Houses

Number Theory Level 2

The houses of a row are numbered consecutively from 1 to 49. Find the value of x x such that the sum of the numbers of houses preceding the house numbered x x is equal to the sum of the numbers of the houses following it.


The answer is 35.

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Ayush G Rai by Ayush G Rai , 20, India

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1 solution

Ma Pm
May 25, 2016

(((X-1)+1)×(X-1))÷2=(((X+1)+49)×(49-X) )÷2

X=35

5 Helpful 0 Interesting 0 Brilliant 0 Confused

good,simple solution!!!..+1

Ayush G Rai - 5 years ago

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ACCORDINGLY TO THE QUESTION,

No. Of houses before x = (x-1) &

No. Of houses after x = (49-x) ,

Now using the formula for sum of A.P ,

[ (x-1)(1+ x-1)] ÷ 2 = [ (49-x)(x+1+49)

→On simplification , U get x=35 !

Nice problem Ayush ! +1 !

Rishabh Tiwari - 5 years ago

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good solution.....+1

Ayush G Rai - 5 years ago

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