Stock Number of shares Before and After transaction
V - 68 - 68
W - 112 - 112
X - 56 - 36
Y - 94 - 118
Z - 45 - 45
Previous range - 67 (112-45)
Range after transaction - 82 (118-36)
Increase = 82 - 67 = 15 D
k^4 is divided by 32, which means k^4> = 32 and a multiple of 32
The minimum possible value of k^4 = 256; and k = 4
Hence, k = 4n
Possible remainders would be - all multiples of 4 from 4 till 28 and 0
0
4
8
12
16
20
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28
What is the "following"?
h(n) = ( 2*4*6*...n-2*n)
h(100)+1 = (2*4*6*.....*98*100) + 1
= 2^50(1*2*...49*50) + 1
= 2^50(50!) + 1
Wilsons Theorm
n!+1 cannot be divisible by any number less than or equal to n.
so n has to be 50 or above...
Ans E
Students didnt participate for maths only = 10 -2 = 8
Students didnt participate for science only = 15 -2 = 13
Students participated for maths and science = 50 - 2 = 48
Students participated in maths = 48 - 8 = 40
Students participated in science = 48 - 13 = 35
Hence students participating in both = 40 + 35 - 48 = 27
There will be 50 digits in S50, and the first number will be and starting from (49*50)/2+1 = 1225+1 =1226
S50 = {1226, 1227,.......,1275}
so sum = 50/2 * (1226+1275) = 62525