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If A, B and C are digits and AB#0, what is the value of B?

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If A, B and C are digits and AB#0, what is the value of B? [#permalink]

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If A, B and C are digits and AB#0, what is the value of B?

(1)
AB
+BA
________
AAC

(2) A=1


[Reveal] Spoiler:
I am confused on the OA. Consider following situations -
82 91
+28 +19
____ _____
110 110

Hence, B can be 2 or 1. So (1) is not sufficient.
[Reveal] Spoiler: OA

Last edited by Bunuel on 10 Dec 2012, 02:53, edited 2 times in total.
Edited the question.
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Re: If A B C are digits and AB not equals to 0, what is the val [#permalink]

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New post 08 Apr 2012, 14:32
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babusona wrote:
If A B C are digits and AB not equals to 0, what is the value of B?
(1) AB
+BA
_______________
AAC

(2) A=1


I am confused on the OA. Consider following situations -
82 91
+28 +19
____ _____
110 110

Hence, B can be 2 or 1. So (1) is not sufficient.


In your first example A has different values, which cannot happen.

If A, B and C are digits and AB#0, what is the value of B?

(1) AB + BA = AAC --> A=1 (A can not be more than 1, as the sum of 2 two-digit numbers is always less than 200) --> 1B+B1=11C --> B=9 (B can not be less than 8 as 18+81=99, not a three digit number) --> 19+91=110. Sufficient.

(2) A = 1. Not sufficient.

Answer: A.
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Re: If A B C are digits and AB not equals to 0, what is the val [#permalink]

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New post 13 Apr 2012, 22:58
Bunuel wrote:
babusona wrote:
If A B C are digits and AB not equals to 0, what is the value of B?
(1) AB
+BA
_______________
AAC

(2) A=1


I am confused on the OA. Consider following situations -
82 91
+28 +19
____ _____
110 110

Hence, B can be 2 or 1. So (1) is not sufficient.


In your first example A has different values, which cannot happen.

If A, B and C are digits and AB#0, what is the value of B?

(1) AB + BA = AAC --> A=1 (A can not be more than 1, as the sum of 2 two-digit numbers is always less than 200) --> 1B+B1=11C --> B=9 (B can not be less than 8 as 18+81=99, not a three digit number) --> 19+91=110. Sufficient.

(2) A = 1. Not sufficient.

Answer: A.


Hi what does AB#0 mean? what is the approach to solve such question in Data Sufficiency?
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Re: If A B C are digits and AB not equals to 0, what is the val [#permalink]

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New post 14 Apr 2012, 01:49
Expert's post
ps25 wrote:
Hi what does AB#0 mean? what is the approach to solve such question in Data Sufficiency?


AB#0 means \(AB\neq{0}\), the product of A and B does not equal to zero. This way we are told that neither A nor B equals to zero.

As for the solution it's given in above post. Please ask if anything remains unclear.
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If A,B and C are digits and AB is not 0, what is the value [#permalink]

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New post 10 Dec 2012, 02:51
amitdgr wrote:
If A,B and C are digits and AB is not 0, what is the value of B ?

(1) AB + BA = AAC

(2) A = 1



I think the answer is D.

Statement 1: this statement has already been established as sufficient in the previous posts.

Statement2: A=1

AB
+BA
-------
AAC


In the above addition, observe the units place: (digit) B + (digit) A = (digit) C
Now observe the tens place: (digit) A + (digit) B = (digit) A? -----> this means that a digit has carried over from the addition of the units digits. Now, because a digit has carried over, this implies that the digit A+B is a two digit number----> Now, the only way A+B or (1+B) will be a two digit number is if B = 9.

therefore statement B is sufficient as well.
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Re: If A,B and C are digits and AB is not 0, what is the value [#permalink]

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New post 10 Dec 2012, 02:58
Expert's post
geezer0305 wrote:
amitdgr wrote:
If A,B and C are digits and AB is not 0, what is the value of B ?

(1) AB + BA = AAC

(2) A = 1



I think the answer is D.

Statement 1: this statement has already been established as sufficient in the previous posts.

Statement2: A=1

AB
+BA
-------
AAC


In the above addition, observe the units place: (digit) B + (digit) A = (digit) C
Now observe the tens place: (digit) A + (digit) B = (digit) A? -----> this means that a digit has carried over from the addition of the units digits. Now, because a digit has carried over, this implies that the digit A+B is a two digit number----> Now, the only way A+B or (1+B) will be a two digit number is if B = 9.

therefore statement B is sufficient as well.


You cannot use information given in the first statement (AB + BA = AAC) for the second.

Check complete solution here: if-a-b-and-c-are-digits-and-ab-0-what-is-the-value-of-b-130419.html#p1071580

Hope it helps.
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Re: If A, B and C are digits and AB#0, what is the value of B? [#permalink]

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New post 10 Dec 2012, 04:42
Ans: The only possibility of getting AA after adding A and B is if A=1 (adding two digits cannot give a number greater than 20). Since the addition of two numbers gives a three-digit number, therefore A+B>equal to 10 , that leaves B to be only 9. Therefore the answer is (D).
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Re: If A, B and C are digits and AB#0, what is the value of B? [#permalink]

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New post 10 Dec 2012, 04:45
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priyamne wrote:
Ans: The only possibility of getting AA after adding A and B is if A=1 (adding two digits cannot give a number greater than 20). Since the addition of two numbers gives a three-digit number, therefore A+B>equal to 10 , that leaves B to be only 9. Therefore the answer is (D).


Correct answer is A, not D. Check here: if-a-b-and-c-are-digits-and-ab-0-what-is-the-value-of-b-130419.html#p1071586
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DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If A, B and C are digits and AB#0, what is the value of B? [#permalink]

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Re: If A, B and C are digits and AB#0, what is the value of B? [#permalink]

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Re: If A, B and C are digits and AB#0, what is the value of B? [#permalink]

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New post 05 Nov 2015, 04:45
If A, B and C are digits and AB#0, what is the value of B?

(1)
AB
+BA
________
AAC

Important takeaway here is that for the tens digits: A+B results in AA. This means that:

1. A+B is at least 10

Therefore the B+A in the units place is at least 10 and we have to carry a 1 over to the tens digits (cannot be 2 since A+B is at most 9+9=18)

2. A+B in the tens places has a units digit of A

This means that A+B+1 (carried over from B+A in the units places) has a units digit of A. To get a units digit of A, B+1 must be 10.

Therefore B=9

SUFFICIENT

(2) A=1

We know A is 1 but we have no idea what B is

INSUFFICIENT

Answer is A
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Re: If A, B and C are digits and AB#0, what is the value of B? [#permalink]

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New post 06 Nov 2015, 14:30
Algebraic really works fast for this kind of question:

A=x, B=y

it means

y+y=10x+x, 2y=11x

since 1<=x<=9, 0<=y<=9

so this possibility can't rise. there must be one from z+x=c

so 2y+1=11x

so x=1, y=5

sufficient
Re: If A, B and C are digits and AB#0, what is the value of B?   [#permalink] 06 Nov 2015, 14:30
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