Quant Boosters - Anubhav Sehgal, NMIMS Mumbai - Set 2
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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.
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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
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Q28) Find n if sqrt(17^2 + 17^2 + ... n times) = 3 * 17^2
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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
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Q29) a!b! = a! + b! and find (a + b). (Positive integers)
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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
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Q30) Which is the third smallest number when subtracted from 6300 results in a perfect square ?
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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 - 59|29 = 371.
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79............? ??
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@anubhav_sehgal Hey! Can you please tell me that why is power of 3 inside the bracket 0? (In the question 58!-38!)
