How many numbers between 10 and 300 leave remainder 3 when divided by 4?
73
Step 1: Understand the condition.
A number leaves remainder 3 when divided by 4 if it looks like:
\(4k + 3\), where \(k\) is an integer (whole number).
Step 2: Find the smallest number greater than 10 of this form.
Check numbers just after 10:
Step 3: Find the largest number less than 300 of this form.
Check numbers near 300:
Step 4: Notice the sequence.
The numbers are: 11, 15, 19, 23, …, 299.
This is an arithmetic progression (AP) with:
Step 5: Use the formula to find the number of terms in AP:
\(n = \dfrac{l - a}{d} + 1\)
\(n = \dfrac{299 - 11}{4} + 1\)
\(n = \dfrac{288}{4} + 1 = 72 + 1 = 73\)
Final Answer: There are 73 numbers between 10 and 300 that leave remainder 3 when divided by 4.