Question : How many numbers are there between 501 and 701 which are divisible by 10 but are not divisible by 3?
Option 1: 20
Option 2: 14
Option 3: 15
Option 4: 13
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Correct Answer: 13
Solution :
The number of terms ($n$) in an arithmetic progression where $d$ is the common difference is given by the formula:
$n = \frac{\text{last term - first term}}{d} + 1$
The numbers between 501 and 701 that are divisible by 10 are: 510, 520, ..., 700.
The common difference = 10
$⇒n_1 = \frac{700 - 510}{10} + 1 = 20$
So, there are 20 numbers between 501 and 701 that are divisible by 10.
Next, we exclude the number that are also divisible by 3.
These numbers are 510, 540, ..., 690.
The common difference = 30
$⇒n_2 = \frac{690 - 510}{30} + 1 = 7$
So, the required numbers = $n_1 - n_2$
= 20 – 7 = 13
Hence, the correct answer is 13.
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