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# Is a 3-digit number divisible by 6? 1). The sum of tens' and

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Manager
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Is a 3-digit number divisible by 6? 1). The sum of tens' and [#permalink]  27 Jun 2009, 22:08
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Is a 3-digit number divisible by 6?
1). The sum of tens' and hundreds' digit is 6
2). The units' digit is 6
GMAT Tutor
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Re: divisibility [#permalink]  28 Jun 2009, 06:02
Expert's post
vcbabu wrote:
Is a 3-digit number divisible by 6?
1). The sum of tens' and hundreds' digit is 6
2). The units' digit is 6

Neither statement is sufficient alone, clearly. Together:

-the sum of the digits is 12, so the number is divisible by 3
-the units digit is even, so the number is even, and thus divisible by 2

Since the number is divisible by both 2 and 3, it must be divisible by the LCM of 2 and 3, which is 6. C.
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Re: divisibility [#permalink]  28 Jun 2009, 06:56
C for me as well. For a number to be divisible by 6, it needs to be divisible by both 2 and 3. A number is divisible by 2 if its units digit is even, and divisible by 3 if the sum of its digits is divisible by 3.

From stat 1, we need to know what the last unit is. For example, if its 0, then the number will be divisible by 2 and 3 ... if its 1, for example, it wont be. Insuff.

From stat 2, we know that since the unit is 6, the number is even and therefore divisible by 2. But we dont know anything about the first two. Insuff.

Together, we know that the sum of the digits is divisible by 12 (6+6), and that its also divisible by 2 since the units digit is 6.
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Re: divisibility [#permalink]  28 Jun 2009, 13:43
I will go with C too. I worked it out with the examples.. First explaination it to the point..
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Re: divisibility [#permalink]  28 Jun 2009, 16:42
Stmt 1 and 2 alone are insuff.

Combining, (I took an algebric approach)
Let the number be 100X + 10Y + Z......................1
Stmt 1 tells that X + Y = 6 or X = Y - 6
Stmt 2 tells that Z = 6
So eq. 1 can be written as
100(Y-6) + 10Y + 6
or (606 - 90Y).Now we need to determine if (600 - 90Y) is divisible by 6 or not.
Take 6 common and it becomes
6 (101 - 30Y) which indicates that it divisible by 6.
Re: divisibility   [#permalink] 28 Jun 2009, 16:42
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