If N is a positive integer, is the...

[BernardK777]

If N is a positive integer, is the units digit of N equal to zero?

1) 14 and 35 are factors of N.

2) N = (2^5)(3^2)(5^7)(7^6)

Here was my thought process:

Statement 1:

I broke down 14 and 35 down into their prime factors and found their LCM.

14 = 2 x 7
35 = 5 x 7

LCM = 2 x 5 x 7

We know N must be divisible by its LCM --> In other words, N must have 2,5,7 as prime factors --> 2 x 5 = 10 whose unit digit is equal to 0 --> Regardless of N's other factors, N's unit digit must be equal to 0 since any other number's units digit multiplied by the unit digit 0 will be 0. --> Sufficient

Eliminate BCE

Statement 2: N has prime factors 2 and 5 (same reasoning as above) --> Sufficient

Eliminate A --> Answer = D

Is my reasoning above correct? Have I successfully proven that if a number has prime factors 2 and 5 it will have a units digit equal to 0?

Thank you for the help!

[RonPurewal]

Your reasoning is OK. You're doing too much thinking for statement 2, though.

For statement 2, you shouldn't be thinking about anything beyond the following:
* That's a single number.
* So, there's exactly one answer.
* If there's only one answer, the statement is sufficient. (The answer is either zero or not. We don't care. The only thing that matters is that we can't get both.)

[RonPurewal]

In other words, if you actually thought you had to DO THINGS with the number in statement 2, then you need to work on clarifying the goals of data sufficiency.

If you see a situation in which there's only one possibility, you should immediately realize the significance (i.e., sufficient every time). And you should be horrified at the thought that someone would actually work that lone possibility out mathematically.

[BernardK777]

Ron,

Got it! Thank you for the help!

[tim]

:)