Thanks Ian.
What made you start the question by factorizing 96 and go down that route. What was your thinking behind this ... what was the trigger in the question which sent you down this route.
when I tackled this question, I didnt even think about factoring 96 ... I basically approached it as follows.
Q-Stem:
m = HTU (where H=hundreds digit, T=Tens digit, U=Units digit)
H*T*U = 96
Question is asking us to find U (the units digit of m)
(1) m is odd.
This means that the units digit (U) could be either 1,3,5,7, or 9 so that m is odd.
We know that H*T*U = 96
Lets run through the values 1,3,5,7, and 9 to see if they are factors of 96. By applying the div rules we can quickly eradicate some of the values:
96 doesnt end in a 5 or 0 ... so it cannot be div by 5. So we can cross this out.
96. 9+6 = 15 ... this is not div by 9. cross out 9.
we have 1,3, and 7 left.
there is no div shortcut for 7. but we can quickly find out that 96 is not div by 7. So cross out.
left with 1 and 3.
96/1 = 96 ... so this mean H*T have to equal 96. the largest number H*T can be is 9*9 which equals 81. So we from this we know U cannot be 1. Which means it has to be 3.
96/3 = 32.
32=8*4
This means Units digit is 3. SUFF.
(2) huindreds digit of m is 8
96/8 = 12
What are the (single digit) factors of 12: 1,2,3,4,6
So which two numbers make 12 (2*6, 3*4, 4*3, 6*2).
From this we can see that the units digit could be 6, 4, 3, or 2. INSUFF.
Hence answer A.
