i am a two-digit number over 50. when you put me in groups of seven, two are left over. the sum of my digits is 11. what number am i
Two digit numbers over 50 which are 2 more than a multiple of 7:
51, 58, 65, 72, 79, 86, 93
In which of the above numbers do the digits add up to 11?
65
Its 65 !
56
65
group of 7 which is more than 50: 56,63,70 etc.
here 63 if we take then only (63+2) will be 65.
i.e. 65 we take then 2 will be left over.
To find the two-digit number that satisfies the given conditions, we can break down the problem step by step.
Let's assume the unknown two-digit number is represented as "AB," where A is the tens digit and B is the units digit.
1. "I am a two-digit number over 50": According to this clue, A (the tens digit) must be greater than 5 to form a two-digit number over 50.
2. "When you put me in groups of seven, two are left over": This condition implies that the unknown number, AB, must be one less than a multiple of 7.
To satisfy this condition, we can test values of A (greater than 5) until we find a number that is one less than a multiple of 7:
A = 6: 6 is not one less than a multiple of 7.
A = 7: 7 is one less than a multiple of 7, so we continue with this value.
3. "The sum of my digits is 11": The sum of the digits A and B must equal 11.
Since A = 7, we can calculate B by subtracting A from 11:
B = 11 - A = 11 - 7 = 4.
Therefore, the two-digit number that satisfies all the given conditions is 74.