Data Sufficiency

Is the three digit number “n” less than 550?

1) The product of the digits in “n” is 30.

2.) The sum of the digits in “n” is 10.

OA is C

Please explain your answer. Thanks,

Data 1: I could only find two different answers for it - 2x3x5 and 5x6x1. So I put Insufficient.

Data 2 - I found a couple, 7+3+0, 6+4+0 3+3+4 and 2+3+5. Enough answers for me to realize it is Insufficient.

Then when I did both, I found 2+3+5 is the only one for Data 1 and Data 2 and the numbers could be 532, 235...all under 550. So both are sufficient together.

Another way to look at it is algebraically.

We can model the question as is x + 10y + 100z < 550?
x being the units digit
y being the tens digit
z being the hundreds digit

(1) we are given xyz = 30
Then factors of 30 are: 1,2,3,5,30

choosing some examples:
if z=5, y=3, x=2 then the answer is yes
but if z=6, y=5, x=1 answer is no
Insufficient

(2) we are given x + y + z = 10

choosing some examples:
if z=8, y=1, x=1 answer is yes
but if z=1, y=8, x=1 answer is no
Insufficient

Taking the two together, from (1) the only factors which fit (2) are 5,3,2 therefore (as georgeung said) we know x + 10y + 100z < 550 is true because no matter how you arrange the factors they are always less than 550.
Sufficient

C