units, tens and hundred digits

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units, tens and hundred digits

by maoriba » Sat Nov 20, 2010 2:41 am
HEllo, here is Question 110 of the D.S. from O.g.

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

(1) if m is odd, the units digit is 1, 3, 5, 7, 9

96= 2*48= 2*2*24= 2*2*2*12=2*2*2*2*6
96= 1*96
96= 3*32= 3*4*8
5, 7, 9 we cannot consider them as they are not factors of 96.
so only 1 and 3 can be the units digits of integer m.
if units digit is 1, than we cannot explain 96 in 2 single digit factors.
if units digit is 3, than we can explain the other two factors in 8 and 4. SUFFICIENT!

(2) cannot say, it can be 3 or 4 NOT SUFFICIENT
riba made
Source: — Data Sufficiency |

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by Rahul@gurome » Sat Nov 20, 2010 3:58 am
Solution:
Now 96 is the product of 3 single digit numbers.
96 = 12 * 8 = 3*4*8 = 2*6*8 =4*4*6.
So the units digit, tens digit and hundreds digit can be either 3, 4 and 8 or 2, 6 or 8 or 4, 4, 6 in any order.
Consider first statement (1) alone.
m is odd.
So the units digit of m is odd.
Only possibility is 3 from the combination of 3, 4 and 8.
So (1) alone is sufficient.

Next consider (2) alone.
The hundreds digit is 8.
So any of the 2 combinations 3, 4, 8 or 2, 6, 8 are possible.
So if hundreds digit is 8, units and tens digit can be any of 2, 3, 4 or 6.
Since we do not get a unique answer, (2) alone is not sufficient.

The correct answer is (A).
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