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The product of the units digit, the tens digit, and the hundreds digit [#permalink]
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12 Jan 2008, 02:21
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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
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Last edited by Bunuel on 08 Oct 2014, 07:43, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to DS forum.



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Re: The product of the units digit, the tens digit, and the hundreds digit [#permalink]
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12 Jan 2008, 05:21
it is C. the number is 843.
statement1, although useful still insufficient. the only odd factor in 96 is 3. so if units digit is 3, the product of the first two ones must be 32 (32*3=96).
statement2 says hundreds is 8. alone is insuff
but both statements are suff. 843



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Re: The product of the units digit, the tens digit, and the hundreds digit [#permalink]
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12 Jan 2008, 06:14
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CaspAreaGuy wrote: it is C. the number is 843.
statement1, although useful still insufficient. the only odd factor in 96 is 3. so if units digit is 3, the product of the first two ones must be 32 (32*3=96).
statement2 says hundreds is 8. alone is insuff
but both statements are suff. 843 OA is A if m is odd, then the unit digit is 3, since 96= 2^5 *3. any other combination would give us an even number



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Re: The product of the units digit, the tens digit, and the hundreds digit [#permalink]
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12 Jan 2008, 10:03
marcodonzelli wrote: 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. prime factors m= xyz962 482 242 122623311 so: hundreds and tens digits can be either 8 or 2 then units digit has to be 3. suff. 2. m=xyz then y=8, then x and z can either be 4 or 3 so we cannot say anything from this statement. insuff. A for me.



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Re: The product of the units digit, the tens digit, and the hundreds digit [#permalink]
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12 Jan 2008, 14:40
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Agree with Marco. A.
2^5X3, You can't have 2 (or any of its multiples e.g. 4, 8, etc) as Units digit, otherwise it will be even.



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The product of the units digit, the tens digit, and the [#permalink]
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19 Mar 2008, 23:21
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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. I know, this Q has been discussed before. I need your take on this. i can not understand the logic, a thorough explanation would be great thanks



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Re: Set29 q11 [#permalink]
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19 Mar 2008, 23:50
(C) Assume abc, axbxc=96 (1) > c is odd (2) > a=8 > bc=12
from either 1, 2 can't tell Combine > try only c=3 satisfies so...



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Re: Set29 q11 [#permalink]
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20 Mar 2008, 00:32
I'll try: 1. Let m=htu: h*t*u=96 2. 96=2*2*2*2*2*3 3.1. consider first condition: m is odd. 3.2. u can be 1 or 3, because if m were 5, for example, we would see 5 as a prime number in the product. 3.3. consider u=1. h*t=96 but it is greater than the max possible product: 9*9=81. 3.4. u=3 remains. sufficient 4.1. consider second condition: h=8 4.2. h*t*u= 2*2*2*2*2*3 4.3. we have t*u=2*2*3. Both t=2, u=6 and t=4, u=3 satisfy second condition but m have different units digits. 4.4. Insufficient. 5. Therefore, Answer A. Hope this help
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Re: Set29 q11 [#permalink]
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20 Mar 2008, 01:04
A, the same aproach with Walker 96=8*4*3 1. m is odd, the unit digit of m must be 3, it can not be 2, 4, or 8 sufficient 2. the hundred digit of m is 8, > the unit digit can be 4 or 3 : insufficient
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Re: product of the units digit [#permalink]
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09 Nov 2009, 22:12
If you approach this from the order of units, tens and then hundreds, you know 96 must be divisible by each digit, otherwise you get a decimal. So, to start, you only have 2, 3, 4, 8 that are divisible into 96. Statement 1, if this is true, then the units must be 3. No other odd number (19; 0 out because 0 * anything = 0) is divisibile into 96. So 96/3 = 32. This only gives us 2 options, 8 and 4. No other pair of singledigit numbers gives us 32. (1) is insufficient because 843 and 483 both give us a product of 96, and m = odd, but we cannot narrow it to a single possible value for m. Statement (2). Insufficient. We know the hundreds digit is 8, but we DO NOT have the same information from (1). 96 / 8 = 12. The other two numbers could be 3 and 4 or 6 and 2. We do not know and therefore, (2) is insufficient. Together = SUFFICIENT. Because we know units must be 3 from statement (1) and then must have 8 and 4. Statement (2) tells us that hundreds is 8, so that means m = 843. jade3 wrote: The product of the units digit, the tens digit, and the hundreds digit of the positive integer m is 96. What is m? (1) m is odd. (2) The hundreds digit of m is 8.
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Re: product of the units digit [#permalink]
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11 Nov 2009, 00:49
jade3 wrote: The product of the units digit, the tens digit, and the hundreds digit of the positive integer m is 96. What is m? (1) m is odd. (2) The hundreds digit of m is 8. Yes guys the question was wrongly typed The product of the units digit, the tens digit, and the hundreds digit of a three digit positive integer m is 96. What is m? (1) m is odd. (2) The hundreds digit of m is 8 For this question the OA is C



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Re: product of the units digit [#permalink]
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11 Nov 2009, 09:26
I got C, too.
First I broke 96 down into its prime factors and got 2, 2, 2, 2, 2, 3.
A states that it's an odd number so 3 has to go into the ones diget. But the statement by itself is not sufficient bc the five 2s, can form two single diget number, 4 and 8 and you don't which goes in the tens and which goes in the hundreds.
B tells you the hundreds diget is 8. This statement by itself is not sufficent. But combined with A, you know that the number has to be 843.
Therefore the answer is C.



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Re: product of the units digit [#permalink]
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10 Dec 2009, 10:59
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I saw this question in one of the Gmat paper tests. The only difference there was that they had asked for a the unit's digit of m. In which case 483 or 843 both lead to 3. There the answer was A.



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Re: product of the units digit [#permalink]
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11 Sep 2011, 02:02
C is the answer. This was my approachGiven in the problem: h*t*u = 96. Need us to find u Stmt1  m is odd If m is odd it has to end with 3, 5, or 7. This is inconclusive. You can only go as far as saying u = 3 because 96 is only divisible by from the odd numbers 0  9. Further, t and h can be 8 and 4 in any order since 8 and 4 are the only two other numbers 0  9 that divide 96 (they cannot be 3 because 96/3=32 and 3 is not a factor of 32) Insufficient. Stmt2  h = 8. But this doesn't tell us anything since we know nothing about the other two digits in the number. Using statements 1 and 2, we get 843 =. Therefore, C.
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Re: product of the units digit [#permalink]
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05 Oct 2011, 11:20
The product of the units digit, the tens digit, and the hundreds digit of the positive integer m is 96. What is m? (1) m is odd. (2) The hundreds digit of m is 8.
Product = 96
1 m is odd  not sufficient 2 The hundreds digit of M is 8 So the product of next two digits is 12 There are 4 combinations possible for the last two digits{26,62,34,43}
Putting together only odd from the set is 43
so it is C



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Re: product of the units digit [#permalink]
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08 Nov 2011, 10:59
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96 = 2^5 * 3
1) m is odd so units digit can be 1 or 3 based on the factors. but it cannot be 1 as no two single digits integers can give a product of 96. So units digit is 3  SUFFICIENT
2) hundreds digit is 8 Insufficient as number could be 843 or 826 or 834 or 862
Ans: A



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Re: The product of the units digit, the tens digit, and the hundreds digit [#permalink]
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08 Nov 2011, 11:00
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96 = 2^5 * 3
1) m is odd so units digit can be 1 or 3 based on the factors. but it cannot be 1 as no two single digits integers can give a product of 96. So units digit is 3  SUFFICIENT
2) hundreds digit is 8 Insufficient as number could be 843 or 826 or 834 or 862
Ans: A



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Re: product of the units digit [#permalink]
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15 Nov 2011, 14:42
icaniwill wrote: 96 = 2^5 * 3
1) m is odd so units digit can be 1 or 3 based on the factors. but it cannot be 1 as no two single digits integers can give a product of 96. So units digit is 3  SUFFICIENT
2) hundreds digit is 8 Insufficient as number could be 843 or 826 or 834 or 862
Ans: A Unless I am missing something or the purpose of your post (if replying to someone else), the question is asking for the value of m not the digit value. so it could be 483 or 843 and those are the only two options. You know you have a 3 digit integer from the question and the factorization gives you 2^5*3. Because you have a 3 digit that is odd you know that the other two numbers HAVE to be an 8 and 4. Anything else gives you a number greater > 10. example. 2^2 = 4, 2^3=8 or 2^1= 2, 2^4 = 16. 16 can not be an option because we are looking for unit values. so you know that you have 2^2 or 2^3 but you dont know which one is in the hundreds spot stmt 2 tells you that the hundreds digit is 8 and you're able to narrow it down from the previous two



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Re: The product of the units digit, the tens digit, and the hundreds digit [#permalink]
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08 Oct 2014, 09:58
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 This was a sitter. 96 can be factored into  3*2^5 1. m is odd  Thus last digit has to be 3  This gives answer to the question 2. Hundreds digit is 8  The number can be 384 or 483, thus the last digit can not be determined. Ans. A
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Re: The product of the units digit, the tens digit, and the hundreds digit [#permalink]
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15 Apr 2015, 08:59
m mean [abc] 96 = 2 x 2 x 2 x 2 x 2 x 3 = 3 x 2^5 (1) m odd => c odd => 3 (2) a = 8 = 2^3 remain: b.c = 2 x 2 x 3 4 cases: 843, 834, 826, 862
A is right.




Re: The product of the units digit, the tens digit, and the hundreds digit
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