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Data Sufficiency - Find value of B

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Intern
Affiliations: CA - India
Joined: 27 Oct 2009
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Data Sufficiency - Find value of B [#permalink]  08 Nov 2009, 07:09
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If A, B and C are digits such that AB is not equal to 0, what is the value of B.
1. AB
+BA
AAC

2. A = 1.

I am confused with the answer explanation provided to me. need explanation.
VP
Joined: 05 Mar 2008
Posts: 1473
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Re: Data Sufficiency - Find value of B [#permalink]  08 Nov 2009, 07:48

Statement 1:

AB + BA = AAC

10A + B + 10B + A = 100A + 10A + C
11A + 11B = 110A + C
11B -C = 99A
B = 9
C = 0
A = 1

19 + 91 = 110

B cannot equal 10 because the question assumes they are single digits
Senior Manager
Joined: 18 Aug 2009
Posts: 304
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Kudos [?]: 123 [0], given: 9

Re: Data Sufficiency - Find value of B [#permalink]  08 Nov 2009, 08:07
If A, B and C are digits such that AB is not equal to 0, what is the value of B.
1. AB
+BA
AAC

2. A = 1.

I am confused with the answer explanation provided to me. need explanation.

You can also go about it like following:

AB
BA
---
AAC

Left most A has to be 1 as it is carried over from previous addition (max possibility 9+9=18). So we can write:

1B
B1
----
11C

Now second row B has to be 9 to be able to carry over 1. So this changes to:

19
91
----
110 <-C calculated to be 0.
Intern
Affiliations: CA - India
Joined: 27 Oct 2009
Posts: 45
Location: India
Schools: ISB - Hyderabad, NSU - Singapore
Followers: 11

Kudos [?]: 499 [0], given: 5

Re: Data Sufficiency - Find value of B [#permalink]  08 Nov 2009, 08:20
Ok, i got my mistake. I was considering equation given in statement 1 to be the stem

The answer should be A only
Intern
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Re: Data Sufficiency - Find value of B [#permalink]  09 Nov 2009, 22:48
smtripathi wrote:
10A+B
10B+A
------
10(A+B)+(A+B)

or, 11(A+B)
here , 11(A+B) signifies AAC that means AA means 11 and C means A+B

hence quick answer for A = 1.
For C, substitute the answers and you will see, C=0, since B=9 (B can't be zero)

thankx .. this is cleaner way to do this kind of problems.
Intern
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Re: Data Sufficiency - Find value of B [#permalink]  10 Nov 2009, 00:28
smtripathi wrote:
10A+B
10B+A
------
10(A+B)+(A+B)

or, 11(A+B)
here , 11(A+B) signifies AAC that means AA means 11 and C means A+B

hence quick answer for A = 1.
For C, substitute the answers and you will see, C=0, since B=9 (B can't be zero)

Thanks buddy... I was searching for some generic rule like this.

thanks
Manager
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Re: Data Sufficiency - Find value of B [#permalink]  11 Nov 2009, 21:02
If A, B and C are digits such that AB is not equal to 0, what is the value of B.
1. AB
+BA
AAC

2. A = 1.

I am confused with the answer explanation provided to me. need explanation.

I used this approach:
Using 1---A,B#0 since A+B gives a different digit. Also, since AB+BA is giving a 3 digit #, When we add units place (B+A) we need to carry forward 1. When we add the ten's digit , we have A+B+1 giving the unit's place "A". This is only possible if B=9
So statement 1 is sufficient.
Manager
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Re: Data Sufficiency - Find value of B [#permalink]  12 Nov 2009, 08:28
Here is how I solved the problem:

From Statement 1:

I started by seeing what the problem would look like if we assumed A = 0

1B
+B1
11C
Possible!

Then seeing what it would look like if we assumed A = 2
2B
+B2
22C
Impossible! There is no way we can add two two digit numbers if and get over 200! So we know that A cannot be greater than 1.

From
1B
+B1
11C

It is easy to see that B must be a high number like 8 or 9 to hold true:
19
+91
110

SUFFICIENT!
Re: Data Sufficiency - Find value of B   [#permalink] 12 Nov 2009, 08:28
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