The number of numbers between 100 and 1000 which are divisible by 7 is

1.	The number of numbers between 100 and 1000 which are divisible by 7 is A) 7 B) 128C) 132 D) None
Answer» Correct option is (B) 128 The first number which is divisible by 7, between 100 & 1000 is 105 and last number which is divisible by 7 between 100 & 1000 is 994. \(\therefore a_1=105,d=7\;\&\;a_n=994\) \(\Rightarrow a+(n-1)d=994\) \((\because a_n=a+(n-1)d)\) \(\Rightarrow105+(n-1)7=994\) \(\Rightarrow7(n-1)=994-105=889\) \(\Rightarrow n-1=\frac{889}7=127\) \(\Rightarrow n=1+127=128\) Hence, total 128 numbers between 100 & 1000 which are divisible by 7. Correct option is B) 128

The number of numbers between 100 and 1000 which are divisible by 7 is A) 7 B) 128C) 132 D) None

Answer»

Correct option is (B) 128

The first number which is divisible by 7, between 100 & 1000 is 105 and last number which is divisible by 7 between 100 & 1000 is 994.

\(\therefore a_1=105,d=7\;\&\;a_n=994\)

\(\Rightarrow a+(n-1)d=994\) \((\because a_n=a+(n-1)d)\)

\(\Rightarrow105+(n-1)7=994\)

\(\Rightarrow7(n-1)=994-105=889\)

\(\Rightarrow n-1=\frac{889}7=127\)

\(\Rightarrow n=1+127=128\)

Hence, total 128 numbers between 100 & 1000 which are divisible by 7.

Correct option is B) 128