Question

I NEED help with a math problem.

The problem is: If I’m thinking about a number which isn’t larger than 150. If you take away 5, you get a number that’s divisible with 13. If u take away 11 you get a number that’s divisible with 14. Which number am I thinking about?

Answer 1

109

Explanation:

a) x - 5 = 13 x n x = 13n + 5

b) x - 11 = 14 x m x = 14m + 11

13n + 5 = 14m + 11

13n = 14m + 6

n = (14m + 6) / 13 means 14m + 6 is the multiple of 13

14m + 6 could be 13 , 26, 39, 52, 65, 78, 91, 104, 117

if m = 1 , 2 3 4 5 6 7

14m + 6 will be 20 34 48 62 76 90 104

m = 7

n = 8

x = 109

Answer 2

109

Explanation:

You can brute-force this:

Candidate numbers that are divisable by 13 if you take away 5: 18 , 31 , 44 , 57 , 70 , 83 , 96 , 109 , 122 , 135 , 148

Candidate numbers that are divisable by 14 if you take away 11: 25 , 39 , 53 , 67 , 81 , 95 , 109 , 123 , 137

Only 109 is in both lists.