If x ≡ 4 (mod 5), which of the following values of x is NOT possible?
Practice Questions
Q1
If x ≡ 4 (mod 5), which of the following values of x is NOT possible?
4
9
14
19
Questions & Step-by-Step Solutions
If x ≡ 4 (mod 5), which of the following values of x is NOT possible?
Step 1: Understand what 'x ≡ 4 (mod 5)' means. This means that when x is divided by 5, the remainder is 4.
Step 2: Write the general form of x based on the equation. We can express x as x = 4 + 5k, where k is any integer (like 0, 1, -1, etc.).
Step 3: Calculate some possible values of x by substituting different integers for k. For example, if k = 0, x = 4; if k = 1, x = 9; if k = -1, x = -1, and so on.
Step 4: Check the given values of x to see if they can be expressed in the form 4 + 5k.
Step 5: For each value, divide it by 5 and check the remainder. If the remainder is 4, then that value is possible. If not, it is NOT possible.
Step 6: Identify which value does not give a remainder of 4 when divided by 5.
