TheLostOne wrote:
So I understand that divisibility rules are imperative here. That said, I sort of think my strategy for tackling these problems is wrong. It is taking me too long to figure out the prime factors.
Can someone walk me through how they would look at the numbers? For instance:
1.) 9450
2.) 1478
3.) 437
My mind likes to start with trying to divide by 2 if they are even, but maybe that isn't the smartest approach.
Dear Lost One,
I am happy to help with these.
First of all, take comfort --- the GMAT is not likely to expect you to factor strange numbers this large. The would be more likely to give you something like 13500, in which your first step could be factor out 100 so that you are immediately down to a nice three digit number.
Second, here are a few blogs you may find helpful:
http://magoosh.com/gmat/2012/gmat-math-factors/http://magoosh.com/gmat/2012/gmat-divis ... shortcuts/http://magoosh.com/gmat/2012/advanced-n ... -the-gmat/OK, here's what I notice about these number.
the first number --- for any number divisible by 10, start by factoring out the 10
9450 = 945 * 10
Since 45 is divisible by 9, it must be that 945 is divisible by 9. Also, 9 + 4 + 5 = 18, which is divisible by 9, so 945 is divisible by 9.
945 = 900 + 45 = 9*100 + 9*5 = 9*105
105 = 5*21 = 3*5*7
So the whole prime factorization is:
9450 = 945 * 10 = 9*105*(2*5) = (3*3)*(3*5*7)*2*5 = (2)(3^3)(5^2)(7)
Each step here should be something understandable, but the combination, using all of this to factor one number --- this would be possible only on the very hardest GMAT Quant problems.
the second number --- this number is obvious even. The digits add up to 20, so it's not divisible by 3. 1400 and 70 are divisible by 7, but 8 isn't, so the whole number is not divisible by 7. Other than a single factor of 2, this number has no prime factors under ten. Hmm.
1478 = 2*739
As it happens, I did a little checking with my calculator --- 739 is a prime number, so this is the prime factorization. The GMAT does not, repeat, DOES NOT, expect you to recognize or identify three-digit prime numbers. The people who can look at 739 and immediately tell it's a prime number without dint of a calculator are scary people who don't bath regularly and need various medications. They are not people who take the GMAT, and the GMAT is most certainly not designed for such people. You would not have to recognize anything about 1478, other than that it is even, it is not divisible by 3, and therefore not divisible by 6.
the third number ---
437
Looking at it, we can tell
(a) it's not even
(b) 4 + 3 + 7 = 14, so the number 437 is not divisible by 3
(c) 437 = 430 + 7 --- 430 = 43*10, so it's not divisible by 7, therefore the whole number is not divisible by 7 (Even this is a little beyond the mainstream of what the GMAT expects you to see)
If you were really really mathematically astute, you might notice that
437 = 441 - 4
Which is special, because it's a difference of two squares, and therefore can be factored via the formula from algebra:
437 = 441 - 4 = (21^2) - (2^2) = (21 + 2)*(21 - 2) = 23*19
If you can see that sort of thing, great, but again, the GMAT does not expect you to be conversant with simplifications such as this. This is differently over and above what the GMAT expects you to see.
Does all this make sense?
Mike
You're the man.