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Question

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

A
71
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B
72
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C
73
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D
74
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Solution

The correct option is C 73
The first number greater 10 which when divided by 4 leaves a remainder 3 is 11.
So, the next number will be 11+4=15
The other numbers in this will be =15+4=19;19+4=23;23+4=27
So, the AP =11,15,19,23,27,32......
The last term of this AP will be 299.
We have to find the total numbers that lie between 10 and 300, which when divided by 4 leaves a remainder 3.
an=a+(n1)d
Here, an=299,a=11 and d=4
299=11+(n1)4
299=11+4n4
29911+4=4n
292=4n
n=2924
n=73
So, total 73 numbers lie between 10 to 300 which when divided by 4 leaves a remainder 3.

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