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If the number 12341234B1234A, in which A and B represent digits, is di

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If the number 12341234B1234A, in which A and B represent digits, is di  [#permalink]

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New post 18 Mar 2015, 23:54
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If the number 12341234B1234A, in which A and B represent digits, is divisible by 6, then what is the maximum value of |A−B|?

a) 9
b) 8
c) 7
d) 6
e) 5
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If the number 12341234B1234A, in which A and B represent digits, is di  [#permalink]

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New post 19 Mar 2015, 00:32
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All number should be divisible by 3 and 2. We can see that sum of digits without A and B is already divisible by 3,
so we should care that sum of A and B is divisible by 3

We should highest/lowest A - lowest/highest B. Maximum possibility is 9, so let's start testing from it

Picking: A=0 and B=9, it is divisible by 2 (because even) and divisible by 3 (sum is divisible by 3)

A
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Re: If the number 12341234B1234A, in which A and B represent digits, is di  [#permalink]

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New post 23 Dec 2015, 19:29
tricky one, as I tried to make some assumptions which were way too unnecessary. clearly if A=0, then the number is divisible by 2. to be divisible by 3, B can be 0, 3, 6, 9. maximum value of B is 9, so |0-9|=9. note that A can't be 9, because in this case, the number would not be divisible by 2, and thus, not divisible by 6.
good question.
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Re: If the number 12341234B1234A, in which A and B represent digits, is di  [#permalink]

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New post 29 Sep 2016, 14:39
Bunuel VeritasPrepKarishma

Where am I going wrong?
a+b+30 should be divisible by 6. This means a+b should be divisible by 6. So, possibilities of a+b can be 6,12,18

Max difference between a and b can be (6-0) = 6

Please assist.
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Re: If the number 12341234B1234A, in which A and B represent digits, is di  [#permalink]

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New post 07 Oct 2016, 00:53
chetan2u Can you please help me with the above query ^^ Thank you in advance.
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Re: If the number 12341234B1234A, in which A and B represent digits, is di  [#permalink]

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New post 07 Oct 2016, 09:14
Keats wrote:
chetan2u Can you please help me with the above query ^^ Thank you in advance.


Hi
a+b+30 is div by 6...
Where you are going wrong is that a+b+30 should be div by 3...
So a+b can be 9, 12, 15 ,18 etc..

But we are looking at a-b....
Since a and b are single digit number, a-b can be max 9....
if we take a as 0, the number 1234...... will be EVEN and then b can take max value of 9 and still be div by 3..
A number div by 2 and 3 will be div by 6..

So |a-b|=|0-9|=9
A
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Re: If the number 12341234B1234A, in which A and B represent digits, is di  [#permalink]

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Re: If the number 12341234B1234A, in which A and B represent digits, is di  [#permalink]

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New post 29 Jul 2018, 10:46
Three times sum of 1+2+3+4 =10*3=30
Now, the expression becomes 30+A+B.What we want is a number divisible by 6( which as per divisibility rule should be divisible by both 2 and 3), ending with an even number or zero.
So, by hit and trial our number can be 30+0+9= 39
Hence, 9-0 = 9.
It can be maximum difference.Hence A.
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Re: If the number 12341234B1234A, in which A and B represent digits, is di  [#permalink]

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New post 31 Jul 2018, 11:54
If number divisible by 6- Sum of digits divisible by 3 and should be even.

1+2+3+... A + B should be divisible by 3

A+B should be divisible by 3

and B is even.

Max A-B ----

B is 0
A is 9
Answer should be 9

A is Answer
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Re: If the number 12341234B1234A, in which A and B represent digits, is di  [#permalink]

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New post 08 Aug 2018, 04:15
ynaikavde wrote:
If the number 12341234B1234A, in which A and B represent digits, is divisible by 6, then what is the maximum value of |A−B|?

a) 9
b) 8
c) 7
d) 6
e) 5


Responding to a pm:

A and B can take values from 0 to 9. We need them to be as far apart as possible so get the maximum value of |A - B| since absolute values show distance between the two. The maximum distance between them can be 9 (if one of them is 9 and other is 0) and the minimum distance between them would be 0 if both A and B must take the same values. Let's find out.

Divisibility by 6 - The number would be divisible by both 2 and 3.
To be divisible by 2, the number's units digit should be 0/2/4/6/8 - value of A

To be divisible by 3, the sum of all digits should be divisible by 3.
1+2+3+4+1+2+3+4+1+2+3+4+A+B = 30 + A + B
(or we can make groups of multiples of 3 and keep ignoring them)

Since 30 is divisible by 3, we need A + B to be divisible by 3 too. If A = 0, B can be 9 which makes A + B divisible by 3.

Hence A should be 0 and B should be 9.

Answer (A)
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Re: If the number 12341234B1234A, in which A and B represent digits, is di  [#permalink]

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New post 06 Oct 2018, 03:00
A lot of people have taken the max value of A as 9, which is incorrect as the last digit needs to be even to be divisible by 2, thus A will be 0 and B will be 9, as posted by Karishma.
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Re: If the number 12341234B1234A, in which A and B represent digits, is di &nbs [#permalink] 06 Oct 2018, 03:00
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If the number 12341234B1234A, in which A and B represent digits, is di

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