81
Prime numbers less than 70 are:
2, 3, 5, 7, 13, 17, 19, 23, 29, 31, 41, 43, 47, 53,
59, 61, and 67,
their number is 19
82.
There is only one even prime number, namely 2.
83
Required sum = (61 + 67 + 71 + 73)= 272.
84
100 is divisible by 2, so it is not prime.
101 is not
divisible by any of the numbers 2, 3,5, 7, so, it is prime.
Hence, the smallest 3-digit prime number is 101.
85
161 is divisible by 7. So, it is not prime 221
is divisible by 13. So, it is not prime
Now, 20 > 
373. Prime numbers less
that 20 are 2, 3, 5, 7, 11, 13, 17, 19.
373. Prime numbers less
that 20 are 2, 3, 5, 7, 11, 13, 17, 19.
Any, 373 is not divisible by any of them.
So, 373 is prime.
Since 437 is divisible by 19, so it is
not prime
.
86. ( 2x 1 + 1) = 3, ( 2 x 2 +1 ) = 5, (2x 3 + 1 ) 7, ( 2x 4
+ 1) 9, which is not prime.
N+ 4.
87. X + (X
+ 36) + y = 100 2X + y = 64.
Y
must be even prime, which is 2.
2X
+ 2 = 64 X = 31.
Third prime number = ( X +36) = (31 + 36) = 67.
88.
Let the given prime numbers be a, be, c, d. then, abc = 385 and bcd = 1001.
Abc/ bcd = 385/1001 a/d = 5/13, so, a =5 d,=13.
89.
Numbers satisfying the given conditions are 405, 415, 425, 435, 445, 45, 465,
475,
485,
495, and 500 to 599.
Numbers of such
numbers = (10 + 100) = 110.
90. Required numbers from 200 to 300 are 207, 217, 227, 237, 247,257, 267, 270, 272, 272, 272, 272, 275, 276,278, 279, 287, 297, their number is 18.
Similarly, such numbers between 300 and 400 are also 18 in number.
Total number of such numbers 36.
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