72 is the original number
72 - 27 = 45
(7+2)*(7-2) = 9*5 = 45
Here's how to do it via algebra:
Choose x as ten's & y as the one's digit of your number.
So your original number is 10x+y
When you reverse the digits of the number the new number (10y+x) is 45 less than the original so:
10y+x =10x+y-45
10y-10y+x-x =10x-x+y-10y-45+45 (rearrange)
9x-9y=45 (you can simplify by dividing by 9)
x-y =5 [1st equation]
Next the sum of the digits times the difference of the digits is 45 so we have this equation:
(x+y)*(x-y)=45 [2nd equation]
Now we have 2 equations with 2 unknowns. From the first equation : (x-y)= 5 we can substitute that value into the 2nd equation, so:
(x+y)*(5)=45
(x+y) =9 [3rd equation]
Now using the 3rd equation and the 1st equation we can solve for x & y.
x-y= 5
x+y=9
--------------- (add the 2 equations)
2x =14
x= 7
Substitute 7 into either equation above to solve for y.
(7) + y=9
y= 9 - 7 = 2
So the tens digit is 7 & ones digit is 2 hence 72 is the original number.
Possibility of two digit no whose sum is 17 89 and 98 Reverse of 89 is 98. 98 is 9 less than the original no 89. 89 is original no
Possibility of two digit no whose sum is 10 19,28,37,46,55,64,73,82,91 Now add 54 to each no mentioned above 73,82,91,100,109,118,127,136,145 See after 1st comma 28 and 82 Reverse of 28 is 82. That no 82 is 54 more than the no 28. So 28 is the original
If a number An consisting of n consecutive digits in ascending order is subtracted from the number An' obtained by reversing the digits of An, then the difference is always a constant. This constant is termed as the 'Unique number' Un as reported by me earlier in. For example, a 3-digit number 345 if subtracted from its reverse 543, yields a difference of 198. Thus U3 = 198. Another 3-digit number, say, 678 if subtracted from its reverse 876 will also yield the same difference, that is, 198. Thus for any number consisting of 3 consecutive digits, the Unique number U3 is always 198. Similarly for a number consisting of 4 consecutive digits, the Unique number U4 = 3087.
34.
Possibility of two digit no whose sum is 13 49,58,67,76,85,94 Now add 27 to each no mentioned above 76,85,94,103,112,121 See after first comma 58 and 85. Reverse of 58 is 85. That 85 is 27 more than the original no 58. 58 is
whats the answer please??
38
Reverse the digits then check of the new number is the same as the original number.
Possibility of two digit no whose sum is 17 89 and 98 Reverse of 89 is 98. 98 is 9 less than the original no 89. 89 is original no
Possibility of two digit no whose sum is 10 19,28,37,46,55,64,73,82,91 Now add 54 to each no mentioned above 73,82,91,100,109,118,127,136,145 See after 1st comma 28 and 82 Reverse of 28 is 82. That no 82 is 54 more than the no 28. So 28 is the original
2178 x 4 = 8712
If a number An consisting of n consecutive digits in ascending order is subtracted from the number An' obtained by reversing the digits of An, then the difference is always a constant. This constant is termed as the 'Unique number' Un as reported by me earlier in. For example, a 3-digit number 345 if subtracted from its reverse 543, yields a difference of 198. Thus U3 = 198. Another 3-digit number, say, 678 if subtracted from its reverse 876 will also yield the same difference, that is, 198. Thus for any number consisting of 3 consecutive digits, the Unique number U3 is always 198. Similarly for a number consisting of 4 consecutive digits, the Unique number U4 = 3087.
There isn't one. The only two digit numbers whose sum of digits is 12 are: 39, 48, 57, 66. (I didn't include 75, 84, or 93 since interchanging their digits and subtracting from the original number will be a negative result.) None of the four remaining numbers will exceed the original by 25. 66 won't work since the difference will be zero. Using 39, the new number (93) will exceed the original by 54; using 48 the difference will be 36; and using 57 the difference will be 18
The most efficient method is to reverse the digits in the number and then check if the reversed number is equal to the original number. In C, we can implement this as follows (using long-hand notation for clarity). Note the use of base (defaulting to base 10) so that we can check values in other bases. bool is_palindrome (unsigned num, unsigned base = 10) { // local variables unsigned rev, digit, digits; // copy the input number digits = num; // initialise the accumulator rev = 0; // repeat while there are digits while (digits) { // extract the low-order digit using modulo (%) operator digit = digit % base; // shift the accumulated digits (if any) one position to the left rev = rev * base; // add on the new digit rev = rev + digit; // shift the remaining digits one position to the right digits = digits / base; } // end while // return true if the number and its reverse are equal return num == rev; }
Since the sum of the digits is divisible by 3, the original number is also divisible by 3.Since the sum of the digits is divisible by 3, the original number is also divisible by 3.Since the sum of the digits is divisible by 3, the original number is also divisible by 3.Since the sum of the digits is divisible by 3, the original number is also divisible by 3.
34.
Possibility of two digit no whose sum is 11 Are 29,38,47,56,65,74,83,92 Subract 45 to each no mentioned above -16,-7,2,11,20,29,38,47 See after 6th comma 83 and 38 Reverse of 83 is 38. The no 38 is 45 less than 83. Original no is=83