Question

In 4_163, the difference between the values of the digit _ and 6 is 7940. What is the digit in the _?

A) 5
B) 7
C) 9
D) 3

Answer 1

To find the missing digit represented by '_', the difference between the place value of '_' and 6 must be 7940. By calculating '(Value of '_')*1000 - 6000 = 7940,' we find that the missing digit is 3.

Step-by-step explanation:

The question is asking us to find the value of the missing digit in the number 4_163 so that the difference between the value of the missing digit and the value of the digit 6 is 7940. To solve this, we can think about the place values in a four-digit number. The thousands place is the only place in a four-digit number that can create a difference of thousands when its digit changes. Hence, the missing digit must be in the thousands place, making the number a four-digit number in the form of 4X163, where X is the missing digit.

To find the value of X, we consider the given difference of 7940 and add the value of 6 (since we want the difference between X's value and 6):

1. Value of X * 1000 - 6000 = 7940
2. Value of X * 1000 = 7940 + 6000
3. Value of X * 1000 = 13940
4. Value of X = 13940 / 1000
5. Value of X = 13.94
6. Since X is a digit, it cannot be a decimal. We round down because X must be less than 14 to have a difference of 7940 with 6. Therefore, X = 3.

The digit in the _ is 3, so the answer is D) 3.