brain teaser =(?

Question

When the digits of a two-digit number are reversed, the new number is 9 more than the original number, and the sum of the digits of the original number is 11. what is the original number? show me how you got the answer too.

Answer 1

56

5+6=11

65-56=9

Answer 2

Let the original digits be a and b, where a and b are both integers between 0 and 9 inclusive. This number is equal to 10a + b.
So a + b = 11, or b + a = 11.
When you reverse the digits, the new number is 10b + a.
So, since the difference between the two numbers is 9, this tells you that
(10b + a) - (10a + b) = 9, or
9b - 9a = 9, or
b - a = 1.
So, now, setting this up as a pair of easy simultaneous equations, you get
b + a = 11
b - a = 1
So 2b = 12, so b = 6.
Since a + b = 11, a = 5.
(Note that if a & b are integers between 0 & 9 inclusive, then the difference between a number, and the number with the digits reversed is always a multiple of nine.)

Answer 3

Let xy represent the number where x stands for the first digit and y stands for the second digit.

Since the sum of the digits of the original number is 11,
we get,
x + y = 11

then we enumerate all possible answers for the above equation
x y
2 9
3 8
4 7
5 6
6 5
7 4
8 3
9 2

From the statement "When the digits of a two-digit number are reversed, the new number is 9 more than the original number", we can say that the reserve of the number is close to the original value.

Looking back at the enumerated numbers we pick a number nd its reverse having the closest value.
So we get,
56 and 65.

Basing again from the statement "When the digits of a two-digit number are reversed, the new number is 9 more than the original number" we can conclude that the new number is greater than the original number so we substitute our number to the statement and see if it is true.
65 = 56 + 9?
65 = 65

therefore the original number is 56.

Answer 4

Let n be this mystery number. Also, let x be the digit in the 10s place, and y be the digit in the 1s place. Then

n = 10x + y

When the digits are reversed, the new number is 9 more than the original number. Therefore,

10y + x = n + 9

Since the sum of the digits of the original number is 11,
x + y = 11.

Three equations, three unknowns:

n = 10x + y
10y + x = n + 9
x + y = 11.

Let's change the form of these equations making it easy to solve.

10x + y - n = 0
x + 10y - n = 9
x + y = 11

Let's try this by elimination. I'm going to subtract equations #2, and #3..

10y - n - y = 9 - 11
9y - n = -2

Now, I'm going to subtract the first equation with 10 times the second equation; i.e I want to subtract these equations.

10x + y - n = 0
10x + 100y - 10n = 90

This will give us

-99y + 9n = -90, which reduces into
11y - n = 10

So now we have these two equations:
9y - n = -2
11y - n = 10

Let's now subtract these two equations; this will give us

-2y = -12; therefore
y = 6

Substituting y = 6 into
9y - n = -2, we get
9(6) - n = -2
54 - n = -2
-n = -56
n = 56

Therefore, since we declare our number n to be 56, that is the answer.

Let's check:

"When the digits of a two-digit number are reversed"...

56 reversed is 65

"The new number is 9 more than the original number."

65 is definitely 9 more than 56.

Answer 5

After viewing all the answers,

The conclusion is

1) If a two digit number is reversed and added the sum will be always 11 times
the sum of the two digits involved.

2) If a two digit number is reversed and subtracted the difference will be always 9 times the difference between the two digits.

In the problem, the second one is taken.
9 (x- y) = 9 and (x+y) = 11.

x =5 and y= 6.

Answer 6

The original number is 56.

65 - 56 = 9

When you reverse two digits of a number the difference is a multiple of 9. If you want the difference to be one times nine, then the digits need to differ by one. They also have to add up to eleven. So the equation for the digits is:

x + (x + 1) = 11
2x + 1 = 11
2x = 10
x = 5
x + 1 = 6

So the two digits are 5 and 6 and the original number is 56.
The original number starts with the smaller of the two digits because when you reverse them, the new number is bigger.

Answer 7

56 and 65. Since it is a 2 digit number, all I did was write out all of the numbers that add up to 11. 92, 83, 74, 65, 56, 47, 38, 29. When you look at the two middle numbers 65 and 56, they are 9 digits away from each other.

So the first answer is 56 and when you add 9 to 56, you get 64 which is your second answer. Good Luck!!

Answer 8

let
x=first digit
y=second digit

since y is the second digit its value is multiplied by ten and y is to one
now if the y becomes the first digit the value is 9 more than the original then
10x+y=9+10y+x
then the sum of the digit is 11
then x+y=11
solving for a variable to subtitute the derive equation to the first equation will give the value for a digit
x=11-y subtituting this to the fist equation will give
10(11-y)+y=9+10y+(11-y)
110-10y+y=9+10y+11-y
110-9y=20+9y
transposing y to the right
110-20=18y
90=18y
5=y using this value to get x will yield
x+y=11
x+5=11
x=6
then your original number is 56

Answer 9

the whole question is a common sense question.. you just got to think of two numbers reverest that are 9 digits apart.. so first i thought of 12 and 21 but they dont add up to 11 .. so i took two numbers that add up to 11 and i got 5 & 6


56 is the original number : 5+6 =11

65 is the new number b/c 56+9 = 65 .. & b/c reversed it equals to 56..

kk hope i was help.

Answer 10

5+6=11 65-56=9 and there you have it