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The product of the units digit, the tenth's digit and the hu

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by aspirant2011 » Sat Jun 25, 2011 9:57 am
The product of the units digit, the tenth's digit and the hundred's digit of the positive integer m is 96. What is the units digit of m?

1) m is odd
2) The hundredth's digit of m is 8

[spoiler]OA: I am confused with 1st option i.e m can't be odd in any case since m=96, when I factorise 96 then I get 2^5 * 3, therefore m would always be even. Please clear my doubt and let me know how to resolve the above mentioned problem. I couldn't understand OG explanation[/spoiler]
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by Ashley@VeritasPrep » Sat Jun 25, 2011 10:34 am
I am confused with 1st option i.e m can't be odd in any case since m=96, when I factorise 96 then I get 2^5 * 3, therefore m would always be even.
m istelf doesn't equal 96; the product of its digits does. Since you've found an odd factor in its factorization, that factor could very well be the units digit!
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by Ashley@VeritasPrep » Sat Jun 25, 2011 10:38 am
Now, further explanation in case that doesn't unlock the problem:

Statement (1) tells us that m is odd, and we already know m is a 3-digit number. So it must end in 1,3,5,7, or 9. But it can't end in 5,7, or 9 because then there'd by no way to make the product of its digits 96 (since neither 5 nor 7 nor 9 goes into 96 cleanly). It also can't end in 1 because there'd be no way to get to the whole product of 96 from just the remaining two digits in that case (since the highest a digit can be is 9, and 9*9 only brings you to 81). So from Statement (1) we glean that the last (units) digit must be 3.
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by aspirant2011 » Sat Jun 25, 2011 10:39 am
Ashley@VeritasPrep wrote:
I am confused with 1st option i.e m can't be odd in any case since m=96, when I factorise 96 then I get 2^5 * 3, therefore m would always be even.
m istelf doesn't equal 96; the product of its digits does. Since you've found an odd factor in its factorization, that factor could very well be the units digit!
yes I agree that if 3 is in unit's place then my unit place becomes odd but I have to get m as 96 and for that I need to have Tenth and Hundredth digit as even, then tell how will m become odd if I have even on Hundredth and Tenth place and odd on one's place
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by aspirant2011 » Sat Jun 25, 2011 10:49 am
ohhhh sorry yup I got it, I got confused with something else, anyways thanks a lot :-)
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