number properties,chapter 10 ,#5, page 178

[sowjanyaangara]

5) suppose that M and N are positive 2-digit integers and that N=M+5/2. If M/3 is not an integer,what is the largest possible value of N?

why M is not equal to 98 ,the next maximum value of M after 99. M is not equal to 99 as it is divisible by 3. so 98+5/2= 51.5. But the answer is 51.

Thanks

[tommywallach]

Hey Sowjan,

I'm not quite sure I understand your logic here.

If M = 98:

N = (98 + 5)/2 = 51.5

So M cannot equal 98. We can't use 99 either, because, as you said, it's divisible by 3. So the biggest possible M must be smaller than either of these two numbers.

If M = 97:

N = (97 + 5)/2 = 51

Tada!

-t

[sowjanyaangara]

So N= (98+5)/2 =51.5. 51.5 has decimal value. but the problem stated that M,N is a positive integers. so N cannot equal to 51.5 . Is that right?

[tommywallach]

Hey Sowjan,

Absolutely right. If the problem says one variable must be an integer, than the value of another, interdependent variable cannot be any value that would force the original variable to be a non-integer. In short, M can't be 98, because that would force N to be a non-integer.

-t