Question

If x and y are positive integers less than 8, how many distinct values can the expression ( 3x + 7y ) take?

1. 49
2. 28
3. 21
4. 36 

Answer 1

Here x and y can have 7 possible values from 1-7.

Now, if any of the sums happen to be same we will get

3x + 7y = 3a + 7b, 0 < a,b,x,y < 8
3(x-a) = 7(b-y)
Happens only if b-y is a multiple of 3 and x-a is a multiple of 7. So, minimum value of x should be 8 as a is positive. But this is not possible and hence all the sums must be distinct.

The answer is 1. 49

Answer 2

1.49