The question in the image asks how many multiples of 4 lie between 10 and 250.

Solution:

To find how many multiples of 4 are there between 10 and 250:

1. The first multiple of 4 after 10 is $12$ (since $4 \times 3 = 12$).
2. The last multiple of 4 less than or equal to 250 is $248$ (since $4 \times 62 = 248$).

Now, we count the number of multiples of 4 from $12$ to $248$:

• The multiples of 4 form an arithmetic sequence: $12, 16, 20, ..., 248$, with a common difference of 4.
• The first term $a = 12$ and the last term $l = 248$.

To find the total number of terms, we use the formula for the nth term of an arithmetic sequence: $l = a + (n-1) \times d$ where:

• $l = 248$ (last term),
• $a = 12$ (first term),
• $d = 4$ (common difference).

Substitute these values into the formula: $248 = 12 + (n-1) \times 4$ Simplifying: $248 = 12 + 4(n-1)$ $248 - 12 = 4(n-1)$ $236 = 4(n-1)$ $n-1 = \frac{236}{4} = 59$ $n = 59 + 1 = 60$

Thus, there are 60 multiples of 4 between 10 and 250.

The correct answer is C) 60.

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Related Questions:

1. How would you find the number of multiples of 5 between 15 and 300?
2. What is the general formula to find the number of multiples of any number between two given numbers?
3. How do arithmetic sequences help in solving problems with multiples?
4. What are the common mistakes to avoid while counting multiples in a range?
5. How can you use divisibility rules to quickly find multiples in competitive exams?

Tip:

When counting multiples of a number in a range, always check the first and last multiples that fit within the limits.