If all the numbers from 7 to 51 which are divisible by 7 are removed, then how many numbers will be left?
The correct answer and explanation is:
Correct Answer: 38 numbers will be left.
Explanation:
To solve the problem, we need to follow a step-by-step approach:
- Identify the range:
The numbers from 7 to 51 are being considered. This is an inclusive range, so both 7 and 51 are included. - Count the total numbers from 7 to 51:
To count how many whole numbers lie between two given numbers (inclusive), use the formula: Total numbers=(Last number)−(First number)+1\text{Total numbers} = (\text{Last number}) – (\text{First number}) + 1 =51−7+1=45= 51 – 7 + 1 = 45 So, there are 45 numbers from 7 to 51, including both. - Find numbers divisible by 7 in this range:
The smallest number in the range divisible by 7 is 7.
The largest number in the range divisible by 7 is 49. We list the multiples of 7 from 7 up to 51: 7,14,21,28,35,42,497, 14, 21, 28, 35, 42, 49 Count these values: Number of multiples of 7=7\text{Number of multiples of 7} = 7 - Subtract the number of removed elements:
If we remove all numbers divisible by 7 (which are 7 in total), then the remaining count is: 45−7=3845 – 7 = 38
Conclusion:
There are 45 numbers between 7 and 51 inclusive. Out of those, 7 are divisible by 7. After removing them, 38 numbers are left. The key idea is recognizing how to count inclusively and identify divisible numbers by using basic division and multiplication rules.