Topic : Number-Remainder
1.
2.
from: category_eng

1.Mathematical Writing
k=12q+3 or use any number for k such as 12
Why don't u plug in the k into each statement?

(1)2k=2(12q+3)=12*2q+6
(2)6k=6(12q+3)=12*6q+18
(3)4k+6=4(12q+3)+6=12*4q+18

Ans: E

2.Mathematical Writing
What is the tens digit of 237? What is the remainder when u divide 237 by 100? What is the remainder when u divide 237 by 110?
(1)the remainder show the tens digit of inger x
(2)the remainder can't show the tens digit of inger x

Ans: A

1.
Use a number
It works for any prime number greater than 3!!
2.
Guess
It's like a sequence problem. See the position of w. r,g,w,b,y, r,g,w,b,y, r
3.
The remainder is always less than the divider 7.
4.
X can be expressed as x=y*q+9 (y>9)
1. B
Understanding
It works for any prime number greater than 3!!
I will use the prime number 5.
5^2=25 so that we can see the remainder is 1 because 25=12*2+1.
2. 23
Understanding
It's like a sequence problem. See the position of w. r,g,w,b,y, r,g,w,b,y, r
We can express the the position of w as a number 5k+3

3, 8, 13, 18,...
3. B
Understanding
The remainder is always less than the divider 7.
The remainders are less than 7.
(1) The range only tells u that the difference between biggest and smallest.
(2) If the seven numbers are consecutive, the remainder should be 0,1,2,3,4,5,6 so that we can find the sum.
4. B
Mathematical Writing
X can be expressed as x=y*q+9 (y>9)
I will use the property of integer and y>9 to solve the question.
x/y= q+9/y = 96.12
Here, 9/y is less than 1 so that 9/y=.12
Therefore, y =9/.12 =75