A 2009 digit number is multiplied by 54. The last two digits of the product are 6 and 8 in this order.If the same number is multiplied by 46, the last two digits are
Options
A) 0,9
B) 8,6
C) cannot be found
54*42 = 2268
so the long number ends in 42
42*46 = 1932
How come 42 number
To find the last two digits of a number multiplied by another number, we only need to consider the last two digits of the original number. Let's analyze the problem step-by-step.
1. Multiply a 2009-digit number by 54:
- Since we are only interested in the last two digits of the product, we will focus on the last two digits of the original number: 09.
- Multiply 09 by 54: 09 x 54 = 486.
- The last two digits of the product are 6 and 8 in this order.
2. Multiply the same number by 46:
- Again, we are only interested in the last two digits of the original number: 09.
- Multiply 09 by 46: 09 x 46 = 414.
- The last two digits of the product are 4 and 14 in this order.
Since the problem asks for the last two digits of the second product, the answer is 4 and 14. However, the number provided does not match any of the options given. Therefore, the correct answer is option C) cannot be found.
To find the answer, we need to analyze the given information.
We know that when a 2009 digit number is multiplied by 54, the last two digits of the product are 6 and 8 in this order. This implies that the last two digits of the original number are either 3 and 4 or 8 and 2 in this order.
Now, we need to find out what happens when the same number is multiplied by 46. To do that, we can use the fact that multiplication is distributive over addition. We can express the original number as a sum of its digits, each multiplied by the corresponding power of 10.
Let's assume the last two digits of the original number are 3 and 4. Hence, the original number can be expressed as n = (10^1) * 4 + (10^0) * 3 = 40 + 3 = 43.
When we multiply this number by 46, we get n * 46 = 43 * 46 = 1978. In this case, the last two digits of the product are 7 and 8 in this order.
Now, let's assume the last two digits of the original number are 8 and 2. Hence, the original number can be expressed as n = (10^1) * 2 + (10^0) * 8 = 20 + 8 = 28.
When we multiply this number by 46, we get n * 46 = 28 * 46 = 1288. In this case, the last two digits of the product are 8 and 8 in this order.
By considering both cases, we can see that the last two digits of the product when the same number is multiplied by 46 are 7 and 8 in this order.
Therefore, the correct answer is C) cannot be found, as neither of the given options matches the result.