2 votes

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

- 49
- 28
- 21
- 36

2 votes

Best answer

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

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