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Q.

From the choices given below, the number of integers between 200 and 400 which are divisible by 7 are


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a

7829

b

8729

c

9287

d

7789 

answer is C.

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Detailed Solution

We have to find the number of integers between 200 and 400 that are divisible by 7.
We know that the three-digit numbers that are completely divisible by 7 and that are between 200 and 400 are 203, 210, 217,…, 399.
The above numbers are in the form of an AP.
So,
a 1 =203 d=7 a n =399
The nth term of an AP is given by,
a n =a+(n−1)d .
To find the value of n, substitute the known values in the formula.
203+(n−1)×7=399 203+7n−7=399 203+7n=406 7n=406−203 n= 203 7 n=29
There are 29 three digit numbers that are between 200 and 400 and are divisible by 7.
The sum of the terms is given by the formula,
S n = n 2 [a+l] , where l is the last term.
Substitute the known values in the above formula.
S 29 = 29 2 [203+399]
= 29 2 (602) =8729
Hence, option 3) is correct.
 
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