When an integer is divided by 5 the remainder is 3. What is the remainder when 4 times that integer is divided by 5?
ans is 2
5x+3 is the integer, the new equation will be: (5x+3)4/5
Remainder 34=12, 12/5 = 2, with 2 as remainder. so the answer is 2
I just plugged in a number. Took about 5 seconds to use x = 1. That makes I = 8. Then, multiply 8*4/5 = 32/5 = 6 remainder 2. Not very elegant but it works and you can clearly see the remainder.
The tricky part of this problem, at least for me, would be that using nice and neat algebra can trip you up. In the original equation, I = 5x + 3, the constant and the remainder are the same value: 3. In the new equation, 4/5I = 4/5(5x+3), the constant is 12/5, or 2.2, or 2 R2. So the remainder is NOT the same thing as the constant. Also, many will unthinkingly start with something like I/5 = x+3 which will start you off on the wrong foot.
Step 1: Plug in a number that works for the integer (8)
Step 2: Since 8 is the integer, multiply it by 4 to get the new integer and you get 32.
Step 3: Divide 32 by 5 and you get 6 remainder 2.
Step 4: Since the remainder is 2, the answer is 2.
An alternative way to do this would be to use algebra (set the integer to 5x+3), but there’s no need when you can plug in a number that fits the description of the integer given.
If you have 3 left after dividing a number by 5, then you have 4*3 = 12 left after dividing four of that number by 5. Then that 12 can be divided by 5 with 2 left over.
This question was posted in November. I’m guessing he has his answer, or no longer cares.
Math test occur every year, mathematical approaches to solutions don’t change, people read these forums for years and might get value from reading them. People still learn from Brahmagupta’s solutions from 1000 years ago.