Brain exercise: Quantitative Reasoning A housewife forgot her Bank account PIN Code which is a 5 digit number, but luckily she remembered some hints on how to recall this PIN Code. Here are some of the clues: 1) The first digit is the square of the 2nd. 2) The sum of the 2nd and 3rd is 10. 3) The 4th is equal to the 2nd plus 1. 4) The 3rd and 5th makes 14. 5) The sum of all the digits is 30. What's the PIN Code? #2 3x-2y=3 x+4y=8
Answer:
Therefore, the PIN Code is 819147.
Step-by-step explanation:
To solve this system of equations, we can use substitution or elimination methods. Let's use the substitution method.
First, let's find the values of x and y.
From the second clue, we know that the sum of the 2nd and 3rd digits is 10. So we can write the equation:
x + y = 10
From the fourth clue, we know that the 4th digit is equal to the 2nd digit plus 1. So we can write the equation:
x + 1 = 10
Now, let's solve this equation for x:
x = 10 - 1
x = 9
Now, let's substitute this value of x into the first equation:
9 + y = 10
Now, solve this equation for y:
y = 10 - 9
y = 1
So, we have found the values of x and y. x = 9 and y = 1.
Therefore, the PIN Code is a 5-digit number, so we can combine the digits as follows: 9_1__.
Now, let's use the other clues to find the missing digits.
From the first clue, we know that the first digit is the square of the 2nd. Since the 2nd digit is 9, the first digit is 9 * 9 = 81. So the PIN Code is 81_1__.
From the third clue, we know that the 3rd digit is equal to the 2nd digit plus 1. Since the 2nd digit is 9, the 3rd digit is 9 + 1 = 10. So the PIN Code is 8191__.
From the fourth clue, we know that the 3rd and 5th digits make 14. Since the 3rd digit is 10, the 5th digit is 14 - 10 = 4. So the PIN Code is 81914_.
Finally, from the fifth clue, we know that the sum of all the digits is 30. We have 8 + 1 + 9 + 1 + 4 + _ = 30. Solve for the missing digit:
23 + _ = 30
_ = 7