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Question

Quantitative Aptitude Question on Number Systems

If xm+1x_m +1 and xm=xm+1+(m+1)x_m=x_{m+1}+(m+1) for every positive integer mm, then x100x_{100 } equals

A

-5151

B

-5150

C

-5051

D

-5050

Answer

-5050

Explanation

Solution

The correct answer is (D): −5050-5050

xm+1=xm−(m+1)x_m+1=x_m-(m+1)

x2=x1−2=−1−2=−3x^2=x_1-2=-1-2=-3

x3=x2−3=−1−2−3=−6x_3=x_2-3=-1-2-3=-6

Similarly,

xn=−(1+2+3+...+n)=−n(n+1)2x_n=-(1+2+3+...+n)=-\frac{n(n+1)}{2}

Hence x100=−100(101)2=−5050x_{100}=-\frac{100(101)}{2}=-5050