Solutions to Power Play 1

The Answer key is as

1) C  2)  E  3) B  4) A 5) E  6) D 7) B 8) E 9) C  10) E

Question 1 is easy just use a-1/a= 1 and 1/a-a=1 will give two roots sum them

Question 2  10^j-1o^i=10^i(10^(j-1)-1)

1001=7.11.13=10^3+1

so clearly 10^3+1 divides 10^6-1 and therefore 10^6k-1

hence j-i=6k, k is a natural number

applying other constraints we get option e

Question 3) 1+2+3..30=30.31/2=31.15=465

[465/2]=232 now suppose a subset A of S doe not have sum more than 232 then A' must have sum more than 232 hence 1/2 of the subsets of S will have sum more than 232

so 2^30/2=2^29

question 4 use the concept of reflection we will get min distance sum as 5root(2)

Question 5) Function is not correctly defined as 0 is not a natural number

so option e)

Question 6)

let the radius be r
and the point of tangency be P and Q and triangle be ABC. P lies on AB and Q on BC

let AP = m and BQ = n

m^2 = 15^2-x^2
n^2 = 20^2-x^2
m = 9 and n = 16 x =12 arcPQ = 6pi

question 7) see n numbers product is n and sum is zero

if n is odd then sum can't be zero

similalry check for other cases it will easily come out n =4k

question 8 toughest problem of the test

let g(n)=p(n)-n

then g(17)=-7=g(24)

let a,b be integers such that p(n)=n+3

then a-17 divides g(a)-g(17)=3-(-7)=10

similarly for 24

hence we find a-17 and a-24 both divide 10 this means k=a-17 and k+7 both divide 10

this means k=-5 or-2

a=19 b=22

hence ab=418

question 9 can be easily done

question 10) tricky enough problem

look for a series and solve it you will get E