The product of the units digit, the tens digit, and

[jgranchi]

Question seen when taking GMAT Focus Test:

The product of the units digit, the tens digit, and the hundreds digit of the positive integer m is 96. What is the units digit of m?

(1) m is odd
(2) The hundreds digit of m is 8

The answer given in the explanation says that (1) is sufficient and m must be 3. I don't see how this is sufficient because the number could also be 961. I think this is an error, or am I missing something?

[anil_yarasi]

^^How come 9*6*1= 96.
As per the question"The product of the units digit, the tens digit, and the hundreds digit of the positive integer m is 96". So, 96 is the product of three numbers. We want the units digit value?? Consider various combinations:

96 =

6*8*2 or 2*8*6 or 826 or 628.....
3*8*4 or 483 or 843 or ....
According to 1: the number is odd; We have only one odd digit: 3. - correct
while II says: hundreds digit of m is 8; There are many combination: 682 or 483 or.... incorrect.

[nisarg]

^^How come 9*6*1= 96.
As per the question"The product of the units digit, the tens digit, and the hundreds digit of the positive integer m is 96". So, 96 is the product of three numbers. We want the units digit value?? Consider various combinations:

96 =

6*8*2 or 2*8*6 or 826 or 628.....
3*8*4 or 483 or 843 or ....
According to 1: the number is odd; We have only one odd digit: 3. - correct
while II says: hundreds digit of m is 8; There are many combination: 682 or 483 or.... incorrect.

Now I am missing something here...

You said above that 96 = 6*8*2(m = 682 - even) or 8*2*6 (m = 826 - even) or 8*4*3 (m = 843 - odd)

So how is 1 correct?

Thanks for the clarifiaction.

[kamalsinghy]

96 = 2*2*2*2*2*3,

statement 1: m is odd, so unit's digit could be 1,3,5,7,9.
But we have only one odd factor in 96(product of digits of m) i.e. 3. Therefore, unit's digit of m is 3. - sufficient

statement 2: hundred's digit is 8, so we are left with 2*2*3. Therefore, m could be 826, 843, 834, 862. So no unique unit's digit. insufficient

[RonPurewal]

Now I am missing something here...

You said above that 96 = 6*8*2(m = 682 - even) or 8*2*6 (m = 826 - even) or 8*4*3 (m = 843 - odd)

So how is 1 correct?

Thanks for the clarifiaction.

it appears that you don't understand how data sufficiency works.

basically, you take each numbered statement AS A GIVEN, and see WHETHER YOU CAN DEDUCE A UNIQUE ANSWER TO THE PROMPT QUESTION with that given statement taken as true.

if statement (1) is taken AS GIVEN, then the only possible units digit is 3. (see your own list of possibilities to verify this statement.)
therefore, statement (1) is SUFFICIENT to determine a unique answer to the problem.
this is how data sufficiency works.

i've noticed that you're listed as a "prospective student". if you attend our class, you will come away from session #1 with a thorough knowledge of the basics of this vexing question type.

[ashish.jere]

(A)

[Ben Ku]

Hmmm ... I don't know what (A) means. If there's a specific follow up question, please post that. Otherwise, I hope you're enjoying the class!