A) 102
B) 114
C) 126
D) 128
Correct Answer: D
Solution :
(d): We know that, 102 is the first, and 994 is the last 3 digit number divisible by 7. Thus, we have to determine the number of terms in the list 105, 112, 119,??994. Common difference, \[d=112-105=7\] Let there be n terms in this AP, nth term = 994 \[\because {{a}_{n}}=a+(n-1)d\] \[\Rightarrow 105+(n-1)7=994\] \[\Rightarrow 7(n-1)=994-105\] \[\Rightarrow 7(n-1)=889\] \[\Rightarrow n-1=\frac{889}{7}=127\] \[\Rightarrow n=127+1=128\] So, there are 128 numbers of three ? digits which are divisible by 7.
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