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Digits

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by GmatKiss » Sun Oct 16, 2011 10:37 am
A and B are both two-digit numbers, with A > B. If A and B contain the
same digits, but in reverse order, what integer must be a factor of (A - B)?

(A) 4 (B) S (C) 6 (D) 8 (E) 9
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by knight247 » Sun Oct 16, 2011 10:45 am
Answer is E. Go to the following link and read point number 6 from the bottom.

https://blog.gmatboost.com/2011/09/17/me ... ame-thing/
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by fcabanski » Sun Oct 16, 2011 10:50 am
Even without knowing that rule, this is still a quick problem.

A = 32
B = 23

32-23 = 9

None but 9 are a factor, so the answer has to be 9.

If you had picked something else, it might take a bit longer.

A = 42
B = 24

42-24 = 18 (only 6 and 9 are factors)

Still have to find out which is always.

52-25 = 27 (only 9 is a factor)

It's faster if you know the rule, but still about 15 seconds if you don't.
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by neelgandham » Sun Oct 16, 2011 1:19 pm
GmatKiss wrote:A and B are both two-digit numbers, with A > B. If A and B contain the
same digits, but in reverse order, what integer must be a factor of (A - B)?

(A) 4 (B) S (C) 6 (D) 8 (E) 9
Knowing the rule helps, but not-knowing does no harm except for a 15 sec loss :-).

A = 10p + q
B = 10q + p

A - B = 9p - 9q = 9*(p-q). Shows that 9 is always a factor !


P.S: FYI A + B = 11p + 11q = 11(p + q). Shows that 11 is a factor :-)
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