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Re: In the multiplication problem above, A, B, and C represent distinct [#permalink]

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03 Jan 2012, 03:05

A and B have to be a non-negative integer --> distinct digit The fact that the question shows you the multiplication in a vertical display gives you a strong hint on how to solve it. Neither A nor B can be zero --> B=0 then the product is 0, A=0 -->b=5 2A*B=100 Hence A,B are between 1-9 Using a vertical multiplication (which yields the same result as a horizontal multiplication, just a matter of convenience) the product of the factors' unit digits equals to the unit digit of their product. If the product is lower then 10 then it only has a unit digit. That is the case here as the sum of the two factors (in this case A+B) equals 5 and they are both<>0. Therefore A*B=C For the same reason the tens digit is equal to B*2 Hence 2*B=C The third equation is given A+B=5

In the multiplication problem above, A, B, and C represent distinct digits. If the sum of A and B is equal to 5, what is the value of C?

6 5 4 3 2

No idea how to solve this, I think I do not understand the question!

The letters are placeholders for some specific digits. You need to plug in digits for the letters such that the multiplication relation holds. Also, a letter stands for the same digit in each occurrence i.e. the product is CC means both the digits of the product are the same.

In such questions, it is sometimes a good idea to look at the overall picture. A two digit number starting with 2 is multiplied by a single digit number to give CC i.e. 00 or 11 or 22 or 33 or 44 or 55 or 66 or 77 or 88 or 99 The only numbers out of these which can be obtained by multiplying 2A by B are 00 (If B = 0 but B and C must be distinct) or 22 (If A = 2 and B = 1 but A, B and C must be distinct), 44 (If A = 2 and B = 2 but again, A, B and C must be distinct) or 66 (If A = 2 and B = 3. Also, A + B = 5 so condition satisfied. This must be the answer.)

The multiplication will look like this: __22 x__3 ____ _66

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