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16 Sep 2014, 00:58
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How many positive three-digit integers are not divisible by 3 ?
A. 599
B. 600
C. 601
D. 602
E. 603
A. 599
B. 600
C. 601
D. 602
E. 603
16 Sep 2014, 00:58
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Official Solution:
How many positive three-digit integers are not divisible by 3 ?
A. 599
B. 600
C. 601
D. 602
E. 603
The total number of three-digit integers is: \(999 - 100 + 1 = 900\).
The number of three-digit multiples of 3 is \(\frac{\text{last} - \text{first}}{\text{interval}} + 1 = \frac{999 - 102}{3} + 1 = 300\).
To determine the number of three-digit integers not divisible by 3, subtract the multiples of 3 from the total: \(900 - 300 = 600\).
Therefore, there are 600 positive three-digit integers that are not divisible by 3.
Answer: B
How many positive three-digit integers are not divisible by 3 ?
A. 599
B. 600
C. 601
D. 602
E. 603
The total number of three-digit integers is: \(999 - 100 + 1 = 900\).
The number of three-digit multiples of 3 is \(\frac{\text{last} - \text{first}}{\text{interval}} + 1 = \frac{999 - 102}{3} + 1 = 300\).
To determine the number of three-digit integers not divisible by 3, subtract the multiples of 3 from the total: \(900 - 300 = 600\).
Therefore, there are 600 positive three-digit integers that are not divisible by 3.
Answer: B
30 Oct 2014, 20:33
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Hi,
Total 3-digit numbers: 999 - 100 + 1 = 900
We know that the range goes from 100 to 999
There will always be a 2:1 ratio between numbers not divisible by 3 and numbers divisible by 3.
For example: 100, 101, 102... 103, 104, 105... 997, 998, 999
We can infer that the 900 integers in the desired range will also fulfil this 2:1 ratio. Thus, 600 integers are not divisible by 3 and 300 are divisible by 3.
Is my apporach correct?
Total 3-digit numbers: 999 - 100 + 1 = 900
We know that the range goes from 100 to 999
There will always be a 2:1 ratio between numbers not divisible by 3 and numbers divisible by 3.
For example: 100, 101, 102... 103, 104, 105... 997, 998, 999
We can infer that the 900 integers in the desired range will also fulfil this 2:1 ratio. Thus, 600 integers are not divisible by 3 and 300 are divisible by 3.
Is my apporach correct?
