Question
Download Solution PDFRamu had to select a list of numbers between 1 and 1000 (including both), which are divisible by both 2 and 7. How many such numbers are there?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Ramu had to select numbers between 1 to 1000 ( including both)
which are divisible by both 2 and 7
Formula used:
an = a + ( n - 1) × d
Where, an = last number, a = 1st term, n = number of terms, d= common difference
d = 2nd term - 1st term = 3rd term - 2nd term = 4th term - 3rd term etc.....
Calculation:
Here, it is given a list of numbers between 1 to 1000 (including both) , which are divisible by both 2 and 7
So, to be divisible by both 2 and 7, the number has to be divisible by 14
As, we know that,
an = a + ( n - 1) × d
So, a = 1st term = 14 , 2nd term = 28 , last term = 994
d = 2nd term - 1st term = 28 - 14 = 14
⇒ 994 = 14 + ( n - 1) × 14
⇒ 980 = 14n - 14
⇒ 994 = 14n
⇒ n = 71
Hence, there are 71 terms between 1 to 1000 (including both ) which are divisible by both 2 and 7.
Last updated on May 28, 2025
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