In the multiplication problem at the right different letters stand for different digits, and ABC and DBC each represent a three digit number. What number does DBC represent? Two answer possible; give one
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To solve the multiplication problem, let's analyze the given information:
ABC
x DBC
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Since each letter represents a different digit, we can assign variables to the unknown digits:
A B C
x D B C
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To find the possible number that DBC represents, we can start by looking at the units column:
B
x C
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In multiplication, when multiplying a single-digit number by a larger number, the product will remain a single digit. Thus, it means the digit B must be multiplied by a 3-digit number resulting in a single digit.
Since the minimum multiplication result is 1*100 = 100, and the maximum multiplication result is 9*111 = 999, the only possibility is B = 1.
Now, let's analyze the tens column:
A 1 C
x D 1 C
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If B = 1, C must be multiplied by a 3-digit number resulting in a two-digit number. We can again analyze the minimum and maximum possibilities:
Minimum: 100 * D = 100D
Maximum: 999 * D = 999D
So, DBC can represent any 3-digit number between 100D and 999D, where D can be any digit from 0 to 9.
Therefore, one possible number that DBC represents is 100D, where D can be any digit from 0 to 9.
To determine the value of DBC in the multiplication problem, we need to look for any information or clues provided in the question.
The given information states that "different letters stand for different digits." This means that each letter (A, B, C, and D) represents a unique digit.
Since ABC and DBC are three-digit numbers, the most significant digit in each number must not be zero.
Now, let's analyze the multiplication problem and find any clues that can help us determine the value of DBC.
Without any specific equations or additional information, we cannot directly calculate the exact value of DBC. However, we can narrow down the possibilities based on the conditions mentioned.
Let's consider an example to illustrate this better:
ABC
x DBC
_______
XYZ
In this example, A, B, C, D, X, Y, and Z represent different digits.
Since a multiplication problem is being solved, let's consider the units place first. The product of C (the units digit of ABC) and B (the units digit of DBC) should give us Z (the units digit of XYZ). Since the product is expected to result in a three-digit number (BC * B = XYZ), we can deduce that C multiplied by B results in a number with two digits. Therefore, C cannot be 1 or 2, as the product would exceed three digits. This narrows down our possibilities for C.
Next, let's consider the tens place. We need to find a value for A (the tens digit of ABC) and D (the tens digit of DBC) such that A * B + B * C + A * D = Y (tens digit of XYZ). Here, the sum of the individual products, including a carryover if any, should result in a three-digit number (XY). We can try different combinations of values for A and D to satisfy this condition.
Finally, we can examine the hundreds place. We can assign a value for B (the hundreds digit of DBC) such that A * B + B * C + A * D = X (the hundreds digit of XYZ). Again, the sum of these products should result in a three-digit number (XZ).
By trying different combinations of values for A, B, C, and D, satisfying the given conditions, we can determine one possible value for DBC.