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Question

# What is the remainder when p - q is divided by 100, if p=299+499+699+899+.........+10099 and q=199+399+599+799+..........+9999?

A

50

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B

10

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C

20

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D

30

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Solution

## The correct option is A 50 99=4k+3 Thus, if you take the individual differences (upto 10) For (299+499+699+899+1099)−(199+399+599+799+999)⇒ Last digit of this expression = (8+4+6+2+0) -(1+7+5+3+9) = -5 = 5 (10-5) However, since there are 10 such groups; (since 1099 or multiples of 1099 are exactly divisible by 100) =5×10=50 (which will always end in zero) Thus the remainder when divided by 100 is the last two digits = 50 itself

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