EUREKA! SEE FULL WORKING & SOLUTION TO OUR TODAYS BRAIN BUSTER MATHEMATICS QUESTION. QUESTION WAS: A boy forgot his pin code which was of 5 digits, but luckily remembered some hints on how to remind that password. Here are those clues: 1. The first digit is the square of the second. 2. The sum of the 2nd and 3rd is 10. 3. The 4th is equal to the 2nd plus 1. 4. 3rd and 5th make 14. 5. The sum of the 5 digit is 30. what is the pin code? ####Got Myschool New Study App Yet? FREE download here: goo.gl/VnDLYD SOLUTION BY MYSCHOOL STAFF: Let the digits be: a, b, c, d, e. 1st statement: a = b^2 2nd statement: b + c = 10 3rd statement: d = b + 1 4th statement: e + c = 14 5th statement: a + b + c + d + e = 30 If we parameterize about b (re-write in terms of b), we have: a = b^2 b = b c = 10 - b d = b + 1 e = 14 - c = 14 - (10 - b) = 14 - 10 + b = b + 4 This implies that, a + b + c + d + e = 30 b^2 + b + (10 - b) + (b + 1) + (b + 4) = 30 b^2 + 10 + 2b + 5 = 30 b^2 + 2b - 15 = 0 (b + 5) (b - 3) = 0 solving the quadratics above; b = -5 and b = 3 Negative values cannot be a pin code, thus b = 3. Therefore, substituting we have; a = b^2 = 3^2 = 9 b = b = 3 c = = 10 - b = 10 - 3 = 7 d = b + 1 = 3 + 1 = 4 e = b + 4 = 3 + 4 = 7 So the pin-code is: 9 - 3 - 7 - 4 - 7 CROSSCHECK/PROOF: a = b^2 ---> OK b + c = 3 + 7 = 10 ---> OK d = b + 1 ==> 4 = 3 + 1 ==> 4 = 4 ----> OK e + c = 14 ==> 7 + 7 = 14 ==> 14 = 14 ----> OK 9 + 3 + 7 + 4 + 7 = 30 ==> 30 = 30 ----> OK Full working/solution provided by Wilfred (a.k.a Ask Wilfred) ####Got Myschool New Study App Yet? FREE download here: goo.gl/VnDLYD |comment| like | share this solution if you like his answer!
Posted on: Sun, 01 Dec 2013 11:11:37 +0000