collection of tough problems from G PREP - 36

[abhasjha]

If k is a positive integer, is K the square of an integer?

1) k is divisible by 4

2) k is divisible by exactly four primes

[harsh.champ]

If k is a positive integer, is K the square of an integer?

1) k is divisible by 4

2) k is divisible by exactly four primes

1:-8 also div. by 4.
2:- many no. s have 4 primes.

both:- 1x2x3x5= 60 hence E.

[sanju09]

If k is a positive integer, is K the square of an integer?

1) k is divisible by 4

2) k is divisible by exactly four primes

(1) NOT all k divisible by 4 are the square of an integer. Take 8, 12, 20... for example. Insufficient

(2) If k is divisible by exactly four primes, then k could be 210 or its square. Insufficient

taken together

k is divisible by 4 and k is divisible by exactly four primes. When k is split to its primes, at least 2*2 is a must to be appearing there. 420 proves coalescing worthless.

[spoiler]E[/spoiler]

[ajith]

If k is a positive integer, is K the square of an integer?

1) k is divisible by 4

2) k is divisible by exactly four primes

1) insufficient (20 divisible by 4 is not a square 16 divisible by 4 is a square)
2) Insufficient (210 is divisible by exactly four primes, 210^2 is also divisible exactly by 4 primes)


Combining also not sufficient

E