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How many natural numbers less than 1001 are divisible by 4 but not by 12?
- a)165
- b)167
- c)168
- d)192
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
How many natural numbers less than 1001 are divisible by 4 but not by...
To find the total number of natural numbers less than 1001 that are divisible by 4 but not by 12, we can follow a step-by-step approach.
Step 1: Find the number of natural numbers less than 1001 that are divisible by 4.
- To find this, we divide 1001 by 4 and take the floor value to account for only natural numbers.
- Floor(1001/4) = 250
Step 2: Find the number of natural numbers less than 1001 that are divisible by 12.
- To find this, we divide 1001 by 12 and take the floor value to account for only natural numbers.
- Floor(1001/12) = 83
Step 3: Find the number of natural numbers less than 1001 that are divisible by both 4 and 12.
- To find this, we divide 1001 by the least common multiple (LCM) of 4 and 12, which is 12.
- Floor(1001/12) = 83
Step 4: Find the number of natural numbers less than 1001 that are divisible by 4 and not divisible by 12.
- This can be found by subtracting the number of natural numbers divisible by both 4 and 12 from the number of natural numbers divisible by 4.
- 250 - 83 = 167
Therefore, the correct answer is option B) 167.
Step 1: Find the number of natural numbers less than 1001 that are divisible by 4.
- To find this, we divide 1001 by 4 and take the floor value to account for only natural numbers.
- Floor(1001/4) = 250
Step 2: Find the number of natural numbers less than 1001 that are divisible by 12.
- To find this, we divide 1001 by 12 and take the floor value to account for only natural numbers.
- Floor(1001/12) = 83
Step 3: Find the number of natural numbers less than 1001 that are divisible by both 4 and 12.
- To find this, we divide 1001 by the least common multiple (LCM) of 4 and 12, which is 12.
- Floor(1001/12) = 83
Step 4: Find the number of natural numbers less than 1001 that are divisible by 4 and not divisible by 12.
- This can be found by subtracting the number of natural numbers divisible by both 4 and 12 from the number of natural numbers divisible by 4.
- 250 - 83 = 167
Therefore, the correct answer is option B) 167.
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Community Answer
How many natural numbers less than 1001 are divisible by 4 but not by...
Number of natural numbers less than 1001 and divisible 4 is 250
Number of natural numbers less than 1001 and divisible by 12 (and 4) is 83
So, required answer is 250-83 = 167
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How many natural numbers less than 1001 are divisible by 4 but not by 12?a)165b)167c)168d)192Correct answer is option 'B'. Can you explain this answer?
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