BTGModeratorVI wrote: ↑Wed Dec 16, 2020 12:33 pm
When integer a is divided by 4 the remainder is 2, and when integer b is divided by 5 the remainder is 1. How many integers between 20 and 29, inclusive, CANNOT be the sum a + b?
A. Zero
B. One
C. Two
D. Three
E. Four
Answer:
A
Source: Veritas Prep
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.
------NOW ONTO THE QUESTION----------------------------
When integer a is divided by 4 the remainder is 2
So, the possible values of a are:
2, 6, 10, 14, 18, 22, 26,....
When integer b is divided by 5 the remainder is 1
So, the possible values of b are:
1, 6, 11, 16, 21, 26, 31,....
How many integers between 20 and 29, inclusive, CANNOT be the sum a + b?
Let's see which sums we CAN get:
20 =
14 +
6
21 =
10 +
11
22 =
6 +
16
23 =
2 +
21
24 =
18 +
6
25 =
14 +
11
26 =
10 +
16
27 =
26 +
1
28 =
22 +
6
29 =
18 +
11
We can get ALL of the sums.
Answer: A
