An important question from ML Agarwal of Class10 for board examination. How many numbers lie between 10 and 300, which when divided by 4 leave a remainder 3?

ML Agarwal (avichal publication) arithmetic progression chapter 9 question no 20(ii)

Rajan@2021Guru

# How many numbers lie between 10 and 300, which when divided by 4 leave a remainder 3?

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## The number lies between 10 to 300, which when divided by 4 leaves the remainder 3 are 11,15,19,...299. Clearly, it is an AP with first term a=11, common difference d=4 and last term l=299.

Let the are n terms in the given AP.

Then, an=299

a+(n−1)d=299

11+(n−1)4=299⇒n−1=72⇒n=73

Hence, there are 73 such terms.