the given information to find a 4-digit number.
We will get the number: 8,875
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A general 4-digit number can be written as:
a*1,000 + b*100 + c*10 + d
Where a, b, c, and d are whole numbers between [0, 9].
We also know that:
"The thousands digit (a) and the hundreds digit (b) are the same"
a = b.
"The sum of all 4 digits is 28"
a + b + c + d = 28
"The 4-digit number is an odd multiple of 5"
All the multiples of 5 end with a 0 or a 5, this is an odd one, so it must end with a 5, then we know that:
d = 5
"Two of the digits are even".
Ok, now let's write the equations that we found
a = b
a + b + c + d = 28
d = 5
Because of the last statement, only two digits are even, and we have that a is equal to b, the two even numbers must be these two, then we know that:
a is even.
And from the first equation, we can rewrite the second one as:
a + a + c + d = 28
Using the third equation and replacing it here, we have:
a + a + c + 5 = 28
2*a + c = 23
Now we can try to input different values of a in the equation, and see what value of c we get:
if a = 2, then:
2*2 + c = 23
4 + c = 23
c = 23 - 4 = 19
But c can be, at max, 9, then we can discard this.
Now let's try with a larger value for a, this time a = 8.
2*8 + c = 23
16 + c = 23
c = 23 - 16 = 7
c = 7
This is correct, then we can conclude that:
- a = 8
- b = 8
- c = 7
- d = 5
Then the 4-digit number is:
8,875
If you want to learn more, you can read:
https://brainly.com/question/13163346
