N is a two-digit positive even integer where the sum of the digits is 3. If none of the digits are 0, what is N?

2 Answers
Jun 3, 2018

Answer:

#12#

Explanation:

If #N# is a two-digit positive number, where the sum of the digits is #3#, the only two possibilities for #N# is:

#12# and #30#

But since none of the digits are #0#, that excludes #30# from being an option, and so the answer is #12#.

Jun 3, 2018

Answer:

12

You can get this quite easily through just thinking about it, but I'll demonstrate an algebraic approach.

Explanation:

If #N# is a two digit number, we can write this as #N=10x+y#, where #x# and #y# are positive non-zero integers less than 10.
Think about it - every 2 digit number is 10 times something (your 10s digit) plus another number.

We also know that #N# is even i.e. it is a multiple of 2. This means that #y# must be equal to #2xx"something"#. If we let this something be another variable #u#, #y=2u#

#:. N=10x+2u#
where #x in NN, 0< x <10 # and #u in NN, 0< u<5#

We know that we are looking for #x+y#, or #x+2u#

#x+2u=3#

We can use a graph to find all the solutions that satisfy our previous limits on x and u.

graph{x+2y=3 [-0.526, 3.319, -0.099, 1.824]}

The only integer solutions in this range are #x=1# and #u=1#

#:. N=10(1)+2(1)#
#N=10+2#
#N=12#