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16 Jan 2012, 14:38
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A
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Difficulty:
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Question Stats:
53% (01:49) correct
47%
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If A, B and C are digits between 0 and 9 inclusive, what is the value of B?
(1) AB + BA = AAC
(2) A = 1.
Kaplan.png [ 20.26 KiB | Viewed 9827 times ]
Kaplan Math Workbook (6th Edition) official answer states:
statement 1:
that a sum of a two-digit number plus another two-digit number gives a three-digit number. The sum of 2 two-digit numbers must be less that 200, therefore A must be 1.
Then it concludes that this statement is true only when b=9 ----> Sufficient
Statement 2 is Insufficient (obviously) and therefore the AC is A.
Evaluating the red phrase: it assumes that A and B must be two-digit numbers. Isn't it possible that A=0? Isn't the following addition correct? (B has to equal 0 for it to be correct, but still...)
+ 0 B
+ B 0
-------
0 0 B
Or because no one writes the 0's therefore it implies that A and B can't equal 0?
I would really appreciate any comments.
(1) AB + BA = AAC
(2) A = 1.
Attachment:
Kaplan.png [ 20.26 KiB | Viewed 9827 times ]
Kaplan Math Workbook (6th Edition) official answer states:
statement 1:
that a sum of a two-digit number plus another two-digit number gives a three-digit number. The sum of 2 two-digit numbers must be less that 200, therefore A must be 1.
Then it concludes that this statement is true only when b=9 ----> Sufficient
Statement 2 is Insufficient (obviously) and therefore the AC is A.
Evaluating the red phrase: it assumes that A and B must be two-digit numbers. Isn't it possible that A=0? Isn't the following addition correct? (B has to equal 0 for it to be correct, but still...)
+ 0 B
+ B 0
-------
0 0 B
Or because no one writes the 0's therefore it implies that A and B can't equal 0?
I would really appreciate any comments.
16 Jan 2012, 15:04
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SonyGmat
I think one thing we can assume safely is that A, B and C are distinct digits.
Next, even if we don't assume that A>0 (because of AB and AAC as you mention) then still A can not be zero as 0B+B0=00C doesn't hold true for any values of B and C (single digit number B plus two-digit number B0 can not equal to C, also a single digit number).
If A, B and C are digits between 0 and 9 inclusive, what is the value of B?
(1) AB + BA = AAC --> well from above 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.
Hope it helps.
General Discussion
16 Jan 2012, 16:50
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Bunuel
Thanks for your post Bunuel! +1
why should we assume that they are distinct digits?
Let me try to illustrate my point with another example:
Can the sum of two prime numbers, A and B, be an even number?
Of course it can. If a=b=2 then 2+2=4. It doesn't state that x and y are distinct values, therefore to my understanding, I can assume that they could have the same value.
Now back to my post:
Since the question stem doesn't state that A,B,C are distinct values, why should we assume it? isn't it possible for A=B=C=0?
