Quant Boosters  Anubhav Sehgal, NMIMS Mumbai  Set 2

Q27) A positive integer p is called almost prime, when it has only 1 divisor aside from 1 and p. Find the sum of the 6 smallest almost primes.

Only squares of primes have exactly 3 factors.
Hence your required sum
= 2^2 + 3^2 + 5^2 + 7^2 + 11^2 + 13^2 = 377

Q28) Find n if sqrt(17^2 + 17^2 + ... n times) = 3 * 17^2

3 * 17^2 = sqrt(9 * 17^4) = sqrt(9 * 17^2 * 17^2)
i.e. 9 * 17^2 times 17^2 inside the square root.
i.e 51^2 times
i.e 2601

Q29) a!b! = a! + b! and find (a + b). (Positive integers)

General approach to solve such equations
a!b!  a!  b! + 1 = 1
(a!  1)(b!  1) = 1
a!  1 = b!  1 = 1
a! = b! = 2
a = b = 2
a + b = 4

Q30) Which is the third smallest number when subtracted from 6300 results in a perfect square ?

6300  n = k^2
80^2 = 6400
79^2 will give us the first smallest number on subtracting..
77^2 will give us the third
6300  5929 = 371.

79............? ??

@anubhav_sehgal Hey! Can you please tell me that why is power of 3 inside the bracket 0? (In the question 58!38!)