In the long division above, A, B, C, and D represent 4 different...

Question

https://gmatclub.com/forum/download/file.php?id=73473 In the long division above, A, B, C, and D represent 4 different integers from the set {1, 2, 3, 4, 5, 7, 8, 9}. The dividend is ABCB , the divisor is 6, the quotient is BDA , and the remainder is A . What is the value of A ? A) 7 B) 4 C) 3 D) 2 E) 1 long division.PNG dd.png

gmatophobia · Accepted Answer

We can pick up clues from the long division performed in the image.

Clue 1  (indicated in red ink): The second subtraction operation,  C - 6 , results in  D .

C - 6 = D  ---------- (1)

Clue 2  (indicated in blue ink): The number  6  is a product of  6  and  D

6 * D = 6

D = 1

From (1), we get  C = 7

Clue 3  (indicated in green ink): The subtraction of  A  from  B  results in  A

B - A = A

B = 2A

Clue 4  (indicated in orange ink): In the last subtraction operation, DA is the product of 6 and A

DA = 6A

We can represent  DA  as  10D + A

10*D + A = 6A

As  D = 1

10 = 5A

A = 2

Option D

KarishmaB · Answer

This is an alphametic. 6 * B = AB B has to be a single digit. Think about the multipication table of 6. 6*2 = 12, 6*4 = 24, 6*6 = 36, 6*8 = 48 (when 6 is multiplied by an even digit, it gives the same even digit in units place). So AB could be any of 12/24/36/48 Next note that 6*D = 6 This means D = 1 Next we see that 6*A = DA. Yet again DA will be of the form 12/24/36/48. Since D must be 1, DA must be 12 and hence A must be 2. Answer (D) Some more questions on alphametics: https://anaprep.com/puzzles-corner-solving-alphametics/ https://anaprep.com/puzzles-corner-mult ... phametics/

EthanTheTutor · Answer

What was your source for this question?

Bunuel · Answer

_______________________________________
The source is GMAT Prep (Focus).

Nidzo · Answer

@ gmatophobia  's method is probably the fastest. I just want to add an alternative method incase the long division threw anyone off.

Focusing solely on the top part (ie.  \frac{ABCB}{6} = BDA  with a remainder of  A ):

From the image one can see that  6  does not divide  a , and thus  a < 6         . As  a  does not divide by 6, the next step in the division becomes:  \frac{10a + b}{6} = b  and becomes  10a = 5b  or simplified  2a = b . As  10a + b  can be written as  12a  then  10a + b  is divisible by 6, and nothing gets carried over.

Next we have,  \frac{c}{6}= d  with a possible remainder. As  6≤c≤9 ,  d  can only be  1 . Let the possible remainder =  x . Carry this over to the next step as  10x .

Next step becomes:  \frac{10x + b}{6} = a  with a remainder of  a . However, we know that  2a = b :   \frac{10x + 2a}{6} = a  plus the remainder  a  becomes:  10x + 2a = 6a + a  simplified:  2x = a . This shows us that  a  is even        .

One can rewrite the original division equation as:
 \frac{1000a + 100b + 10c + b}{6} = 100b + 10d + a  with a remainder of  a

Plugging in  b = 2a  and  d = 1 :

1000a + 100(2a) + 10c + 2a = 6 + a

1202a + 10c  = 1207a + 60

5a + 60 = 10c

a + 12 = 2c

As established from the elimination of answer choices,  a  can either be  B)   4  or  D)   2 .

If  a = 4  , then  b = 8    (because of  2a = b )   and  c = 8 . This will not work as the question stem states ' A, B, C, and D represent 4 different integers'

Therefore  a = 2

ANSWER D

Yes2GMAT · Answer

Am I missing something in this question? It seems fairly straightforward.

ABCB is divisible by 6. A should be less than six. When we multiply B with 6, we should be able to subtract AB without carrying forward a digit as only C is brought forward in the next step.

So, 6 * B = AB which will be a multiple of 6 with 2 digits ~ 12,18,24,30,36,42,48,54,60. We can eliminate 60, 54,42,30,12 as B>A (Divisor has 3 digits only while dividend has more digits for ex 6*600=3600). Now, we are left with 18,24,36,48. Out of the answer choices, we have only 4 and 2 options as for A. So, we eliminate 18,36.

Now, we have 24, 48 for AB values.
Towards the end B - A = A. So, B has to be 4 and A has to be 2?

PS:- You dont have to worry about A,B,C,D (mainly A or B in AB) being 0 as it is not mentioned within the set in the question.

siddd30 · Answer

I dont think ABCB is divisible by 6, it literally has a remainder of 'A'

Yes2GMAT · Answer

siddd30  Sorry, I think I meant AB is divisible by 6. I mistyped that.
Could u read the rest of the comment and see if there is anything wrong with the logic?

siddd30 · Answer

Hey, No problem!

TBF, the logic is a little difficult to follow for me- but there is no one approach fits all for these type of questions.
My approach was different i.e., I solved it through 10A+B= 6B; so B=2A; and then estabilished that 6D= 6, so D=1; and went from there on.

I'd do whatever is more intuitive, if you can think clearly with your logic, and test it out on a couple of other questions to test its solidity, then nothing wrong with it

Cheers, Have a good day!

Oppenheimer1945 · Answer

Had got this up in a mock#5. With a "mocked-mindset" i had to use Brute-Force method to mark the ans.

Used ABCB=2474 (3rd digit >6 as per condition given)

When divided by 6, leaves remainder of 2 (back-testing gives A=2 as well)

D)

Kinshook · Answer

pablovaldesvega 
 https://gmatclub.com/forum/download/file.php?id=73473

Given: In the long division above,  A, B, C,  and  D  represent 4 different integers from the set {1, 2, 3, 4, 5, 7, 8, 9}. The dividend is  ABCB , the divisor is 6, the quotient is  BDA , and the remainder is  A .

Asked: What is the value of  A ?

Since AB is a multiple of 6 & B*6 = 10A + B; 5B = 10A; B = 2A
C - 6 = D ; C = D + 6
6*D = 6; D= 1
Since DA is a multiple of 6; A = 2; B=2A = 4; C = D+6 = 1 + 6 = 7

6*412 + 2 = 2474

IMO D

DonBosco7 · Answer

Few things that should be immediately clear upon reading the stem are:-

1] A < 6 , so from the given list of numbers, only possible values of A will be 1,2,3,4,5, out of these in the option choices you have 4,3,2,1.
2] From the given long division, the values of C & D are clearly 7 & 1 respectively.
3] From the given long division we see that AB - AB leaves no remainder. This means that 6*B should give "_ B", there are 4 option for AB, where dividend B matches the quotient B  , from these option you not only get B, but also value for A which are (1,2,3,4), now one of these values should match with the value of remainder A in the end, 2 comes out to be the contender.

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