gmat prep 1

[navalpike]

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,

[georgeung]

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.

[tim0thy]

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