swerve wrote:How many two-digit numbers are there whose remainder when divided by 10 is 1, and whose remainder when divided by 6 is 5?
A. 3
B. 4
C. 5
D. 6
E. 7
IMPORTANT: When it comes to remainders, we have a nice rule that says:
If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.
Let's start with the second piece of information...
The remainder is 5 when the number is divided by 6
So, the possible values are: 5, 11, 17, 23, 29, 35, 41, 47, 53, 59, 65, 71, 77, 83, 89, 95,... (we'll stop here, since the questions specifies that the number is a 2-digit number)
The remainder is 1 when the number is divided by 10
So, the possible values are: 1, 11, 21, 31,...
Notice this this basically tells us that the number has a UNITS DIGIT of 1
So, go back to examine the first set of possible values: {5,
11, 17, 23, 29, 35,
41, 47, 53, 59, 65,
71, 77, 83, 89, 95}
3 values have a UNITS DIGIT of 1
So, there are 3 values that satisfy both conditions.
Answer: A
Cheers,
Brent
